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### #1 shaba_levi
Reputation: 2
• Posts: 19
• Joined: 14-December 08
# While Loop Help
Posted 22 January 2009 - 02:44 PM
Hey guys, need a little help again!
My assignment is this: Create a C++ console application that uses a while loop to count, total, and average a series of positive integers entered by a user. The user enters a –1 to signal the end of data input and to display the count, total, and average of the numbers entered.
Im almost there! here is my code:
```//Specification: Find total, sum, and average of user input using While Loop
#include <iostream>
using namespace std;
int main(){
int userInput = 0;
int const endData = -1;
cout << "This program will count, total, and average your numbers\n";
cout << "Please enter a number, enter -1 to display results and exit\n";
cin >> userInput;
//while loop
int totalNums = 0;
int sum = 0;
double average = 0;
int sentinalValue = endData;
int loopControlVariable = userInput; //prime the loop
while (loopControlVariable != sentinalValue){
cin >> loopControlVariable;
totalNums = totalNums + 1;
sum = sum + loopControlVariable;
average = sum / totalNums;
}
cout << "Youve entered " << totalNums << " numbers\n";
cout << "The sum of these numbers is " << sum << endl;
cout << "The average of these numbers is " << average << endl;
return 0;
}
```
My problem is the sum of the numbers...It isnt adding up right and i dont know why..i think it might be skipping the number just above -1 (which ends the loop)
can anyone push me in the right direction here?
Is This A Good Question/Topic? 0
## Replies To: While Loop Help
### #2 bodom658
• Villiage Idiom
Reputation: 114
• Posts: 1,123
• Joined: 22-February 08
## Re: While Loop Help
Posted 22 January 2009 - 02:55 PM
Take a look at how you declared the data types...
All integers right?
This means that if I were to enter 1.003, the program reads this as 1.
Similarly if I enter 2.9, the program sees a 2.
The decimal is truncated.
So how can we solve this?
I'll let you figure that out, it's pretty straight forward.
### #3 Gloin
• Expert Schmexpert...
Reputation: 235
• Posts: 4,489
• Joined: 04-August 08
## Re: While Loop Help
Posted 22 January 2009 - 02:55 PM
You shouldn't calculate the average until after you have collected all the values.
int const endData = -1;
int sentinalValue = endData;
What's the point of this? Isn't one variable enough to store the information? A nicer way would be o use a define.
This post has been edited by Gloin: 22 January 2009 - 02:57 PM
### #4 shaba_levi
Reputation: 2
• Posts: 19
• Joined: 14-December 08
## Re: While Loop Help
Posted 22 January 2009 - 03:05 PM
Gloin, on 22 Jan, 2009 - 01:55 PM, said:
You shouldn't calculate the average until after you have collected all the values.
int const endData = -1;
int sentinalValue = endData;
What's the point of this? Isn't one variable enough to store the information? A nicer way would be o use a define.
The point of that was priming values, for some reason the instructor wanted me to do it...I agree with you that it was redundant, but w/e
Updated code, but i still dont understand..its probably some DOH! thing isnt it... I hate it when that happens!
```//Specification: Find total, sum, and average of user input using While Loop
#include <iostream>
using namespace std;
int main(){
double userInput = 0;
int const endData = -1;
cout << "This program will count, total, and average your numbers\n";
cout << "Please enter a number, enter -1 to display results and exit\n";
cin >> userInput;
//while loop
double totalNums = 0;
double sum = 0;
double average = 0;
int sentinalValue = endData;
double loopControlVariable = userInput; //prime the loop
while (loopControlVariable != sentinalValue){
cin >> loopControlVariable;
totalNums = totalNums + 1;
sum = sum + loopControlVariable;
}
average = sum / totalNums;
cout << "Youve entered " << totalNums << " numbers\n";
cout << "The sum of these numbers is " << sum << endl;
cout << "The average of these numbers is " << average << endl;
return 0;
}
```
### #5 Gloin
• Expert Schmexpert...
Reputation: 235
• Posts: 4,489
• Joined: 04-August 08
## Re: While Loop Help
Posted 22 January 2009 - 03:26 PM
Your loopControlVariable value is always included in the sum. So instead of initializing sum to 0, make it 1.
### #6 shaba_levi
Reputation: 2
• Posts: 19
• Joined: 14-December 08
## Re: While Loop Help
Posted 22 January 2009 - 03:46 PM
Gloin, on 22 Jan, 2009 - 02:26 PM, said:
Your loopControlVariable value is always included in the sum. So instead of initializing sum to 0, make it 1.
Ah, that did it! but my program is now including the -1 into the answer, which i dont want...I tried making the endData value char = "q" and changing the sentinal value as well. I even got rid of the sentinal value and made the necessary changes in the loop, but it gave me this error: Error 1 error C2440: 'initializing' : cannot convert from 'const char [2]' to 'char'
What gives? If i cannot change the value, how do i make the code ignore the -1 value?
Edit: Im hungry and a bit tired from working late yesterday, so if some of this seems kind of "DUH!", please bare with me lol...
This post has been edited by shaba_levi: 22 January 2009 - 03:48 PM
### #7 Gloin
• Expert Schmexpert...
Reputation: 235
• Posts: 4,489
• Joined: 04-August 08
## Re: While Loop Help
Posted 22 January 2009 - 04:00 PM
It's simpler if you show the code but naturally you can't fit a char array of size two into a char of size one. Try filling a 1 litre bottle with 2 litres of water.
This post has been edited by Gloin: 22 January 2009 - 04:00 PM
### #8 shaba_levi
Reputation: 2
• Posts: 19
• Joined: 14-December 08
## Re: While Loop Help
Posted 22 January 2009 - 04:06 PM
Gloin, on 22 Jan, 2009 - 03:00 PM, said:
It's simpler if you show the code but naturally you can't fit a char array of size two into a char of size one. Try filling a 1 litre bottle with 2 litres of water.
```//Specification: Find total, sum, and average of user input using While Loop
#include <iostream>
using namespace std;
int main(){
double userInput = 0;
char endData = "q";
cout << "This program will count, total, and average your numbers\n";
cout << "Please enter a number, enter q to display results and exit\n";
cin >> userInput;
//while loop
double totalNums = 0;
double sum = 1;
double average = 0;
char sentinalValue = endData;
double loopControlVariable = userInput; //prime the loop
while (loopControlVariable != sentinalValue){
cin >> loopControlVariable;
totalNums = totalNums + 1;
sum = sum + loopControlVariable;
}
average = sum / totalNums;
cout << "Youve entered " << totalNums << " numbers\n";
cout << "The sum of these numbers is " << sum << endl;
cout << "The average of these numbers is " << average << endl;
return 0;
}
```
I dont understand why im getting the error..shouldnt that code be right?, what am i missing?
even if i were to:
```char sentinalValue = endData; //delete this
double loopControlVariable = userInput; //prime the loop
while (loopControlVariable != endData){ //changed the value
```
I still get the error..
This post has been edited by shaba_levi: 22 January 2009 - 04:08 PM
• Saucy!
Reputation: 6246
• Posts: 24,014
• Joined: 23-August 08
## Re: While Loop Help
Posted 22 January 2009 - 04:17 PM
Change char endData = "q"; to char endData = 'q';
"q" is an array of two characters, the 'q' and the terminating null ('\0'). 'q' is just the 'q' character only.
### #10 OrganizedChaos
Reputation: 39
• Posts: 153
• Joined: 29-November 08
## Re: While Loop Help
Posted 22 January 2009 - 04:25 PM
Since you already primed the loop, try this:
```while (loopControlVariable != sentinalValue){
totalNums = totalNums + 1;
sum = sum + loopControlVariable;
cin >> loopControlVariable;
}
```
### #11 OrganizedChaos
Reputation: 39
• Posts: 153
• Joined: 29-November 08
## Re: While Loop Help
Posted 22 January 2009 - 04:33 PM
Another problem you're going to have is when you go to enter 'q' the program is not going to work how you want it to because you're trying to store a char, 'q' into a double, userInput.
EDIT: I was just looking back in this thread and noticed you had -1 as the end value to begin with. Get rid of the chars and go back to that -1 since that's what the assignment's looking for anyway. Additionally, what's the point of loopControlVariable? You can get rid of that AND endValue, since that's unneeded also and end up with something like this:
```#include <iostream>
using namespace std;
int main(){
double userInput = 0;
double totalNums = 0;
double sum = 0;
double average = 0;
cout << "This program will count, total, and average your numbers\n";
cout << "Please enter a number, enter -1 to display results and exit\n";
cin >> userInput;
//while loop
while (userInput != -1){
totalNums++;
sum = sum + userInput;
cin >> userInput;
}
average = sum / totalNums;
cout << "Youve entered " << totalNums << " numbers\n";
cout << "The sum of these numbers is " << sum << endl;
cout << "The average of these numbers is " << average << endl;
return 0;
}
```
This post has been edited by OrganizedChaos: 22 January 2009 - 04:47 PM
### #12 shaba_levi
Reputation: 2
• Posts: 19
• Joined: 14-December 08
## Re: While Loop Help
Posted 22 January 2009 - 04:45 PM
Thanks for all your help guys! The program works, im too tired to figure out what did it, but here it is, working as intended
```//Specification: Find total, sum, and average of user input using While Loop
#include <iostream>
using namespace std;
int main(){
double userInput = 0;
int const endData = 0;
cout << "This program will count, total, and average your numbers\n";
cout << "Please enter a number, enter 0 to display results and exit\n";
cin >> userInput;
//while loop
double totalNums = 0;
double sum = 0;
double average = 0;
int sentinalValue = endData;
double loopControlVariable = userInput; //prime the loop
while (loopControlVariable != sentinalValue){
totalNums = totalNums + 1;
sum = sum + loopControlVariable;
cin >> loopControlVariable;
}
average = sum / totalNums;
cout << "Youve entered " << totalNums << " numbers\n";
cout << "The sum of these numbers is " << sum << endl;
cout << "The average of these numbers is " << average << endl;
return 0;
}
```
I switched some values...
This post has been edited by shaba_levi: 22 January 2009 - 04:47 PM | 3,078 | 10,821 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-17 | latest | en | 0.759563 |
https://takeuforward.org/arrays/find-the-smallest-divisor-given-a-threshold/ | 1,696,173,012,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510903.85/warc/CC-MAIN-20231001141548-20231001171548-00724.warc.gz | 600,998,081 | 40,943 | # Find the Smallest Divisor Given a Threshold
Problem Statement: You are given an array of integers ‘arr’ and an integer i.e. a threshold value ‘limit’. Your task is to find the smallest positive integer divisor, such that upon dividing all the elements of the given array by it, the sum of the division’s result is less than or equal to the given threshold value.
Examples
```Example 1:
Input Format: N = 5, arr[] = {1,2,3,4,5}, limit = 8
Result: 3
Explanation: We can get a sum of 15(1 + 2 + 3 + 4 + 5) if we choose 1 as a divisor.
The sum is 9(1 + 1 + 2 + 2 + 3) if we choose 2 as a divisor. Upon dividing all the elements of the array by 3, we get 1,1,1,2,2 respectively. Now, their sum is equal to 7 <= 8 i.e. the threshold value. So, 3 is the minimum possible answer.
Example 2:
Input Format: N = 4, arr[] = {8,4,2,3}, limit = 10
Result: 2
Explanation: If we choose 1, we get 17 as the sum. If we choose 2, we get 9(4+2+1+2) <= 10 as the answer. So, 2 is the answer.
Point to remember:
While dividing the array elements with a chosen number, we will always take the ceiling value. And then we will consider their summation. For example, 3 / 2 = 2.
Observation:
Minimum possible divisor: We can easily consider 1 as the minimum divisor as it is the smallest positive integer.Maximum possible divisor: If we observe, we can conclude the maximum element in the array i.e. max(arr[]) is the maximum possible divisor. Any number > max(arr[]), will give the exact same result as max(arr[]) does. This divisor will generate the minimum possible result i.e. n(1 for each element), where n = size of the array.
With these observations, we can surely say that our answer will lie in the range [1, max(arr[])].
```
Practice:
Disclaimer: Don’t jump directly to the solution, try it out yourself first.
Brute Force Approach Optimal Approach
Brute Force Approach
Algorithm / Intuition
### Naive Approach(Brute-force):
The extremely naive approach is to check all possible divisors from 1 to max(arr[]). The minimum number for which the result <= threshold value, will be our answer.
### Algorithm:
• We will run a loop(say d) from 1 to max(arr[]) to check all possible divisors.
• To calculate the result, we will iterate over the given array using a loop. Within this loop, we will divide each element in the array by the current divisor, d, and sum up the obtained ceiling values.
• Inside the outer loop, If result <= threshold: We will return d as our answer.
• Finally, if we are outside the nested loops, we will return -1.
Dry-run: Please refer to the video for the dry-run.
Code
``````
#include <bits/stdc++.h>
using namespace std;
int smallestDivisor(vector<int>& arr, int limit) {
int n = arr.size(); //size of array.
//Find the maximum element:
int maxi = *max_element(arr.begin(), arr.end());
//Find the smallest divisor:
for (int d = 1; d <= maxi; d++) {
//Find the summation result:
int sum = 0;
for (int i = 0; i < n; i++) {
sum += ceil((double)(arr[i]) / (double)(d));
}
if (sum <= limit)
return d;
}
return -1;
}
int main()
{
vector<int> arr = {1, 2, 3, 4, 5};
int limit = 8;
int ans = smallestDivisor(arr, limit);
cout << "The minimum divisor is: " << ans << "\n";
return 0;
}
```
```
``````
import java.util.*;
public class tUf {
public static int smallestDivisor(int[] arr, int limit) {
int n = arr.length; //size of array.
//Find the maximum element:
int maxi = Integer.MIN_VALUE;
for (int i = 0; i < n; i++) {
maxi = Math.max(maxi, arr[i]);
}
//Find the smallest divisor:
for (int d = 1; d <= maxi; d++) {
//Find the summation result:
int sum = 0;
for (int i = 0; i < n; i++) {
sum += Math.ceil((double)(arr[i]) / (double)(d));
}
if (sum <= limit)
return d;
}
return -1;
}
public static void main(String[] args) {
int[] arr = {1, 2, 3, 4, 5};
int limit = 8;
int ans = smallestDivisor(arr, limit);
System.out.println("The minimum divisor is: " + ans);
}
}
```
```
``````
import math
def smallestDivisor(arr, limit):
n = len(arr) # size of array
maxi = max(arr)
# Find the smallest divisor
for d in range(1, maxi+1):
# Find the summation result
sum = 0
for i in range(n):
sum += math.ceil(arr[i] / d)
if sum <= limit:
return d
return -1
arr = [1, 2, 3, 4, 5]
limit = 8
ans = smallestDivisor(arr, limit)
print("The minimum divisor is:", ans)
```
```
``````
function smallestDivisor(arr, limit) {
let n = arr.length; // size of array
let maxi = Math.max(...arr); // find the maximum element
// Find the smallest divisor
for (let d = 1; d <= maxi; d++) {
// Find the summation result
let sum = 0;
for (let i = 0; i < n; i++) {
sum += Math.ceil(arr[i] / d);
}
if (sum <= limit)
return d;
}
return -1;
}
let arr = [1, 2, 3, 4, 5];
let limit = 8;
let ans = smallestDivisor(arr, limit);
console.log("The minimum divisor is:", ans);
```
```
Output:The minimum divisor is: 3
Complexity Analysis
Time Complexity: O(max(arr[])*N), where max(arr[]) = maximum element in the array, N = size of the array.
Reason: We are using nested loops. The outer loop runs from 1 to max(arr[]) and the inner loop runs for N times.
Space Complexity: O(1) as we are not using any extra space to solve this problem.
Optimal Approach
Algorithm / Intuition
### Optimal Approach(Using Binary Search):
We are going to use the Binary Search algorithm to optimize the approach.
The primary objective of the Binary Search algorithm is to efficiently determine the appropriate half to eliminate, thereby reducing the search space by half. It does this by determining a specific condition that ensures that the target is not present in that half.
Now, we are not given any sorted array on which we can apply binary search. Upon closer observation, we can recognize that our answer space, represented as [1, max(arr[])], is actually sorted. Additionally, we can identify a pattern that allows us to divide this space into two halves: one consisting of potential answers and the other of non-viable options. So, we will apply binary search on the answer space.
### Algorithm:
1. If n > threshold: If the minimum summation i.e. n > threshold value, the answer does not exist. In this case, we will return -1.
2. Next, we will find the maximum element i.e. max(arr[]) in the given array.
3. Place the 2 pointers i.e. low and high: Initially, we will place the pointers. The pointer low will point to 1 and the high will point to max(arr[]).
4. Calculate the ‘mid’: Now, inside the loop, we will calculate the value of ‘mid’ using the following formula:
mid = (low+high) // 2 ( ‘//’ refers to integer division)
5. Eliminate the halves based on the summation of division results:
We will pass the potential divisor, represented by the variable ‘mid’, to the ‘sumByD()‘ function. This function will return the summation result of the division values.
1. If result <= threshold: On satisfying this condition, we can conclude that the number ‘mid’ is one of our possible answers. But we want the minimum number. So, we will eliminate the right half and consider the left half(i.e. high = mid-1).
2. Otherwise, the value mid is smaller than the number we want. This means the numbers greater than ‘mid’ should be considered and the right half of ‘mid’ consists of such numbers. So, we will eliminate the left half and consider the right half(i.e. low = mid+1).
6. Finally, outside the loop, we will return the value of low as the pointer will be pointing to the answer.
The steps from 3-4 will be inside a loop and the loop will continue until low crosses high.
Note: Please make sure to refer to the video and try out some test cases of your own to understand, how the pointer ‘low’ will be always pointing to the answer in this case. This is also the reason we have not used any extra variable here to store the answer.
The algorithm for sumByD() is given below:
sumByD(arr[], div):
arr[] -> the given array, div -> the divisor.
1. We will run a loop to iterate over the array.
2. We will divide each element by ‘div’, and consider the ceiling value.
3. With that, we will sum up the ceiling values as well.
4. Finally, we will return the summation.
Dry-run: Please refer to the video for the dry-run.
Code
``````
#include <bits/stdc++.h>
using namespace std;
int sumByD(vector<int> &arr, int div) {
int n = arr.size(); //size of array
//Find the summation of division values:
int sum = 0;
for (int i = 0; i < n; i++) {
sum += ceil((double)(arr[i]) / (double)(div));
}
return sum;
}
int smallestDivisor(vector<int>& arr, int limit) {
int n = arr.size();
if (n > limit) return -1;
int low = 1, high = *max_element(arr.begin(), arr.end());
//Apply binary search:
while (low <= high) {
int mid = (low + high) / 2;
if (sumByD(arr, mid) <= limit) {
high = mid - 1;
}
else {
low = mid + 1;
}
}
return low;
}
int main()
{
vector<int> arr = {1, 2, 3, 4, 5};
int limit = 8;
int ans = smallestDivisor(arr, limit);
cout << "The minimum divisor is: " << ans << "\n";
return 0;
}
```
```
``````
import java.util.*;
public class tUf {
public static int sumByD(int[] arr, int div) {
int n = arr.length; //size of array
//Find the summation of division values:
int sum = 0;
for (int i = 0; i < n; i++) {
sum += Math.ceil((double)(arr[i]) / (double)(div));
}
return sum;
}
public static int smallestDivisor(int[] arr, int limit) {
int n = arr.length; //size of array.
if(n > limit) return -1;
//Find the maximum element:
int maxi = Integer.MIN_VALUE;
for (int i = 0; i < n; i++) {
maxi = Math.max(maxi, arr[i]);
}
int low = 1, high = maxi;
//Apply binary search:
while (low <= high) {
int mid = (low + high) / 2;
if (sumByD(arr, mid) <= limit) {
high = mid - 1;
} else {
low = mid + 1;
}
}
return low;
}
public static void main(String[] args) {
int[] arr = {1, 2, 3, 4, 5};
int limit = 8;
int ans = smallestDivisor(arr, limit);
System.out.println("The minimum divisor is: " + ans);
}
}
```
```
``````
import math
def sumByD(arr, div):
n = len(arr) # size of array
# Find the summation of division values
total_sum = 0
for i in range(n):
total_sum += math.ceil(arr[i] / div)
def smallestDivisor(arr, limit):
n = len(arr)
if n > limit:
return -1
low = 1
high = max(arr)
# Apply binary search
while low <= high:
mid = (low + high) // 2
if sumByD(arr, mid) <= limit:
high = mid - 1
else:
low = mid + 1
return low
arr = [1, 2, 3, 4, 5]
limit = 8
ans = smallestDivisor(arr, limit)
print("The minimum divisor is:", ans)
```
```
``````
function sumByD(arr, div) {
let n = arr.length; // size of array
let sum = 0;
for (let i = 0; i < n; i++) {
sum += Math.ceil(arr[i] / div);
}
return sum;
}
function smallestDivisor(arr, limit) {
let n = arr.length;
if(n > limit) return -1;
let low = 1;
let high = Math.max(...arr);
while (low <= high) {
let mid = Math.floor((low + high) / 2);
if (sumByD(arr, mid) <= limit) {
high = mid - 1;
} else {
low = mid + 1;
}
}
return low;
}
let arr = [1, 2, 3, 4, 5];
let limit = 8;
let ans = smallestDivisor(arr, limit);
console.log("The minimum divisor is:", ans);
```
```
Output:The minimum divisor is: 3
Complexity Analysis
Time Complexity: O(log(max(arr[]))*N), where max(arr[]) = maximum element in the array, N = size of the array.
Reason: We are applying binary search on our answers that are in the range of [1, max(arr[])]. For every possible divisor ‘mid’, we call the sumByD() function. Inside that function, we are traversing the entire array, which results in O(N).
Space Complexity: O(1) as we are not using any extra space to solve this problem.
Video Explanation | 3,250 | 11,424 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2023-40 | longest | en | 0.818501 |
https://www.physicsforums.com/threads/argument-in-complex-numbers.382864/ | 1,590,706,136,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347400101.39/warc/CC-MAIN-20200528201823-20200528231823-00221.warc.gz | 866,952,631 | 15,851 | # Argument in complex numbers
Homework Helper
## Main Question or Discussion Point
When given a complex number $z=x+iy$ and transforming this into its mod-arg form giving $rcis\theta$ where $r=\sqrt{(x^2+y^2)}$ and $\theta=arctan(y/x)$, we are assuming that $-\pi/2<\theta<\pi/2$.
What if however a student is asked to convert the complex number -1-i into mod-arg form? If they just start to plug-and-chug they'll quickly end up with the result $\theta=\pi/4$ and all of a sudden they've changed the complex number into it's negative, 1+i.
How does one avoid this dilemma?
Homework Helper
Thanks
mathman
When given a complex number $z=x+iy$ and transforming this into its mod-arg form giving $rcis\theta$ where $r=\sqrt{(x^2+y^2)}$ and $\theta=arctan(y/x)$, we are assuming that $-\pi/2<\theta<\pi/2$.
What if however a student is asked to convert the complex number -1-i into mod-arg form? If they just start to plug-and-chug they'll quickly end up with the result $\theta=\pi/4$ and all of a sudden they've changed the complex number into it's negative, 1+i. | 306 | 1,067 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2020-24 | longest | en | 0.863328 |
https://psgolfcourses.com/p3332d7je/yQ33343oG/ | 1,628,002,759,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154459.22/warc/CC-MAIN-20210803124251-20210803154251-00136.warc.gz | 482,552,073 | 8,743 | # Decimals And Fractions Mixed Math Order Of Operations Worksheet Ooo
Ivonne Ellie June 13, 2021 Worksheet
What are the benefits of using goal setting worksheets? Is it not as easy to simply write your goals down? What about action? If forgetting to write it down, and instead acting on it, will that make a better result? Join me as we take a look at the benefits of goal setting worksheets. Let us look at your options, but first we need to know the why! Why are you goal setting in the first place? The main point for almost all people is to achieve the goal. After all why set goals? Obviously we want to grow, to achieve, to be, to have, to do, etc.
A few last helpful ideas: In order to date your expenses and deposits simply add a column entitled ‘Date‘ and enter the dates as you enter transactions. You may also get words in your description moving past the edge of the description text box. This is simply cured by double clicking on the line (in between the letters) of the obstructing word. This will automatically adjust the table to fit the text. You should now have a fairly simple worksheet template that is easy to manage and that is easily modified for various record keeping needs.
After that, label a thread take-up lever. This will be above and also slightly left of a needle. It will move the thread up and also down and it is also partially inside the machine. You need also to label the reverse lever or even switch. It is commonly found on the front of your machine to the left of a needle, but it can sometimes to be located on the far left side of your machine. For the last step, label the hand wheel. It is normally located at the top of the far left side of your machine. On the modern machines it may look more like the large knob, but on the old machines it is the metal wheel.
There needs to be more concrete assurances. You could write your goals down, and that can be great. But, without a system, this can easily be forgotten. Steps can be left out, and now you have problems. A part of the solution is goal setting worksheets. Because goal setting worksheets are like a system, they can produce much more results. After all, think about doing something that works, you can pretty sure be confident that it can work again! If goal setting worksheets work for you, as they have for others, then you can rest assured that they can work with other similar goals. So, worksheets used to achieve a goal to buy a car can likely work for buying a house. There are a lot of uses for goal setting worksheets. The simplicity in them is what makes them successful, not to mention the steps that it gets you to go in. These steps are essential for success. This makes the worksheets a kind of goal setting system. There are many different types of worksheet for setting goals. For example, some of these worksheets are designed for day to day.
### Math Order Of Operations Worksheet
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A goal setting worksheet is essentially a template you can use to set actionable goals. The secret to achieving success in your home business endeavors rests on how you write your goal statements, and whether or not they are actionable. For example, if you have a dream or vision of creating a residual income of say, \$5,000 per month in your network marketing business, it is not enough to simply say, ”I will have a residual income of \$5,000 per month within the next six months.” While such a goal is admirable, and perhaps even possible in the home based network marketing industry, it is not actionable. By that, I mean it does not specify the daily activities you will complete to achieve that objective.
The next step is to create a formula to calculate your total balance of all columns. In the H13 textbox enter the formula =sum(f11:h11), what this will do is total the negative expenses and the positive deposits, creating a grand total amount. You will also want to create a beginning balance (start of the month balance) at J2. If you are using this template for a new project, then your beginning balance will be zero.
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Jun 13, 2021 | 1,013 | 4,452 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2021-31 | latest | en | 0.955147 |
https://keystagewiki.com/index.php/Ion | 1,660,587,965,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00568.warc.gz | 319,804,076 | 8,301 | # Ion
## Key Stage 4
### Meaning
An Ion is a particle that has a different number of protons to electrons.
An atom contains the same number of protons as electrons. When an atom loses or gains electrons it becomes an ion.
Ions can be positively charged or negatively charged.
If an atom gains electrons it becomes a negatively charged ion since there are more electrons than protons and electrons carry a negative charge.
If an atom loses electrons it becomes a positively charged ion since there are more protons than electrons and protons carry a positive charge.
Atom Ion A Lithium atom has 3 protons and 3 electrons so it is neutral. A Lithium ion has 3 protons and 2 electrons so it has a positive charge. It now has a full Outer Shell. A Fluorine atom has 9 protons and 9 electrons so it is neutral. A Fluorine ion has 9 protons and 10 electrons so it is negative charge. It now has a full Outer Shell.
The number of electron in an ion can be found using the Atomic Number (which is the same as the Relative Atomic Charge of the nucleus) and subtracting the charge of the ion.
A Lithium Ion A Fluorine Ion A Boron Ion An Oxygen Ion This ion has an Atomic Number (Z) of 3 and a Relative Atomic Charge (Q) of +1. Number of electrons = A - Q Number of electrons = 3 - 1 Number of electrons = 2 This ion has an Atomic Number (Z) of 9 and a Relative Atomic Charge (Q) of -1. Number of electrons = A - Q Number of electrons = 9 - (-1) Number of electrons = 10 This ion has an Atomic Number (Z) of 5 and a Relative Atomic Charge (Q) of +3. Number of electrons = A - Q Number of electrons = 5 - 3 Number of electrons = 2 This ion has an Atomic Number (Z) of 8 and a Relative Atomic Charge (Q) of -2. Number of electrons = A - Q Number of electrons = 8 - (-2) Number of electrons = 10
### References
#### AQA
Ions, page 112, GCSE Combined Science Trilogy; Physics, CGP, AQA
Ions, page 124, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
Ions, page 50, GCSE Physics; Third Edition, Oxford University Press, AQA
Ions, pages 121-2, 148, 339, GCSE Combined Science Trilogy 1, Hodder, AQA
Ions, pages 16, 38-43, GCSE Chemistry; Third Edition, Oxford University Press, AQA
Ions, pages 23, 29, 70-74, GCSE Combined Science Trilogy; Chemistry, CGP, AQA
Ions, pages 28-30, GCSE Chemistry; The Revision Guide, CGP, AQA
Ions, pages 43, 44, GCSE Physics; The Revision Guide, CGP, AQA
Ions, pages 6-7, GCSE Chemistry, Hodder, AQA
Ions, pages 96, 113-115, 197, GCSE Combined Science; The Revision Guide, CGP, AQA
Ions; charge on, page 35, GCSE Chemistry, Hodder, AQA
Ions; charge on, pages 150-1, GCSE Combined Science Trilogy 1, Hodder, AQA
Ions; electrolysis, pages 102, 104-105, GCSE Chemistry; Third Edition, Oxford University Press, AQA
Ions; periodicity, pages 40-41, GCSE Chemistry; Third Edition, Oxford University Press, AQA
Ions; pH scale, page 99, GCSE Chemistry; Third Edition, Oxford University Press, AQA
Ions; tests, pages 186-191, GCSE Chemistry; Third Edition, Oxford University Press, AQA
Ions; transition elements, page 33, GCSE Chemistry; Third Edition, Oxford University Press, AQA
#### Edexcel
Ions, page 154, GCSE Physics, CGP, Edexcel
Ions, page 53, GCSE Chemistry, Pearson, Edexcel
Ions, page 95, GCSE Physics, Pearson Edexcel
Ions, pages 197, 359, GCSE Combined Science, Pearson Edexcel
Ions, pages 20, 21, GCSE Chemistry; The Revision Guide, CGP, Edexcel
Ions, pages 48-55, GCSE Chemistry, CGP, Edexcel
Ions, pages 49, 50, GCSE Physics; The Revision Guide, CGP, Edexcel
Ions, pages 83, 84, 172, 173, GCSE Combined Science; The Revision Guide, CGP, Edexcel
Ions; neutralisation, pages 208-209, GCSE Combined Science, Pearson Edexcel
Ions; neutralisation, pages 64-65, GCSE Chemistry, Pearson, Edexcel
Ions; spectator ions, page 210, GCSE Combined Science, Pearson Edexcel
Ions; spectator ions, page 66, GCSE Chemistry, Pearson, Edexcel
Ions; test for positive ions, pages 196-197, GCSE Chemistry, Pearson, Edexcel
Ions; tests for negative ions, pages 198-199, GCSE Chemistry, Pearson, Edexcel
#### OCR
Ions, pages 15, 18, 19, 35, Gateway GCSE Chemistry; The Revision Guide, CGP, OCR
Ions, pages 173, Gateway GCSE Physics, Oxford, OCR
Ions, pages 29, 56-57, Gateway GCSE Chemistry, Oxford, OCR
Ions, pages 86, 89-91, 108, 117, 196, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR
Ions; detection/identification, pages 148-151, 272-273, Gateway GCSE Chemistry, Oxford, OCR
Ions; electrolysis, pages 122-127, Gateway GCSE Chemistry, Oxford, OCR
Ions; formulae, page 88, Gateway GCSE Chemistry, Oxford, OCR
Ions; halogen displacement reactions, page 136, Gateway GCSE Chemistry, Oxford, OCR
Ions; transition metals, page 141, Gateway GCSE Chemistry, Oxford, OCR | 1,389 | 4,700 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2022-33 | longest | en | 0.867016 |
http://www.solutioninn.com/sam-smith-owner-and-general-manager-of-campus-stationery-store | 1,506,159,298,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818689615.28/warc/CC-MAIN-20170923085617-20170923105617-00069.warc.gz | 609,873,931 | 8,167 | # Question: Sam Smith owner and general manager of Campus Stationery Store
Sam Smith, owner and general manager of Campus Stationery Store, is concerned about the sales behavior of a scanner at the store. He understands that there may be many factors, which may help explain sales, but he believes that advertising and price are major determinants of sales. Sam collects the data given below with Y = SALES (# of sales), X1 = ADS (# of ads), X2 = PRICE (\$)
Regression Analysis: SALES versus ADS, PRICE
The regression equation is
SALES = 157 + 4.33 ADS - 1.14 PRICE
Predictor Coef SE Coef T P
Constant 157.50 33.78 4.66 0.002
PRICE -1.1428 0.2677 -4.27 0.004
S = 10.1422
R-Sq = 82.9%
Analysis of Variance
Source DF SS MS F P
Regression 2 3502.0 1751.0 17.02 0.002
Residual Error 7 720.1 102.9
Total 9 4222.1
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 52.20 4.67 (41.16, 63.25) (25.80, 78.61)
Values of Predictors for New Observations
1 10.0 130
0.055
PRICE -0.661 0.008
0.037 0.982
Cell Contents: Pearson correlation
P-Value
a. Analyze the above output to determine the multiple regression equation.
b. Find and interpret the multiple index of determination (R-Sq).
c. Perform the t-tests on βˆ1and on βˆ2(use two tailed test with (= .05). Interpret your results.
d. Predict the number of sales given that there were 10 ads and the price was \$130. Use both a point estimate and the appropriate intervalestimate.
Sales4
Views238 | 491 | 1,562 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2017-39 | latest | en | 0.671 |
https://en.khanacademy.org/math/pre-algebra/xb4832e56:one-step-and-two-step-equations-inequalities/xb4832e56:untitled-1103/v/combining-like-terms | 1,709,588,866,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476532.70/warc/CC-MAIN-20240304200958-20240304230958-00527.warc.gz | 229,276,018 | 139,008 | If you're seeing this message, it means we're having trouble loading external resources on our website.
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# Intro to combining like terms
Adding like terms is a fundamental concept in algebra. Coefficients are the numbers in front of variables, and they can be added when the variables are the same. For example, 2x + 3x equals 5x. When dealing with different variables, such as x and y, add them separately, resulting in expressions like 5x + 9y. Created by Sal Khan.
## Want to join the conversation?
• So are we basically just simplifying the answer?
• @EDiaz1786
Exactly right! You're pretty much simplifying the answer. A quick tip: If you see two numbers with the same variable and it tells you to add them... Add it! Below is an example of what I mean.
3x + 4x = 7x
In this case, you would only add the whole numbers and not multiply or add the x's, because if you added/multiplied the x's it would come out to be 7x². But later on in Algebra 1, when you get to factoring and multiplying perfect squares that's when you'll multiply the x's AND the numbers. Here's a quick example of what I mean.
7x(2x+4)
This is saying that we distribute the 7x to the 2x and the 4. So the answer will be 14x² + 28x.
Hope this helps!
• I get it but im lost on the operations. how do you know when to divide, subtract, add, or multiply?
• If you are only combining like terms, stick to adding or subtracting. This depends on the coefficients, but we still use the laws of adding and subtracting positive and negative numbers. You would have to add multiply/divide only if you have to distribute something to everything in the parentheses such as 4(3x-4). Once you distribute, you get back to adding/subtracting.
• so am i adding the X's for my answer?
• Yes, and you can also do this with other variables, as long as the variables are the same. (numerical value is just what you add or subtract)
• this might seem kind of strange but when i was trying to figure out how to add like terms i stumbled upon the fact that adding like terms can be solved by doing the distributive property in reverse. i am not sure if this makes sense or not, but it made sense to me.
for example:
2X + 3X = X(2+3)= X(5) = 5X
i do not like learning rules without understanding why the rules work. i know that you are suppose to simply add the coefficients of like terms and be done with the problem. but is that a shortcut/rule that was made instead of doing the distributive property in reverse ?
• That's precisely right. Most people take a more laid-back approach and think that two things plus three things has got to equal five things, but you're right on target that the distributive law is what's going on behind the scenes to make that simple statement work out.
• Is zero prime, composite or neither?
• Zero is neither. Zero, I've been taught is just zero. Zero is special. So, to answer your question, zero is neither.
• The chuck norris part makes this video better
• Definitely, he is hilarious.
• You had to pick Chuck Norris
hahahahahahahahahahahahahahahahahaha
its beautiful!
but still
heres my question,
Could you take the exponents and divide them by itself if one of them is x^2 and it ends up as x=?
• You can't find the value for anything by dividing it by itself. x^2 divided by x^2 equals 1. So, it still is x=?.
And yes, it's hilarious that he chose Chuck Norris as a variable.
• this is how u make math interesting
• I've had to go back on this video over and over, I still don't understand. It may be the fact that I'm just stupid and too slow to catch up with everyone else.
But seriously, here's what I have to say; When you have a simple question, such as this: -n + (-3) + 3n + 5
How do you solve it? Actually, how do you solve most equations? If anyone has an answer, please help!
• When you're combining like terms, you're not actually solving for anything
(It's not an equation if you don't have the equal sign)
Combining like terms just means you add together anything you can.
-n + (-3) +3n +5
In your example, you have two types of numbers. You have numbers that are a multiple of n and you have regular numbers.
The first thing I usually do is rearrange the numbers so that all the like terms or numbers that can be added together, are next to each other, like this:
-n + 3n + (-3) +5
Then you can rearrange it some more to make it clear how to combine the like terms
3n-n + 5-3
2n + 2
Does that help? | 1,137 | 4,540 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2024-10 | latest | en | 0.924089 |
http://auscblacks.com/ks1-multiplication-worksheets/multiplication-and-division-worksheets-printable-free-ks1-tes-pet-3/ | 1,532,041,573,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676591332.73/warc/CC-MAIN-20180719222958-20180720002958-00457.warc.gz | 30,674,916 | 10,144 | Multiplication And Division Worksheets Printable Free Ks1 Tes Pet Lesson Simple Basic Twinkl Sharing Problem
By Tina C. Kral on May 16 2018 13:44:00
Sing songs with hand movements. There are multiplication albums that sing the times tables. You can listen along and learn the times tables through music instead of rote memorization. Listen to a few different versions and find one that works best for you. Add in hand motions or dance moves that illustrate the different number pairs to make the process more interactive.
What it is about memorizing multiplication tables that make my kids throw their pencil across the room and shout, “I hate math?” It is because, unlike spelling or vocabulary, numbers don’t create pictures for us. Multiplication tables are strings of seemingly random numbers that our children are expected to not only remember, but keep in order and in context with the numbers they are multiplying by.
Use mnemonics and silly stories to help you remember. A mnemonic is a special technique or learning device that helps you remember something. Stories like Times Tales can help you memorize your multiplication facts by associating the numbers with silly characters and stories. Phrases like 5 6 7 8, 56 equals 7 times 8 are also useful. There are many ways to memorize things, you just need to find the way that works best for you.
I have seen a lot of kids quickly pass off their 2’s, 5’s, and 10’s. These tables have an obvious pattern and are much easier to learn. Then there is a serious slow down as kids hit the 3’s, 4’s, and 6’s. By the time they get to the 7’s, 8’s, and 9’s they’ve decided that multiplication is way too hard, and math isn’t their thing.
Get More Samples of Ks1 Multiplication Worksheets
Ks1ication worksheets beginning free printable understanding arraysications
Ks1ication worksheets wordprob ducklegs 1ications picture word problems repeated addition four | 421 | 1,915 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-30 | latest | en | 0.927283 |
http://www.numbersaplenty.com/4101 | 1,597,136,852,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738746.41/warc/CC-MAIN-20200811090050-20200811120050-00337.warc.gz | 166,091,800 | 3,628 | Search a number
4101 = 31367
BaseRepresentation
bin1000000000101
312121220
41000011
5112401
630553
714646
oct10005
95556
104101
113099
122459
131b36
1416cd
151336
hex1005
4101 has 4 divisors (see below), whose sum is σ = 5472. Its totient is φ = 2732.
The previous prime is 4099. The next prime is 4111. The reversal of 4101 is 1014.
Adding to 4101 its reverse (1014), we get a palindrome (5115).
It can be divided in two parts, 4 and 101, that multiplied together give a palindrome (404).
It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4.
It is a cyclic number.
It is not a de Polignac number, because 4101 - 21 = 4099 is a prime.
It is an Ulam number.
It is a D-number.
It is an alternating number because its digits alternate between even and odd.
It is a plaindrome in base 9, base 12, base 14 and base 15.
It is a self number, because there is not a number n which added to its sum of digits gives 4101.
It is a congruent number.
It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 4101.
It is not an unprimeable number, because it can be changed into a prime (4111) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (3) of ones.
It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 681 + ... + 686.
It is an arithmetic number, because the mean of its divisors is an integer number (1368).
24101 is an apocalyptic number.
4101 is the 41-st centered pentagonal number.
It is an amenable number.
4101 is a deficient number, since it is larger than the sum of its proper divisors (1371).
4101 is a wasteful number, since it uses less digits than its factorization.
4101 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 1370.
The product of its (nonzero) digits is 4, while the sum is 6.
The square root of 4101 is about 64.0390505863. The cubic root of 4101 is about 16.0065077694.
The spelling of 4101 in words is "four thousand, one hundred one", and thus it is an iban number.
Divisors: 1 3 1367 4101 | 640 | 2,223 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2020-34 | latest | en | 0.923227 |
https://www.indiabix.com/placement-papers/tcs/4167 | 1,610,852,221,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703509104.12/warc/CC-MAIN-20210117020341-20210117050341-00302.warc.gz | 852,525,442 | 9,060 | # Placement Papers - TCS
## Why TCS Placement Papers?
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### TCS Latest Fresher Job Interview Placement Paper May 2010
Posted By : Ndn Rating : +7, -0
Company Name : TCS
Type : Fresher, Job Interview
Hi friends... This is Mani from Chennai, sharing my experience about the recruitment of TCS.
First round is aptitude.
For this we expected the pattern like section 1 verbal, section 2 apps, section 3 critical reasoning. But we had online test with 35 questions, time duration is 60 minutes. That 35 questions was full of simple age problems, serial problems, speed problems, significance problem alone. Problems are quiet easy but they gave each questions for 10 lines. The thing is how fast your are reading the question and grasping the problem and solving it. All the questions contains many irrelevant data. You have omit those irrelevant things and you have to solve it quickly.
For example,
It is the class with the seating arrangement in 4 rows and 8 columns. When the teacher says 'start' the girl who is sitting in first row and first column will say 1, then the next girl sitting behind her will say 4, the next girl sitting behind that girl will say 7, in a particular order each girl is telling a number, the following girls told 10, 13 next turn is yours what u will say?
Simple series problem na...
But it will consume your precious time to read this problem. My point is please skip the problem with lengthy paragraph, first try to attend small problems, then go to big problems. You can go to any question and answer it within that 60 minutes. We had negative marks 0.33 :-)
To clear apps, manage the time efficiently and answer the prbs. From 1498 students 153 were selected for the next round. Technical round took place on next day only. That was a panel interview. Each panel consist of 4 or 3 HRs. I got 4 HRs. :-)
The interview went like this,
HR1: Hi mani... tell us about yourself. Me: told. HR2: Explain your project. Me: told HR3: Well Mani, you are using database in your project, if it was lost, how will you recover it. Me: I didn't used any recovery systems sir, if we want, we can implement disaster recovery systems sir... HR3: Ok.. (he smiled) HR2: What is a router? Me: told HR2: switch? Me: told HR3: routing protocols. Me: Sorry sir i don't know. ( I studied it , but i couldn't able to recall it there. ) HR3: RP3... (he tried to recall me) Me: ...... HR2: Its okay mani, what is your ambition in your life? Me: My ambition is to become a 'Primary School Teacher'. HR4: Do you know why we recruiting now? Me: I said, and i explained why i want to become a teacher, and when i will do it. (I think they were satisfied with my honest answer, Be honest in interview friends) Hr4: Have u attended any Interview earlier? Me: i answered it. (They asked some questions regarding the previous interview too) Hr4: Asked some question from ppt Me: told HR2: Thank you Ms.Mani... Me: Thanked everyone..
It went up to twenty minutes. In between they asked questions about night shift. I gave positive answer. And they asked about relocating and willing to work anywhere in the world. I gave positive answer. Regarding interview, make perfect eye contact with the HR. When it is Panel interview make perfect eye contact with all the HRs when you are telling about yourself and explaining your project. Be loud. Be honest. Be prepared. Thats it you can achieve it.
We got the result in evening. And 80 of us got selected. I am proud that i am also the part of TCS family. Meet you soon in TCS friends. All the best. :-)
Exam/Interview Date : 17-May-2010
No of Rounds : Screening Test, Aptitude Test, Technical Round-1
Location : Chennai
Contributor Name : Mani | 1,048 | 4,230 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2021-04 | latest | en | 0.910272 |
http://activelearningps.com/2019/04/08/perpetual-anarchy-a-game-of-war-and-peace/?shared=email&msg=fail | 1,555,835,128,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578530505.30/warc/CC-MAIN-20190421080255-20190421102255-00343.warc.gz | 4,699,783 | 14,983 | # Perpetual Anarchy: A Game of War and Peace
Today we have a guest post by Matteo Perlini. He can be contacted at
matteoperlini [at] gmail [dot] com.
In a post from August of last year, Nathan Alexander Sears wrote about a simple game he designed that teaches students about IR theory. Based on Sears’s idea, I created “Perpetual Anarchy,” a two-player game where the goal is to maximize the wealth of one’s state. Unlike Sears’s game, mine does not eliminate players or involve diplomacy.
“Perpetual Anarchy” requires a standard deck of playing cards and paper to record points scored and technological advances. The complete rules of “Perpetual Anarchy” are at https://boardgamegeek.com/boardgame/273757/perpetual-anarchy.
First Strategic Level
Each state must choose an action every turn: defense, attack or production. The choice of attack starts a war with the other state. Defense allows a player to better resist an attack by the opposing player. Production is an entirely peaceful action that helps increase wealth. The game has weak intransitive preference orderings: it is usually preferred (but not always!) to play defense against attack, attack against production, production against defense.
Defense vs. attack: as in the real world, defending is easier than attacking, so the defender has a bonus in the war (higher probability to win the war), but attacker must pay reputation costs for her belligerence.
Attack vs. production: attacker has a bonus in the war (higher probability to win the war) but she must pay reputation costs for her belligerence. By contrast, if the producer wins, she earns points without reputation costs.
Production vs. defense: both states score, but only the defending state has reputation costs, so the producer generally scores more.
The game is not strictly intransitive because the final outcome depends also on the second strategic level.
Second Strategic Level
States must choose how to allocate their budget across two dimensions: war/peace and long-term/short-term. A player must decide whether to give more prominence to one of the following strategies:
Short-term war: armament allocation helps the player win an urgent war, but the player will not use this allocation in the future.
Short-term peace: wealth allocation helps a player score points during peace.
Long-term war: military technology allocation does not increase the likelihood of winning an actual war, but increases marginally the player’s military efficacy forever.
Long-term peace: civilian technology allocation does not increase the actual points scored by a player, but increases marginally the player’s production efficacy forever.
As an example, a player who chooses a short-term war strategy will be more likely to win if a war occurs and will also prevent the opponent from capitalizing on long-term strategies, because the opponent loses any technology allocations in that turn.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 609 | 3,004 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2019-18 | latest | en | 0.951842 |
https://www.jiskha.com/display.cgi?id=1365051343 | 1,516,496,753,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084889798.67/warc/CC-MAIN-20180121001412-20180121021412-00606.warc.gz | 930,636,529 | 4,243 | # algebra word problem
posted by .
To remodel a bathroom a contractor Charles \$25 er hour plus material costs, which amount to \$3825. Therefore, the total cost to remodel he bathroom is given by f(x)=25x+3825 where x is the number of hours the contractor works. Find a formula for f^-1(x). What does f^-1 compute?
• algebra word problem -
Switch the variables x and y
y=25x+3825 would become
x=25y+3825 (solve for y)
x-3825=25y
y=(x-3825)/25
and if you do f(-fx) meaning you plug in the inverse into the x of the original function, you should get x.
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View Full Version : The edge of the universe
luckyfrank
2010-Jan-02, 01:30 AM
It's hard to believe that the universe is not infinite, i mean there is a place where the universe just stops and then there in nothing
no matter no space no time, but surly if the universe is expanding it must be expanding into something that wasnt there before
Ive read before that it's not the universe that's expanding just that the space within it is expanding if that makes sense
Hypothetical question : If i was standing on the very edge of the universe with a tennis ball in my hand and threw that ball over the edge what would happen to the ball ?
01101001
2010-Jan-02, 02:23 AM
Hypothetical question : If i was standing on the very edge of the universe with a tennis ball in my hand and threw that ball over the edge what would happen to the ball ?
You assume there is an edge. Why?
[...] surly if the universe is expanding it must be expanding into something that wasnt there before
No.
From the Sean Carroll Cosmology FAQ (http://preposterousuniverse.com/writings/cosmologyprimer/faq.html#into) (one of many fine resources listed in topic ** FAQs ** Resources On The Web (http://www.bautforum.com/space-astronomy-questions-answers/22865-faqs-resources-web.html)):
What is the universe expanding into?
As far as we know, the universe isn't expanding "into" anything. When we say the universe is expanding, we have a very precise operational concept in mind: the amount of space in between distant galaxies is growing. (Individual galaxies are not growing, as they are bound together by gravity.) But the universe is all there is (again, as far as we know), so there's nothing outside into which it could be expanding. This is hard to visualize, since we are used to thinking of objects as being located somewhere in space; but the universe includes all of space.
Jeff Root
2010-Jan-02, 07:38 AM
Hypothetical question : If i was standing on the very edge of the universe
with a tennis ball in my hand and threw that ball over the edge what would
happen to the ball ?
You assume there is an edge. Why?
Why not? It seems a reasonable and natural assumption. Is there any
other assumption one could make that is as reasonable or as natural?
-- Jeff, in Minneapolis
ccart3r
2010-Jan-02, 08:33 AM
Maybe Space/Universe is not all that "this" is made of. No way of knowing. We view space as nothing beyond that, for all we know there may be some type of other "space" outside of our universe. Or possibly space doesn't end within our universe? We just proceed it within our universe only.
All in the imagination until we know other wise.
cosmocrazy
2010-Jan-02, 03:04 PM
Maybe Space/Universe is not all that "this" is made of. No way of knowing. We view space as nothing beyond that, for all we know there may be some type of other "space" outside of our universe. Or possibly space doesn't end within our universe? We just proceed it within our universe only.
All in the imagination until we know other wise.
Well yes this may be true, but whats your definition of the "universe"?
The observable universe is one thing but the actual size, if one could even define size regarding the universe, is another. As 01101001 stated there may not be an edge in the classical way we might think of one. But then there maybe one but at present its just not observable. The universe could be a finite closed loop or perhaps infinite in space/time.
We just don't know enough to assume either one way or the other. All we can say is that from what we have observed so far the universe appears basically flat, around 14 billion years old and is expanding. Whats beyond that at present is an open book.
speedfreek
2010-Jan-02, 03:19 PM
Why not? It seems a reasonable and natural assumption. Is there any
other assumption one could make that is as reasonable or as natural?
-- Jeff, in Minneapolis
What about the assumption that the thing we live in (the universe) is similar to the thing we live on (the surface of the Earth)?
If the Earth was flat, and had an edge such that if you walked far enough you could fall off, I would understand the assumption that the universe had such an edge.
;)
JohnD
2010-Jan-02, 05:08 PM
Lf,
It's easy to ask the question.
But it's very easy inded to do a search of this website, say for "edge universe"
I found more than the 500 hits that the search can use.
By doing that you will find a great deal of information.
I suggest you do.
Meanwhile, the 'balloon' anology is imperfect, but may be helpful.
Imaginme a universe on the surface of a baloon.
It is a 2 dimensional universe, that expands as the balloon is inflated.
For a 2D inhabitant, it is getting bigger, but into nowhere.
Good luck!
John
luckyfrank
2010-Jan-02, 05:48 PM
Hungry4info
2010-Jan-02, 06:45 PM
It's helpful to think of the universe's expansion as an expansion of space, instead of an expansion in space. So there isn't a need for room to expand into.
If i was standing on the very edge of the universe with a tennis ball in my hand and threw that ball over the edge what would happen to the ball ? It would make a dull thud and bounce back. :lol:
captain swoop
2010-Jan-02, 07:43 PM
or come round and hit you in the back of the head.
cosmocrazy
2010-Jan-02, 09:31 PM
Or just cease to exist. :)
Hungry4info
2010-Jan-03, 04:54 AM
korjik
2010-Jan-03, 08:59 AM
Why not? It seems a reasonable and natural assumption. Is there any
other assumption one could make that is as reasonable or as natural?
-- Jeff, in Minneapolis
Physics is not restricted to what you think is reasonable and natural. As a matter of fact, it quite frequently acts unreasonably.
luckyfrank
2010-Jan-03, 01:15 PM
What about the assumption that the thing we live in (the universe) is similar to the thing we live on (the surface of the Earth)?
If the Earth was flat, and had an edge such that if you walked far enough you could fall off, I would understand the assumption that the universe had such an edge.
;)
Ok fair enough but lets say you were able to throw the ball faster than the universe is expanding ?
Another thing on my mind is when we look to the furthest reaches of the universe we are looking back in time to the start of the universe and everything is expanding from there then surly the origin of the big ban should be in the center of the universe right ? Do we know the location of the inital start of everything
Andrew D
2010-Jan-03, 03:29 PM
Ok fair enough but lets say you were able to throw the ball faster than the universe is expanding ?
Another thing on my mind is when we look to the furthest reaches of the universe we are looking back in time to the start of the universe and everything is expanding from there then surly the origin of the big ban should be in the center of the universe right ? Do we know the location of the inital start of everything
The universe isn't expanding in a way that would allow the ball to surpass the 'expansion' as you suggest. It's apples and oranges.
And there is no 'center' or the universe objects are expanding away from. Search this forum for "expanding universe" and you'll find dozens of posts, including one started by myself a few weeks ago, that will answer your question...I've learned a lot since then...
cosmocrazy
2010-Jan-03, 03:54 PM
Ok fair enough but lets say you were able to throw the ball faster than the universe is expanding ?
Since the universe is believed to be expanding at a rate of C or greater at the furthest detectable distances away from us, then based on relativity this would never be possible.
Another thing on my mind is when we look to the furthest reaches of the universe we are looking back in time to the start of the universe and everything is expanding from there then surly the origin of the big ban should be in the centre of the universe right ? Do we know the location of the inital start of everything
Yes, but based on the BB theory the centre itself is expanding, so the centre of the universe is everywhere.
Hungry4info
2010-Jan-03, 06:54 PM
Ok fair enough but lets say you were able to throw the ball faster than the universe is expanding ?
That isn't possible. The expansion of the universe doesn't quite work that way. Recall the expanding balloon analogy. For anybody in this universe (the surface of the balloon), the local space around them does not seem to be expanding very rapidly, but only things far away seem to be doing so. So to overcome the expansion of space at the observer's location, you can just nudge the tennis ball to a few mm per decade and you'll have overcome the Universe's expansion at your local space. The expansion rate of the universe is ~500 km s-1 Mpc-1. That's 500 kilometres per second... per megaparsec. The expansion of the universe is 500 km s-1 across a million parsecs! Condering a million parsecs, 500 km s-1 is pretty much nothing. As such, if you were a Mpc away from an object, it would seem to receed from you at 500 km s-1. So let's say you throw something at 500 km s-1 so that it'll catch up with whatever object is a Mpc away. Well an object at 2 Mpc is moving away at 1,000 km s-1, so you'll never catch up with that one. So you can throw it harder if you want. Well an object three times as far (6 Mpc) is moving away at 3,000 km s-1. On and on... until you're aiming at something 600 Mpc away, which is moving away from you at 300,000 km s-1. You'll find yourself unfortunately incapable of throwing your tennis ball that fast.
Another thing on my mind is when we look to the furthest reaches of the universe we are looking back in time to the start of the universe and everything is expanding from there then surly the origin of the big ban should be in the center of the universe right ? Do we know the location of the inital start of everything
Again, recall the expanding balloon analogy. There's no point on the balloon's surface that you can identify as the start of the expansion. Any observer on the balloon would see the rest of the balloon expand away from his current location, regardless of where they are.
As such, no matter where you are in the Universe, you appear to be at the centre of expansion. In truth, the Universe lacks a centre much like the balloon lacks any true central point of expansion.
DrRocket
2010-Jan-03, 07:41 PM
Why not? It seems a reasonable and natural assumption. Is there any
other assumption one could make that is as reasonable or as natural?
-- Jeff, in Minneapolis
The usual assumption (see for instance The large-scale structure of spacetime by Hawking and Ellis) is that space time is a 4-dimensional Lorentzian manifold without boundary (without an edge). That seems to be both reasonable and natural.
If you assume the structure of a manifold with boundary, then you have to contend with what is happening in the boundary. That boundary will be a 3-manifold without boundary, so locally 3-dimensional. Now, what is a 3-dimensinal spacetime? Is it locally timeless or is is locally 2-space with some notion of time ? Neither makes sense.
Jeff Root
2010-Jan-03, 07:47 PM
You assume there is an edge. Why?
Why not? It seems a reasonable and natural assumption. Is there any
other assumption one could make that is as reasonable or as natural?
What about the assumption that the thing we live in (the universe) is similar
to the thing we live on (the surface of the Earth)?
Why would anyone make *that* assumption? It appears to be completely
baseless. Not the least bit reasonable or natural!
If the Earth was flat, and had an edge such that if you walked far
enough you could fall off, I would understand the assumption that the
What does the surface of the Earth (or anything else) have to do with
the extent of the Universe??? I see no connection. There is no apparent
reason to assume any connection or any similarity between the two.
The original poster's assumption is completely reasonable and natural.
There is nothing at all reasonable or natural about the assumption you
suggest.
-- Jeff, in Minneapolis
Hungry4info
2010-Jan-03, 07:49 PM
Is it locally timeless or is is locally 2-space with some notion of time ? Neither makes sense.
Why would a 2+1 spacetime not make sense?
What does the surface of the Earth (or anything else) have to do with the extent of the Universe??? I see no connection. There is no apparent reason to assume any connection or any similarity between the two.
The original poster's assumption is completely reasonable and natural. There is nothing at all reasonable or natural about the assumption you suggest.
I think the point he was trying to make was that asking what happens when you move off the edge of the Universe was similar to asking what happens if you move off the edge of Earth in that the two are based on incorrect assumptions.
Jeff Root
2010-Jan-03, 08:02 PM
Physics is not restricted to what you think is reasonable and natural.
Obviously.
Even if it weren't obvious, it would still be a completely reasonable and
natural assumption that physics isn't restricted to what I think is reasonable
and natural. I would not be surprised to learn that the original poster
assumes that physics is not restricted to what I think is reasonable and
natural. Nor would I be surprised to learn that he assumes that physics
is not restricted to what he thinks is reasonable and natural.
Whatever. The assumption that the Universe has an edge is completely
reasonable and natural. Is there any other assumption one could make
that is as reasonable or as natural? Is it your view that unreasonable
and unnatural assumptions are preferable to reasonable and natural
assumptions?
-- Jeff, in Minneapolis
Hungry4info
2010-Jan-03, 08:10 PM
I think what the issue is here is that what is reasonable to one is unreasonable to another, perhaps due to a knowledge gap. Those more familiar with the BBT may find "every point appears to be the centre of the universe" to be reasonable, whereas someone unfamiliar with it wouldn't.
DrRocket
2010-Jan-03, 08:23 PM
Why would a 2+1 spacetime not make sense?
Why would it ? If you travel to the edge do you simply flatten out ?
Huygens principle fails to work in even spatial dimensions, so does physics change at the boundary ? Remnember that this boundary, if it were to exist, would be a part of spacetime. It is not somehow fenced off.
The "cosmological principle" would fail dramatically at the edge.
Since the universe is, by definition, the whole enchilada, what is the importance of an edge ? It is not like there is something on the the other side, since there is no other side.
I think the point he was trying to make was that asking what happens when you move off the edge of the Universe was similar to asking what happens if you move off the edge of Earth in that the two are based on incorrect assumptions.
The huge difference is that the Earth is embedded in something else, the universe. The unverse is not embedded in anything else, since it is, by definition, all that is.
Jeff Root
2010-Jan-03, 09:39 PM
The unverse is not embedded in anything else, since it is, by definition,
all that is.
That's one definition.
Another definition would be the portion of the cosmos which contains
matter. It might be that most of the Universe is empty, and only a very
small part of it contains matter.
Another definition would be the part of the cosmos which is participating
in the Big Bang expansion. There could be many-- perhaps infinitely
many-- universes, some of which are expanding like the one we inhabit.
The "cosmological principle" would fail dramatically at the edge.
Obviously. By definition.
But the cosmological principle is pretty weak. It isn't as strong as the
law of conservation of energy, and that law is only local, not global.
The cosmological principle is a description of what we can see. There
is no apparent reason that it should apply to everything beyond what
we can see.
-- Jeff, in Minneapolis
DrRocket
2010-Jan-04, 06:10 AM
That's one definition.
Another definition would be the portion of the cosmos which contains
matter. It might be that most of the Universe is empty, and only a very
small part of it contains matter.
Another definition would be the part of the cosmos which is participating
in the Big Bang expansion. There could be many-- perhaps infinitely
many-- universes, some of which are expanding like the one we inhabit.
Neither of your two definitions apply to the a general relativistic model of cosmology.
You can, of course, use any ATM definition that pleases you. But such definitions are not amenable to treatment by means of mainstream theory. The only accepted theory that we have to deal with this question is general relativity, which has it limits, but which is supported by a large body of experiment and established theoretical models. Anything else is speculation.
EDG
2010-Jan-04, 09:19 AM
On and on... until you're aiming at something 600 Mpc away, which is moving away from you at 300,000 km s-1. You'll find yourself unfortunately incapable of throwing your tennis ball that fast.
Hang on a sec. You're saying that an object 600 Mpc away is receding from us at the speed of light? 600 Mpc is nearly 2 billion lightyears, but we know of things that are (much) further away from us than that - e.g. the most distant galaxies known are about 13 billion lightyears away - and they aren't receding from us at faster than the speed of light (are they?).
Sententia
2010-Jan-04, 12:02 PM
Have we really come this far as to know the actual age of the Universe? If science says the Universe is 13.5- 14 billion years old.. does that mean its necessarily true? Sure, the most distant galaxy's that we know of are 13 billion light years away.. but I feel that the Universe has to be much larger in comparison to all that is known, in these terms the Universe feels small and compressed.
I feel the Universe can be a unlimited canvas to our comprehension, though I feel it is not infinite. When I think of it, I picture a bubble.. circular like Earth. Before Columbus discovered America, what do you think the people thought of the oceans .. what lay beyond them ? I'm more so inclined to believe in the multi universe theory, and sub dimensions than a infinite nothingness..
EDG
2010-Jan-04, 05:25 PM
but I feel that the Universe has to be much larger in comparison to all that is known, in these terms the Universe feels small and compressed.
I feel the Universe can be a unlimited canvas to our comprehension, though I feel it is not infinite.
Science isn't about "feelings" or "belief" though.
Andrew D
2010-Jan-04, 05:49 PM
Have we really come this far as to know the actual age of the Universe? If science says the Universe is 13.5- 14 billion years old.. does that mean its necessarily true? Sure, the most distant galaxy's that we know of are 13 billion light years away.. but I feel that the Universe has to be much larger in comparison to all that is known, in these terms the Universe feels small and compressed.
Your right, but I don't think you realize why.
http://en.wikipedia.org/wiki/Hubble_volume:
The distance c / H(sub)0 is known as the "Hubble length". It is equal to 13.8 billion light years in the standard cosmological model, similar to but somewhat larger than c times the age of the universe. This is because 1 / H(sub)0 gives the age of the universe by a backward extrapolation which assumes that the recession speed of each galaxy has been constant since the big bang. In fact, recession speeds initially decelerate due to gravity, and are now accelerating due to dark energy, so that 1 / H(sub)0 is only an approximation to the true age.
http://en.wikipedia.org/wiki/Observable_universe:
The age of the Universe is about 13.7 billion years, but due to the expansion of space we are now observing objects that are now considerably farther away than a static 13.7 billion light-years distance. The edge of the observable universe is now located about 46.5 billion light-years away [1].
So, while (the light from) the furthest galaxies we see are (is coming from) 10-13 billion light years away, that's where they were 10-13 billion years ago. The galaxies themselves are now closer to 46.5 billion LY away.
Science isn't about "feelings" or "belief" though.
Correct, but without them, where would science be?
Spaceman Spiff
2010-Jan-04, 06:42 PM
Hang on a sec. You're saying that an object 600 Mpc away is receding from us at the speed of light? 600 Mpc is nearly 2 billion lightyears, but we know of things that are (much) further away from us than that - e.g. the most distant galaxies known are about 13 billion lightyears away - and they aren't receding from us at faster than the speed of light (are they?).
Well, yes they are (by a conventional definition of recession speed), and no they aren't; it all depends on what distance and time intervals one adopts since these intervals are not invariants (coordinates, coordinates, coordinates -- GR allows one to pick any self-consistent set that you want). Ned Wright's FAQs (http://www.astro.ucla.edu/%7Ewright/cosmology_faq.html) discusses several related questions; start here (http://www.astro.ucla.edu/%7Ewright/cosmology_faq.html#FTL). It is also discussed in Lineweaver & Davis' (http://www.mso.anu.edu.au/%7Echarley/papers/LineweaverDavisSciAm.pdf) Scientific American article, although out of simplicity they have adopted the simplest (and most common) explanation.
Jeff Root
2010-Jan-04, 06:57 PM
Have we really come this far as to know the actual age of the Universe?
Pretty much, yes.
I happen to have a somewhat ATM notion that suggests the possibility
of a slightly greater age, but there are several lines of evidence which
all indicate that it isn't very much older than 13.7 billion years.
If science says the Universe is 13.5- 14 billion years old.. does that
mean its necessarily true?
It is what the evidence and reasoning indicate. Some aspects of the
reasoning may be wrong. Important evidence may be as yet unknown.
But it is the best estimate that we currently have, and that estimate
is consistent for several different lines of reasoning.
the most distant galaxy's that we know of are 13 billion light years away..
The most distant galaxies we can see are much farther than 13 billion
light-years away. The light from the most distant galaxies we can see
has travelled a distance of roughly 13 billion light-years. Those galaxies
were much closer than 13 billion light-years when they emitted that light,
and are "now" much farther away than 13 billion light-years. I put the
word "now" in quotes because the concept of "now" has little meaning
for events which are so far apart.
-- Jeff, in Minneapolis
speedfreek
2010-Jan-04, 07:03 PM
So, while (the light from) the furthest galaxies we see are (is coming from) 10-13 billion light years away, that's where they were 10-13 billion years ago. The galaxies themselves are now closer to 46.5 billion LY away.
Almost right, but not quite! (Don't worry, it is complicated!)
The light from the most distant (in time) galaxies we have seen has been travelling for 13 billion years, but those galaxies were only around 3.5 billion light-years away when that light was emitted, and are now around 30 billion light-years away as that light reaches us.
It is the coordinates from which the Cosmic Microwave Background Radiation we currently detect was originally released from, if those coordinates are considered to be moving with the expansion of the universe, that are currently 46.5 billion years away. The light-travel time for the CMBR is nearly 13.7 billion years and galaxies didn't form for a few hundred million years after that.
Jeff Root
2010-Jan-04, 07:27 PM
The unverse is not embedded in anything else, since it is, by definition,
all that is.
That's one definition.
Another definition would be the portion of the cosmos which contains
matter. It might be that most of the Universe is empty, and only a very
small part of it contains matter.
Another definition would be the part of the cosmos which is participating
in the Big Bang expansion. There could be many-- perhaps infinitely
many-- universes, some of which are expanding like the one we inhabit.
Neither of your two definitions apply to the a general relativistic model
of cosmology.
I think you have it backward: The general relativistic model is limited
in that it only applies to a restricted range of possibilities. The actual
Universe might be correctly described by general relativity, but there
is no reason to apply the artificial restrictions of general relativity to
the actual Universe. General relativity accurately describes some of
what we can see. It doesn't accurately describe every possible case
of how the Universe may actually be arranged.
Suggesting that descriptions of the Universe should be limited to what
can be described by the current best existing theory is absurd.
-- Jeff, in Minneapolis
Andrew D
2010-Jan-04, 07:45 PM
Almost right, but not quite! (Don't worry, it is complicated!)
The light from the most distant (in time) galaxies we have seen has been travelling for 13 billion years, but those galaxies were only around 3.5 billion light-years away when that light was emitted, and are now around 30 billion light-years away as that light reaches us.
It is the coordinates from which the Cosmic Microwave Background Radiation we currently detect was originally released from, if those coordinates are considered to be moving with the expansion of the universe, that are currently 46.5 billion years away. The light-travel time for the CMBR is nearly 13.7 billion years and galaxies didn't form for a few hundred million years after that.
You're right. This is what I meant to say:
The most distant galaxies we can see are much farther than 13 billion
light-years away. The light from the most distant galaxies we can see
has travelled a distance of roughly 13 billion light-years. Those galaxies
were much closer than 13 billion light-years when they emitted that light,
and are "now" much farther away than 13 billion light-years. I put the
word "now" in quotes because the concept of "now" has little meaning
for events which are so far apart.
-- Jeff, in Minneapolis
So, I'll add a question if I can, what size was the universe at the time the galaxies formed?
Jeff Root
2010-Jan-04, 08:27 PM
I hope that speedfreek and/or others can add details, but the "size" of
the Universe is completely unknown. It isn't even certain that it is as large
as what we can see! That possibility seems absurdly remote to me, though.
If, as it appears, the visible Universe is geometrically almost "flat" overall, but
not quite perfectly "flat", then the Universe as a whole must be considerably
larger than the part we can see. Some people think that the Universe might
be infinite. I, personally, am convinced that the part of the Universe which
is participating in the cosmic expansion (that is, everything that originated
in the Big Bang) is finite in mass-energy and spatial extent. It must be, in
order to be causally-connected. However, it appears that all that stuff may
have undergone a very brief period of absurdly rapid expansion when it was
a tiny fraction of a second old. During that time its size would have grown
enormously. That period of expansion is called "Inflation". Look up articles
about cosmic Inflation for some guesses about how big the Universe might
have been at that time.
It is vastly easier to say what the density of the Universe was at any given
time. The density at the time of nucleosynthesis, in the first three minutes
after the Big Bang, and at the time the Universe became transparent, about
380,000 years later, are the two best-defined densities. You can look those
up in any description of the early evolution of the Universe.
-- Jeff, in Minneapolis
speedfreek
2010-Jan-04, 09:12 PM
Yes, when cosmologists give the universe a size, they are talking purely in terms of the observable universe. The observable universe contains everything we have seen (and whatever would have been seen from here, all the way backwards through time) and where we estimate all that stuff would be today. What cosmologists really don't know is how much more there is than we have seen - the size of the whole universe. The whole universe might even be smaller than the observable universe, and if this were the case we would be looking at the same distant regions of space when we look in different directions, but we would be seeing them during different respective times so we might not recognise them as such (currently, this is thought not to be the case, but it remains a possibility)! The currently favoured theory of cosmic inflation puts the size of the whole universe many magnitudes larger than our observable part of it.
The size of the observable universe is usually defined using the distance that the CMBR we currently detect was released at, if those coordinates (which form a conceptual sphere around us, known as the particle horizon of the surface of last scattering) were receding with the expansion of the universe. It is thought that the CMBR we detect was originally released around 40 million light-years away, and that the expansion of the universe would put those coordinates at around 46.5 billion light-years away by now.
We have seen galaxies that existed only 800 million years after the Big-Bang and it is thought that galaxies would have formed a few hundred million years before that, so let's assume that galaxies formed around 500 million years after the Big-Bang. This would equate to galaxies with redshifts around z=10, but so far we have only seen galaxies with redshifts of up to around z=7 or so.
500 million years after the Big-Bang, the universe was approximately 1/10th of its current size. If we had telescopes good enough to see galaxies from that time, they would be seen to have been around 3 billion light-years away at that time, and the particle horizon (the edge of the observable universe) would have been somewhere around 4.6 billion light-years away, I think.
EDG
2010-Jan-04, 09:45 PM
Correct, but without them, where would science be?
Exactly where it is today?
Science is based on observation and evidence. If you want a worldview based of feelings and belief, you should be looking at religion instead.
Andrew D
2010-Jan-04, 11:15 PM
Exactly where it is today?
Science is based on observation and evidence. If you want a worldview based of feelings and belief, you should be looking at religion instead.
The thought that the Sun orbited the Earth was based on observations and evidence. The thought that the Earth was flat was based on observation and evidence. My point is only that while 'feelings' and 'belief' can derail good science, personal conviction and intuition are its driving forces. Would Newton have changed the way we look at the universe if the contemporary scientific conventions didn't "feel" wrong to him? While observation and evidence are the engines of science, the belief, the urge to observe and quantify, is its rudder.
DrRocket
2010-Jan-05, 12:00 AM
Suggesting that descriptions of the Universe should be limited to what
can be described by the current best existing theory is absurd.
-- Jeff, in Minneapolis
Suggesting that you can provide a meaningful description that transcends the current best theory is beyond absurd.
If you have a better theory or a better basis for such a description please state it clearly and in terms that allow it to be either supported or falsified.
Yes, there are limitations to GR, as I stated quite clearly. But speculations beyond that which is available with the best available theory is nothing but unsubstantiated rank speculation.
You have just clearly stated that you don't know what you are talking about and are extremely proud of that fact.
pzkpfw
2010-Jan-05, 12:07 AM
Can we now please get back to providing mainstream answers to questions? This is not the place to have meta discussions on science.
EDG
2010-Jan-05, 12:08 AM
The thought that the Sun orbited the Earth was based on observations and evidence. The thought that the Earth was flat was based on observation and evidence.
People also didn't have a rigorous scientific method back then. They misinterpreted (and ignored) their observations and came up with interpretations that did not tally with reality. Plus, the fear of being tried for heresy didn't exactly encourage them to rock the boat.
My point is only that while 'feelings' and 'belief' can derail good science, personal conviction and intuition are its driving forces. Would Newton have changed the way we look at the universe if the contemporary scientific conventions didn't "feel" wrong to him? While observation and evidence are the engines of science, the belief, the urge to observe and quantify, is its rudder.
He didn't "feel" anything was wrong. He made observations and figured out a way to mathematically describe what he was seeing. On could argue that he made an "intuitive leap" perhaps, but intuition is not the same as belief.
Andrew D
2010-Jan-05, 01:18 AM
One could argue that he made an "intuitive leap" perhaps, but intuition is not the same as belief.
One could argue that anything one wanted, if one was so inclined.
On the topic at hand: Once we get to the realm of the 'edge of the universe', or even beyond that which we can observe, whether because of our own limitations or because of physical impossibilities, even the greatest minds can only offer what they think (or believe, or intuitively leap toward, what have you). While some ideas make more sense to some than others, none can be confirmed and few can be discredited, so gather as much evidence as you can and draw your own conclusions.
pzkpfw
2010-Jan-05, 01:32 AM
Last warning before infractions start flowing. Thanks.
Jeff Root
2010-Jan-05, 06:51 AM
Suggesting that descriptions of the Universe should be limited to what
can be described by the current best existing theory is absurd.
Suggesting that you can provide a meaningful description that transcends
the current best theory is beyond absurd.
If you have a better theory or a better basis for such a description please
state it clearly and in terms that allow it to be either supported or falsified.
I said what I wanted to say, and I stand behind what I said.
The Universe may or may not have an edge. The Universe may be finite
or infinite. The Universe may be smaller than it appears, or far, far larger.
The Universe may have overall curvature, or it may be "flat" overall.
The Universe may have finite mass and energy, or it may be infinite.
The entire Universe might be participating in the cosmic expansion which
derived from the Big Bang, or it might be only a portion of the Universe.
Mathematical models can be constructed to describe each of those
possibilities. General relativity can be used to help in their construction.
Logic allows us to rule out some combinations. What I have pointed out
that I have not seen elsewhere is the fact that the Universe cannot be
both infinite in extent and expanding throughout, because that scenario
violates causality. If two parts of the Universe have significant features
in common, there must be a causal connection between them.
-- Jeff, in Minneapolis
Hungry4info
2010-Jan-05, 07:29 AM
Hang on a sec. You're saying that an object 600 Mpc away is receding from us at the speed of light? 600 Mpc is nearly 2 billion lightyears, but we know of things that are (much) further away from us than that - e.g. the most distant galaxies known are about 13 billion lightyears away - and they aren't receding from us at faster than the speed of light (are they?).
I seem to have fudged that one up somehow.
Grey
2010-Jan-05, 04:26 PM
Logic allows us to rule out some combinations. What I have pointed out
that I have not seen elsewhere is the fact that the Universe cannot be
both infinite in extent and expanding throughout, because that scenario
violates causality. If two parts of the Universe have significant features
in common, there must be a causal connection between them.I am not certain that has to be the case. For example, two spiral galaxies share many significant features in common. But I don't think that's because there is a causal link between them; it's just that the laws of physics are the same everywhere, so certain types of structures show up independently in different places. Besides, the whole issue of quantum entanglement suggests that causality might not be as straightforward an issue as we think. Of course, there's nothing wrong with the idea of an infinite universe where only part of that universe is participating in the expansion either. I just don't think we can say a priori that it's the only type of infinite universe that could be possible.
Grey
2010-Jan-05, 04:30 PM
Hang on a sec. You're saying that an object 600 Mpc away is receding from us at the speed of light? 600 Mpc is nearly 2 billion lightyears, but we know of things that are (much) further away from us than that - e.g. the most distant galaxies known are about 13 billion lightyears away - and they aren't receding from us at faster than the speed of light (are they?).
I seem to have fudged that one up somehow.No, you're correct. The effective recession velocity of the most distant galaxies is faster than the speed of light.
Jeff Root
2010-Jan-05, 08:12 PM
Logic allows us to rule out some combinations. What I have pointed out
that I have not seen elsewhere is the fact that the Universe cannot be
both infinite in extent and expanding throughout, because that scenario
violates causality. If two parts of the Universe have significant features
in common, there must be a causal connection between them.
I am not certain that has to be the case. For example, two spiral
galaxies share many significant features in common. But I don't think
that's because there is a causal link between them; it's just that the
laws of physics are the same everywhere, so certain types of structures
show up independently in different places.
The laws of physics are the same in two different locations because
they are causally connected. Two spiral galaxies both contain hydrogen
atoms with a particular mass, electric charge, energy levels, and so on
because they both sprang from the same Big Bang. They share common
properties because they are causally connected.
I have one head, two arms, and two legs, like a monkey has, because
the monkey and I are causally connected: We have common ancestors.
-- Jeff, in Minneapolis
Grey
2010-Jan-06, 03:11 AM
The laws of physics are the same in two different locations because they are causally connected.Are they? Is it possible that somewhere else in the universe the fine structure constant has a different value? I don't know if the answer is yes or no, but I am quite sure that we can't absolutely rule out either answer. We generally assume that the laws of physics are the same everywhere (mostly because it's simpler). Heck, the laws of physics are what allows us to talk about whether two events can be causally connected in the first place. If the laws of physics can be different, then so can the very notion of whether things can be causally linked.
Two spiral galaxies both contain hydrogen atoms with a particular mass, electric charge, energy levels, and so on because they both sprang from the same Big Bang.Again, I don't think you can say this with logical certainty. We don't particularly know why every electron has the same value for properties like mass and charge; we have no theory to suggest why this is the case. So I don't think we know whether it's logically possible for electrons somewhere else in the universe to have different values for those properties or not. We can certainly imagine it, but perhaps there's some elegant reason that we just haven't figured out why all of the various physical constants in the universe simply must have the values we observe. That's certainly just as reasonable a possibility as assuming that they could have had any random value, and just happened to end up with the values that they have. You're free to prefer one or the other, but neither can be ruled out because it's just "illogical".
Simply put, you're adopting as an axiom that two parts of the universe must be causally connected in order for the laws of physics and the properties of elementary particles (or even what elementary particles exist, presumably) to be the same. But we don't know enough about why the laws of physics are what they are, or why there are certain kinds of elementary particles that have certain properties to know whether that's a reasonable axiom or not.
Matthias
2010-Jan-14, 01:05 AM
That isn't possible. The expansion of the universe doesn't quite work that way. Recall the expanding balloon analogy. For anybody in this universe (the surface of the balloon), the local space around them does not seem to be expanding very rapidly, but only things far away seem to be doing so. So to overcome the expansion of space at the observer's location, you can just nudge the tennis ball to a few mm per decade and you'll have overcome the Universe's expansion at your local space. The expansion rate of the universe is ~500 km s-1 Mpc-1. That's 500 kilometres per second... per megaparsec. The expansion of the universe is 500 km s-1 across a million parsecs! Condering a million parsecs, 500 km s-1 is pretty much nothing. As such, if you were a Mpc away from an object, it would seem to receed from you at 500 km s-1. So let's say you throw something at 500 km s-1 so that it'll catch up with whatever object is a Mpc away. Well an object at 2 Mpc is moving away at 1,000 km s-1, so you'll never catch up with that one. So you can throw it harder if you want. Well an object three times as far (6 Mpc) is moving away at 3,000 km s-1. On and on... until you're aiming at something 600 Mpc away, which is moving away from you at 300,000 km s-1. You'll find yourself unfortunately incapable of throwing your tennis ball that fast.
Again, recall the expanding balloon analogy. There's no point on the balloon's surface that you can identify as the start of the expansion. Any observer on the balloon would see the rest of the balloon expand away from his current location, regardless of where they are.
As such, no matter where you are in the Universe, you appear to be at the centre of expansion. In truth, the Universe lacks a centre much like the balloon lacks any true central point of expansion.
So have th analogy of the balloon's surface equalling 3D "surface" of the universe. But the 2D body of the balloon is expanding into the 3D space outside (and inside) its surface. Aren't there supposed to be extra dimensions on top of the 3 we know, and might not the "body" of the universe be expanding into such a hypervolume?
Jeff Root
2010-Jan-14, 05:58 AM
General relativity posits that spacetime consists of three spatial dimensions
and one time dimension. Those four dimensions are sufficient to describe the
effects of gravity. Other theories sometimes posit more dimensions.
-- Jeff, in Minneapolis
cosmocrazy
2010-Jan-14, 08:39 PM
General relativity posits that spacetime consists of three spatial dimensions
and one time dimension. Those four dimensions are sufficient to describe the
effects of gravity. Other theories sometimes posit more dimensions.
-- Jeff, in Minneapolis
Yes at the macroscopic level, but at the microscopic a quantum theory of gravity is required. Such is that they are not yet compatible. This is why sometimes extra dimension are postulated.
DrRocket
2010-Jan-15, 01:04 AM
What I have pointed out
that I have not seen elsewhere is the fact that the Universe cannot be
both infinite in extent and expanding throughout, because that scenario
violates causality. If two parts of the Universe have significant features
in common, there must be a causal connection between them.
-- Jeff, in Minneapolis
Not true.
What you are describing is the "Horizon Problem" -- why does the universe appear to be homogeneous when much of it is causally disconnected from other parts. It is a problem whether the universe is finite or infinite and being infinite has little bearing on the problem.
The resolution, such as it is, lies in inflation. Google "inflation" or "horizon problem", or read Alan Guth's book The Inflationary Unverse.
Jeff Root
2010-Jan-15, 01:58 AM
What I have pointed out that I have not seen elsewhere is the fact
that the Universe cannot be both infinite in extent and expanding
throughout, because that scenario violates causality. If two parts
of the Universe have significant features in common, there must be
a causal connection between them.
Not true.
What you are describing is the "Horizon Problem" -- why does the
universe appear to be homogeneous when much of it is causally
disconnected from other parts.
There is no part of the Universe that we can see that is causally
disconnected from any other part of the Universe that we can see,
in the sense that both parts originate from a common cause. They
might *no longer* be in causal contact, and they may not have
been in causal contact for a very, very long time, but they are
causally connected at some time in the past. They must be, or
they would not share so many features in common -- they would
not be "homogenous".
It is a problem whether the universe is finite or infinite and being
infinite has little bearing on the problem.
The resolution, such as it is, lies in inflation. Google "inflation" or
"horizon problem", or read Alan Guth's book The Inflationary Unverse.
That hypothesis offers two possibilities. One of those possibilities
could work; the other has a fatal flaw. The one that could work is
essentially the same as what I'm saying: Everything involved in the
cosmic expansion was originally in contact. Inflation spread it out.
The possibility that you favor assumes that everything participating
in the cosmic expansion was *never* in contact, but consisted of
the same particles with the same properties at roughly the same
density and same temperature all simultaneously, and spontaneously
it all inflated simultaneously, evening out the density and temperature
even more than they had been.
This version of inflation accounts for the precision of the uniformity
of the temperature and density, but it doesn't account for why the
Universe was filled with uncountable numbers of identical particles
with identical properties, or why those particles were all at a similar
high temperature, or why they were all rushing apart from each other
in a similar way.
I am saying that is unlikely that a small number protons would happen
to appear simultaneously with no common cause. It is absurd that
decillions of them would happen to appear simultaneously with no
common cause. And it is ludicrous that infinitely many of them would
happen to appear simultaneously with no common cause.
We can be sure that there was a Big Bang: Everything in the Universe
was once scrunched tightly together. The Big Bang is the obvious
opportunity for all that matter to have been in causal contact, when
it acquired its common properties. The idea that everything we see
could exist without having been in causal contact is ridiculous.
-- Jeff, in Minneapolis
DrRocket
2010-Jan-15, 04:19 AM
There is no part of the Universe that we can see that is causally
disconnected from any other part of the Universe that we can see,
in the sense that both parts originate from a common cause. They
might *no longer* be in causal contact, and they may not have
been in causal contact for a very, very long time, but they are
causally connected at some time in the past. They must be, or
they would not share so many features in common -- they would
not be "homogonous".
That hypothesis offers two possibilities. One of those possibilities
could work; the other has a fatal flaw. The one that could work is
essentially the same as what I'm saying: Everything involved in the
cosmic expansion was originally in contact. Inflation spread it out.
The possibility that you favor assumes that everything participating
in the cosmic expansion was *never* in contact, but consisted of
the same particles with the same properties at roughly the same
density and same temperature all simultaneously, and spontaneously
it all inflated simultaneously, evening out the density and temperature
even more than they had been.
This version of inflation accounts for the precision of the uniformity
of the temperature and density, but it doesn't account for why the
Universe was filled with uncountable numbers of identical particles
with identical properties, or why those particles were all at a similar
high temperature, or why they were all rushing apart from each other
in a similar way.
I am saying that is unlikely that a small number protons would happen
to appear simultaneously with no common cause. It is absurd that
decillions of them would happen to appear simultaneously with no
common cause. And it is ludicrous that infinitely many of them would
happen to appear simultaneously with no common cause.
We can be sure that there was a Big Bang: Everything in the Universe
was once scrunched tightly together. The Big Bang is the obvious
opportunity for all that matter to have been in causal contact, when
it acquired its common properties. The idea that everything we see
could exist without having been in causal contact is ridiculous.
-- Jeff, in Minneapolis
1. You are wrong and you don't understand the theory. What you have stated is so far off base that there is no point in trying to refute if point by point. You simply have things badly garbled. Better read up.
2, I don't "favor" any hypothesis. I have only stated the facts.
Umbrava
2010-Jan-15, 04:38 AM
The best way to try to answer.
Your perceptions of the universe are actually miniscule to the way the universe actually is. To tell you the honest truth about the size of the universe would be obvious the complete eventual pure cosmilogical weight at the most actively dense time during the universes life. You are wrong about one thing you think about the shape of the universe as 3 dimensional you forgot the other 2 required dimensions pretty much always active in this universe. If you cant think using 5 base dimensions you could not correctly predict pretty much out of your visual range unless almost in direct contact with. While you can have theoreticly more demensions that five you really only need the 5 basic ones more or less the ones that predominatly ahere specific neccessity to this universe. Demensions 10-12 represent actuality but at a much higher level of actual potentiability and really not required for this universe as it is essentuialy potentialy occuring probability as it is identified compared to all the other simalataniusly forming universes exactly in the same spot as this one really because in the envirnment in which srounds this universe the actual space you ocupy is relativly meaningless. since after the universe you simply are unified or you arent. Basicly an entire universe with just one thing in it nothing likse just a bunch of planetiods. Just one massive energised mass in what i wouldnt call any sort of space in any sense of the word but like a completly spectral envirnment.
The Universe is not finite or infinite it is ultimately is as big as it eventually needs to get nothing more nothing less because wasted particles would not have the pure necessity to actually exist at least not in this universe.
Nothing is where it hasn't already always and eventually will be. The universe is completely cycldic in nature it is basically one huge even bigger than your perceptions of the singularity that maintains pure universal cohesion - would prevent this universe from 'bleeding' into any other layers of existence. Nothing hasn't already been preformulated before it always happens ultimately nothing in any layer of theoretical existence layers has never actualy not ever not happened at least one time.
space does not 'expand or get bigger' there is no such thing as pure empty space anywhere in this universe. Even the empty air next to you is composed at least of one single particle at least always at one time. Thats basic 101 in particulate cohesion - your advanced ideas in theoretical particle physics. A single dead particle by itself would almost have no physical adherence in space they would have almost no difinable mass not by current instrumentation. If one particle in this universe were misplaced which is pretty much impossible into another universe not only would it create instability in both universes but it would cause a chain reaction destroys all the other potential universes within basically the basic bonds of the bits that compose them all. Even if this destroyed millions of universes they would always eventually reform. One thing im stating is a particle can be moved anywhere but it can only be moved within this universes barrier.
You can stand on the edge of the universe in a sense but you would basically just remain still you would step to your exact spot. The universe has no physical end it does have what i would call an eventual end in its life span though. It basicly just ends and instantly reforms it really never actualy ends. When it does completly end though when it does reform it does do it from srcatch however. All formations start back as a single particle.
One odd thing i wonder about the universe is its age. Its odd a mass of its size could take such a short time compared to the life of a single star the odd thing thing is for the galaxies to become distributed like the have in the current universe would taken it many more years than just tens of billions. I ultimately think that the eventual life of the universe would be somehwere in the neighborhood of 100 trillion years. I think stars have been reforming for trillions of years i really think that basically when you look at the heavens are glimpses in short time frames of objects many years out of your range. Basically when looking in the visible universe all your seeing is a temporary state. All the old dead stars would probably all eventually just become dark matter the inherent reason for the expansion of the universe. Prior Generational Dead stars would not have the ability to be identified with your instrumentation simply because they would have been composes of slightly different electrochemical composition based chemicals. Basically you probably could see back into the farthest as the oldest visible reaction in this universe. Stars themselves would ultimately probably just show multiple levels of reformation through other stars. Galaxies would probably be able to be aged much older than their individual stars. Galaxies reform just like stars but at about a rate of probably 10 times less frequent. A collection of galaxies could collapse on themselves every i would say 1 trillion years on average and reform a completely new potential of galaxies. Basically the initial reaction of the big bang is continually on going a reaction so large that it will take 100 trillion years to dissipate.
The cohesion layer of particles that keep this universe together comprise what we would call the unprecavable wall of inertia would be identified as the actual natural curve of this universe. Light does not travel in a straight light in this universe no matter where it goes. The coplete natural orientation of the universe is naturaly curved. You cannot breach the inertia layer it doesn't react to anything is pre-ocurers so it would be almost non existent but there so odd that if you touched it you would have no clue it was in anyway influencing you in anyway. Breaching it is not possible simply because it is ultimately so tightly compact it is basically one complete thing. Even if you could destroy the universe they would still be there simply because they could never be anywhere else in any other position they would simply be in place for reformation of universes. Like a honeycomb wall layer existence.
The actual size of things the pure massiveness in complete conceptual weight alone that is an active ongoing pure existence theory is almost bigger than you could ever imagine even on a good day. The universe is not just some groups of galaxies and stars and planets it is an ongoing reaction that regenerates for as long as the initial source of pure energy was released. The big bang reaction or even if you wanted to call the energy source to generate so many electromagnetically charged particles in such confinement. The explosion was so massive that it ultimately caused the curve all of space itself. Inertia walls are like clay though they cant be breached but they can be reorientated. Basically what im getting at is the initial reaction of energy released by the big bang would take around 100 trillion years about 30 stellar cycles. Stellar cycles are periods when all the stars in the universe change slightly in weight. A certain amount of charged particles are consumed by the equalising force needed to shape the reaction generated by the big bang. Would basically completely fry every particle in the universe simultaneously would destroy any life that didnt have the ability to adapt to it physiologically. This energy would penatrate all matter regardless of what it was so technology wouldnt help you.
I find it odd that i can say that the universe is too big or too old but people argue that it can be infinite? If the universe can be finite or infinate why cant it also be somehwere in between?
PetersCreek
2010-Jan-15, 09:09 PM
Umbrava,
Welcome to the BAUT forums. The Space/Astronomy Question & Answer forum is where people get mainstream answers to their questions. You may not post your personal theories that run counter to the mainstream here. If you wish to advance and defend your ideas, you may do so in the Against The Mainstream forum. Before doing so, you should familiarize yourself with our rules and forum-specific advice, linked in my signature line below.
Andrew D
2010-Jan-17, 04:17 PM
Doesn't the evidence we see point to a universe that is not spatially bound, but density bound?
Hornblower
2010-Jan-17, 11:39 PM
Doesn't the evidence we see point to a universe that is not spatially bound, but density bound?
What, in appropriate mathematical detail, do you mean by "density bound"?
WayneFrancis
2010-Jan-18, 02:58 AM
The best way to try to answer.
WayneFrancis
2010-Jan-18, 03:04 AM
Doesn't the evidence we see point to a universe that is not spatially bound, but density bound?
our observable universe has a bound to its density but as far as what is beyond our Hubble volume? If the universe is infinite in size then most likely it is also infinite in mass. I guess if that is true you would only get unbounded density at the centre of black holes but that isn't currently provable.
forrest noble
2010-Jan-18, 05:17 AM
Roobydo & Luckyfrank,
Roobydo quote:
Doesn't the evidence we see point to a universe that is not spatially bound, but density bound?
Not spatially bound is correct, but perhaps best stated as spatially limited to the confines of matter regardless of its density or configuration of space geometry.
Maybe the most prevalent BB model/ interpretation is that both space and time are "tied" to matter in their extension. By this interpretation there would be no such a thing as time before the beginning of the universe, or space outside the confines of matter. A part of the definition of space using this interpretation would be the volume which matter encompasses. Accordingly if the quantity of mass is finite so is space (by definition).
I think this most common standard interpretation/ definition of the bounds of time and space makes sense whether the BB model is valid or not. The idea would be something like: what would be the meaning of time or space if there was no matter, energy, or field of any kind, or a parallel universe with absolutely nothing in it.
DrRocket
2010-Jan-18, 06:01 AM
Roobydo & Luckyfrank,
Roobydo quote:
Not spatially bound is correct, but perhaps best stated as spatially limited to the confines of matter regardless of its density or configuration of space geometry.
Maybe the most prevalent BB model/ interpretation is that both space and time are "tied" to matter in their extension. By this interpretation there would be no such a thing as time before the beginning of the universe, or space outside the confines of matter. A part of the definition of space using this interpretation would be the volume which matter encompasses. Accordingly if the quantity of mass is finite so is space (by definition).
I think this most common standard interpretation/ definition of the bounds of time and space makes sense whether the BB model is valid or not. The idea would be something like: what would be the meaning of time or space if there was no matter, energy, or field of any kind, or a parallel universe with absolutely nothing in it.
Nope.
This thread seems to have departed rather markedly from mainstream physics and is well into ATM territory.
astromark
2010-Jan-18, 10:02 AM
Sorry for being overly simplistic but, The mainstream view. That being the the most wildly excepted theory... That the visible universe and that being all that we have knowledge of had a beginning. That a big bang is or was the most excepted method of creation of this universe. That a acceleration rate increasing is now evident. It makes not unreasonable sense that at a time some 13.7 odd billion years ago all of what we know of was in a very different state and, seemed to have started out as a very dense., very hot, Universe... The Big Bang. Where time and space and all that is in it were born... As much as we can speculate, not a single shreed of evedance has been prosented to support the idea of a multie univeress reality. It seem logical. but proof of fact is lacking... without the methode of confermation this idea has no backbone. We know of NO edge. We do see excelorating mass. Within a million years of birth the universe was rushing of to fill the void as it unfolded... at what you might percieve as the edge, you should expect to see just more of the same and some excelorating away at light speed...
I hope to have helped. mark.
Jeff Root
2010-Jan-18, 12:51 PM
I might be branded a Marksist for saying this... or marked a brand... anyway,
the idea of going with the most wildly excepted theory appeals to me.
-- Jeff, in Minneapolis
Andrew D
2010-Jan-19, 03:21 AM
Doesn't the evidence we see point to a universe that is not spatially bound, but density bound?
I should clarify; I meant energy density.
Isn't total energy density constant?
astromark
2010-Jan-19, 06:09 AM
I might be branded a Marksist for saying this... or marked a brand... anyway,
the idea of going with the most wildly excepted theory appeals to me.
-- Jeff, in Minneapolis
:) its not that I will not listen to new ideas. I will. It could be said that I am always looking for that better idea / solution. I am. BUT...I will show restraint when excepting such as string theory and multi universes... Its clutching at straws and is often an attempt to blind with science. I know something you do not... and I do not.
but sometimes..... ? The mainstream view has stood the tests and survives as the best bet yet.
forrest noble
2010-Jan-19, 06:49 AM
Roobydo,
Isn't total energy density constant?
The energy density of the ZPF, according to theory, remains constant in an expanding universe. But the average density of both mass and energy would seemingly decrease in an expanding universe. | 14,182 | 63,750 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2013-20 | latest | en | 0.95027 |
https://brainmass.com/business/accounting/portfolio-investment-yield-29961 | 1,722,846,954,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640436802.18/warc/CC-MAIN-20240805083255-20240805113255-00693.warc.gz | 116,250,176 | 7,359 | Purchase Solution
# Portfolio Investment Yield
Not what you're looking for?
a. Provide one set of weights for a portfolio of all three assets that will deliver a return of 18%.
b. Show graphically and explain briefly how you would find the minimum variance portfolio set that would have an 18% return.
c. Calculate the above set.
##### Solution Summary
The solution displays the full mathematical calculations necessary to demonstrate the calculation for the three assets.
##### Solution Preview
See attachment for the proper layout.
a. Provide one set of weights for a portfolio of all three assets that will deliver a return of 18%.
By definition, we know that W3 = 1 - W1 - W2
Then W1*R1 + W2*R2 + W1*R3 = 18%
20% W1 + 12%W2 + 16%(1 - W1 - W2) = 18%
4% W1 - 4% W2 = 2%
4% W1 = 2% + 4% W2
W1 = 0.5 + W2
So any combination of W1 = 0.5 + W2 will satisfy a return of 18%
We can pick up W2 = 0.1, then W1 = 0.5 +0.1 = 0.6, and W3 = 1 - 0.1 - 0.6 = 0.3
So the portfolio of (W1, W2, W3) = (0.6, 0.1, 0.3) will deliver a return of 18%.
b. Show graphically and ...
##### Motivation
This tests some key elements of major motivation theories.
##### Understanding the Accounting Equation
These 10 questions help a new student of accounting to understand the basic premise of accounting and how it is applied to the business world. | 396 | 1,335 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.890625 | 4 | CC-MAIN-2024-33 | latest | en | 0.870071 |
https://www.physicsforums.com/threads/what-is-the-proof-validity-of-born-rigidity-in-special-relativity.723683/ | 1,596,909,795,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738015.38/warc/CC-MAIN-20200808165417-20200808195417-00057.warc.gz | 793,767,805 | 25,508 | # What is the proof/validity of Born rigidity in Special relativity?
## Main Question or Discussion Point
Relativity theory always find some ridiculous explanations like "born rigidity or relativity of simultaneity" when in face paradoxes
What is the experimental validity of such predictions?
Related Special and General Relativity News on Phys.org
Dale
Mentor
So far SR has withstood every experimental test within its domain of validity.
Perhaps you should spend some time reading through the sticky on experimental evidence for relativity before using words like "ridiculous", it just makes you look like an uninformed crackpot.
Sorry I've already red most of the experimental evidences that support relativity, but that doesn't prove "born rigidity" happen in SR. What if "the experimental evidences that support relativity has some other kind of explanations? "
Nugatory
Mentor
What if "the experimental evidences that support relativity has some other kind of explanations? "
That would be a more interesting question if someone were to find a reasonable alternative explanation to consider, or a significant hole in the way that relativity explains the experimental evidence. So far, no one has found either... And it's not for want of looking.
Sorry I've already red most of the experimental evidences that support relativity, but that doesn't prove "born rigidity" happen in SR. What if "the experimental evidences that support relativity has some other kind of explanations? "
Born rigidity was introduced in SR, so that the objects can go under Length Contraction (due to inertial relative motion w.r.t an observer, i.e. Lorentz contraction) without breaking the objects in the process(i.e. no permanent damage done) and at the same time maintaining the rigidity(i.e. born rigidity).
The bitter part of this introduction is that we don't have any experimental proof of Length contraction(directly implied), nor of the increase in the density due to length contraction.
The above definition of born rigidity does not include accelerating objects, i.e. every non-point object undergoes permanent deformation along the line of motion when accelerated(i.e. according to theory, the born rigidity breaks every time any real object accelerates).
And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).
ZapperZ
Staff Emeritus
Born rigidity was introduced in SR, so that the objects can go under Length Contraction (due to inertial relative motion w.r.t an observer, i.e. Lorentz contraction) without breaking the objects in the process(i.e. no permanent damage done) and at the same time maintaining the rigidity(i.e. born rigidity).
The bitter part of this introduction is that we don't have any experimental proof of Length contraction(directly implied), nor of the increase in the density due to length contraction.
The above definition of born rigidity does not include accelerating objects, i.e. every non-point object undergoes permanent deformation along the line of motion when accelerated(i.e. according to theory, the born rigidity breaks every time any real object accelerates).
And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).
Try designing particle accelerator structures without incorporating such effects in the design! For example in FELs, from the electron bunch frame, the spacing of the undulator/wiggler is severely contracted. Without taking into such account, the description in that frame and lab frame will be completely off! It works when you use it, it doesn't work when you don't. To me, as an experimentalist, that is a darn strong evidence for its validity.
Furthermore, this appears to be a common misunderstanding of what this effect. It isn't the object that is contracting. It is the spatial dimension!
http://arxiv.org/abs/0906.1919
Zz.
stevendaryl
Staff Emeritus
Sorry I've already red most of the experimental evidences that support relativity, but that doesn't prove "born rigidity" happen in SR. What if "the experimental evidences that support relativity has some other kind of explanations? "
Born rigidity is not something that can be proved or disproved--it's a definition: An object is "Born rigid" if it always has the same length, as measured in its own instantaneous rest frame. Real objects are not perfectly Born rigid. If you push on one end of a long rod, it will compress a little. If you pull on the other end, it will stretch a little. Rigidity is an idealization.
Dale
Mentor
that doesn't prove "born rigidity" happen in SR
Born rigidity is a definition. I don't know what kind of experiment you are talking about.
Try designing particle accelerator structures without incorporating such effects in the design! For example in FELs, from the electron bunch frame, the spacing of the undulator/wiggler is severely contracted. Without taking into such account, the description in that frame and lab frame will be completely off! It works when you use it, it doesn't work when you don't. To me, as an experimentalist, that is a darn strong evidence for its validity.
Theoretical Explanation of FELs, comes under the category of 'suit yourself', the so called rigorous derivation of ${λ_w}/{γ^2}$ from Maxwell's Equations, is based on jumping frames(it is because of this theoretical inconsistency that most texts do not include the derivation) to get the square of the gamma. That is, the only reason the case is studied by jumping frames, so as to make theory(Length contraction) compatible with experimental results.
Furthermore, this appears to be a common misunderstanding of what this effect. It isn't the object that is contracting. It is the spatial dimension!
http://arxiv.org/abs/0906.1919
According to the linked paper, the inertial Length contraction is nothing but illusion, i.e. its an apparent measured effect which we should not worry much about. In other words the length has meaning only in the proper frames.
And, just as the ‘shortening’ of a stick that is rotated in three dimensions is an illusion, we now can see that the ‘shortening’ of a stick that is rotated in four dimensions by a Lorentz transformation is also illusory.
Now, intuitively/logically the definition of inertial length contraction(according to the paper) does not match very well with the explanation of FELs using the inertial Length contraction(frames jumping), because the former is a measured/apparent effect(illusion), whereas later is used to explain non illusory effects(radiation).
...
And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).
I think length contraction is implied by observations of the number of muons that make it from the top of the atmosphere to sea level. The average lifetime of a muon is very short and they would decay before they reached sea level, if the thickness of the atmosphere was not length contracted from their point of view.
Length contraction is also implied by the MMX experiment. If the arm parallel to the motion was not length contracted by the right amount, the famous "null result" would not have been obtained.
bcrowell
Staff Emeritus
Gold Member
Born rigidity was introduced in SR, so that the objects can go under Length Contraction (due to inertial relative motion w.r.t an observer, i.e. Lorentz contraction) without breaking the objects in the process(i.e. no permanent damage done) and at the same time maintaining the rigidity(i.e. born rigidity).
No, this is a complete misunderstanding of Born rigidity. Born rigidity is a definition, not a prediction of SR. Born rigidity does not exist in reality. It's of no interest for an object moving inertially and without rotation. It is not a property of an object (even a hypothetical, idealized object) but rather a theoretically possible motion of an object on which external forces are exerted according to a plan that has to have been constructed before the motion even began.
The bitter part of this introduction is that we don't have any experimental proof of Length contraction(directly implied), nor of the increase in the density due to length contraction.
This is total nonsense. Length contraction is part of the Lorentz transformation, and Lorentz invariance is one of the most accurately tested theories in the history of science. See, e.g., http://relativity.livingreviews.org/Articles/lrr-2005-5/ [Broken]
The above definition of born rigidity does not include accelerating objects, i.e. every non-point object undergoes permanent deformation along the line of motion when accelerated(i.e. according to theory, the born rigidity breaks every time any real object accelerates).
More nonsense.
And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).
More nonsense.
Furthermore, this appears to be a common misunderstanding of what this effect. It isn't the object that is contracting. It is the spatial dimension!
http://arxiv.org/abs/0906.1919
This is an interesting and subtle point that is not going to get the discussion it deserves in a thread as contaminated with nonsense as this one. Franklin's interpretation is fine, but it's not the only correct one. Bell's interpretation differs markedly from Franklin's, and Bell isn't betraying his "misunderstanding" of SR. Everybody agrees on the mathematics and the experimental validation of the mathematics, but the interpretation is a matter of philosophy, not science.
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stevendaryl
Staff Emeritus
According to the linked paper, the inertial Length contraction is nothing but illusion, i.e. its an apparent measured effect which we should not worry much about. In other words the length has meaning only in the proper frames.
I don't quite agree with the use of the word "illusion". Length has a very precise (if frame-dependent) definition: the length of an object at time t is the spatial distance between the locations of the two endpoints at time t. It's not an illusion that a moving object has a shorter length than the same object when at rest, it's true. (Assuming relativity is correct.)
I would reserve the word "illusion" to apply in a case where someone is given misleading information that leads him to make an incorrect conclusion. For example, someone holding his hand up in such a way that an elephant seems to be sitting in his hand--in actuality, the elephant is far away, and seems smaller by perspective. For a more physics-relevant illusion, moving objects appear rotated, because of the Terrell rotation.
PAllen
2019 Award
According to the linked paper, the inertial Length contraction is nothing but illusion, i.e. its an apparent measured effect which we should not worry much about. In other words the length has meaning only in the proper frames.
Now, intuitively/logically the definition of inertial length contraction(according to the paper) does not match very well with the explanation of FELs using the inertial Length contraction(frames jumping), because the former is a measured/apparent effect(illusion), whereas later is used to explain non illusory effects(radiation).
This is one of the few weak points of a pretty good paper. A simple counter argument is there is nothing illusory about rotating an object in 3-space. You can fit long, thin, objects through small openings because of the ability to rotate them. Similarly, the reality of spacetime rotation (=length contraction) produces phenomena that would not otherwise be possible. For example, the muon reaching the ground, in the muon's frame.
Meir Achuz
Homework Helper
Gold Member
Bell does 'misunderstand' SR, because he wants to use both Lorentz's (and Fitzgeralds0 notion that there is a real contraction of the object AND Einstein's contraction due the transformation between frames. You can argue for one or the other, but they can't be combined.
stevendaryl
Staff Emeritus
This is total nonsense. Length contraction is part of the Lorentz transformation, and Lorentz invariance is one of the most accurately tested theories in the history of science.
I think that it is correct to say that Lorentz contraction has not been directly observed in the way that time dilation has been. I mean, we don't have any objects of accurately known rest length that have been accelerated to high enough speed to measure their contraction. Not that there is very much doubt about the reality of Lorentz contraction (There is, as far as I know, no alternative to relativity that agrees with all known experiments but does not predict length contraction.)
I think length contraction is implied by observations of the number of muons that make it from the top of the atmosphere to sea level. The average lifetime of a muon is very short and they would decay before they reached sea level, if the thickness of the atmosphere was not length contracted from their point of view.
Length contraction is also implied by the MMX experiment. If the arm parallel to the motion was not length contracted by the right amount, the famous "null result" would not have been obtained.
I didn't say one cannot imply inertial length contraction, instead I said it cannot be directly implied. (For example, I can also think of different theories that implies something else or may be nothing). The quote that you used from my post is about the length contraction due to acceleration for non-point objects(i.e. real effects)
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Meir Achuz
Homework Helper
Gold Member
The Lorentz contraction of SR has not been tested experimentally, and probably can't be, but it is implied by all the other experimental successes of SR. SR would have to be radically changed (destroyed) if Lorentz contraction (in the SR sense) were dropped. Many things in physics have that kind of 'evidence'.
stevendaryl
Staff Emeritus
Bell does 'misunderstand' SR, because he wants to use both Lorentz's (and Fitzgeralds0 notion that there is a real contraction of the object AND Einstein's contraction due the transformation between frames. You can argue for one or the other, but they can't be combined.
I don't think that Bell misunderstands it. I'm not exactly sure what you mean by those two alternatives (1) contraction is real, and (2) contraction is due to transformation between frames, but they don't seem incompatible to me.
I think that it is correct to say that Lorentz contraction has not been directly observed in the way that time dilation has been. I mean, we don't have any objects of accurately known rest length that have been accelerated to high enough speed to measure their contraction. Not that there is very much doubt about the reality of Lorentz contraction (There is, as far as I know, no alternative to relativity that agrees with all known experiments but does not predict length contraction.)
I think it is correct to say that the "observed" time dilation is the reciprocal? of length contraction. (SR)Time dilation doesn't somehow exist on it's own.
I presume by time dilation has been "observed" you are referring to differential aging, which itself isn't time dilation. Has time dilation even been observed, or is it merely calculated...just like length contraction?
No, this is a complete misunderstanding of Born rigidity. Born rigidity is a definition, not a prediction of SR. Born rigidity does not exist in reality. It's of no interest for an object moving inertially and without rotation. It is not a property of an object (even a hypothetical, idealized object) but rather a theoretically possible motion of an object on which external forces are exerted according to a plan that has to have been constructed before the motion even began.
I didn't say born rigidity is a prediction of SR, ofcourse it is an idealized condition of an object so that the effects of acceleration on real objects can be ignored, and so only the geometrical effects are left to be analysed.
This is total nonsense. Length contraction is part of the Lorentz transformation, and Lorentz invariance is one of the most accurately tested theories in the history of science. See, e.g., http://relativity.livingreviews.org/Articles/lrr-2005-5/ [Broken]
More nonsense.
More nonsense.
Lorentz transformation is based on Lorentz in-variance of Electromagnetic phenomenon(Maxwell's equations) under relative motion. This implies being a transformation, LT is a set of transformation equations which give the same absolute result(For ex.- acceleration etc.) irrespective of the frame we choose to see the effects from. In other words, just as under the rotation of a stick in 3-D gives us different spatial co-ordinates (without changing the actual length), LT gives us different co-ordinates (spatial, temporal) for a same absolute property.
My point being co-ordinates does not mean anything, I can always choose a different co-ordinate system and get the same results. That is the length of the stick never changes.
This is an interesting and subtle point that is not going to get the discussion it deserves in a thread as contaminated with nonsense as this one. Franklin's interpretation is fine, but it's not the only correct one. Bell's interpretation differs markedly from Franklin's, and Bell isn't betraying his "misunderstanding" of SR. Everybody agrees on the mathematics and the experimental validation of the mathematics, but the interpretation is a matter of philosophy, not science.
Labeling is easy!, the more important point is not betraying the one's 'understanding'.
Last edited by a moderator:
I don't quite agree with the use of the word "illusion". Length has a very precise (if frame-dependent) definition: the length of an object at time t is the spatial distance between the locations of the two endpoints at time t. It's not an illusion that a moving object has a shorter length than the same object when at rest, it's true. (Assuming relativity is correct.)
I would reserve the word "illusion" to apply in a case where someone is given misleading information that leads him to make an incorrect conclusion. For example, someone holding his hand up in such a way that an elephant seems to be sitting in his hand--in actuality, the elephant is far away, and seems smaller by perspective. For a more physics-relevant illusion, moving objects appear rotated, because of the Terrell rotation.
You are in direct contradiction with the author if you suggest that Inertial Length Contraction is true. Since it is an (just like simultaneity)measured effect and it does not imply the length of an object actually contracted {i.e. it produced strain or stress).
stevendaryl
Staff Emeritus
I presume by time dilation has been "observed" you are referring to differential aging, which itself isn't time dilation.
I was using those two synonymously. What do you mean by "time dilation"?
stevendaryl
Staff Emeritus | 3,994 | 18,958 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2020-34 | latest | en | 0.945198 |
https://digitalcommons.library.umaine.edu/etd/3350/ | 1,660,736,007,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572898.29/warc/CC-MAIN-20220817092402-20220817122402-00779.warc.gz | 208,209,183 | 9,016 | ## Electronic Theses and Dissertations
Spring 5-8-2021
#### Level of Access Assigned by Author
Open-Access Thesis
#### Degree Name
Master's of Science in Teaching (MST)
#### Department
Science and Mathematics Education
Michael C. Wittmann
John R. Thompson
#### Third Committee Member
Franziska Peterson
#### Abstract
Student difficulties surrounding motion have been well documented for many years. This work was inspired by the work of former MST students into the instruction of Newton‟s Second Law of Motion at the middle school level. The purpose of this study was to further investigate how middle school students talk and reason about motion. Particular attention was paid to how students defined the term “motion,” how those definitions fit into a larger framework of what encompasses understanding motion at the middle school level, and how students justified negativity of a calculation of a negative velocity.
A tutorial lesson was developed to help students gain an understanding of what motion is when discussed in the science classroom and how the math they are learning about can play a role in understanding terms like “uniform motion.” Students were asked to define motion before and after the learning event, along with other questions including asking them to justify the negativity of a velocity they calculated.
Student definitions of motion ranged from undefined conceptualizations of motion to well-thought-out definitions of complex terms like changes in speed or velocity. Furthermore, the way in which students justified the negativity of the third trial velocity illuminated two distinct models for reasoning. The first, with the systemically locked model, was the reliance on the location to justify the negativity. The second, with the directionally locked model, showed a reliance on the direction of motion in order to justify the negativity.
This study begins the process of illuminating the complexity of the understanding of motion that is required of middle school students. We outline the ways in which students discuss different categories of motion and how their justifications of the negativity of a velocity can show us which model they are more likely to utilize to potentially help push their understanding further. | 415 | 2,272 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2022-33 | latest | en | 0.957457 |
https://math.stackexchange.com/questions/2383675/on-inequalities-for-norms-of-matrices | 1,571,338,332,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986675598.53/warc/CC-MAIN-20191017172920-20191017200420-00132.warc.gz | 592,353,320 | 32,179 | # On inequalities for norms of matrices
I have a matrix $A \in \mathbb{R}^{n \times n}$ and would like to know about the relationship between the $\| A \|_\infty$ (i.e., the maximum element of the matrix) and the operator-induced norm $\| A \|$.
I know that the following upper-bound holds (from Matrix Norm Inequality): $\| A \|_\infty \leq \sqrt{n} \| A \|$?
But, I am trying to find a lower-bound? (Would the lower-bound possibly be comprised of the minimum singular value times some factor of $n$?)
Also, I need this lower bound to have a norm that has the sub-multiplicative property: given square matrices $A,B \Rightarrow \| A B \|_{\infty} \geq \| A \|_p \| B \|_p$
But, is there an appropriate norm/$p$ that suits this?
• Your last inequality can't always hold. Just take $A,B\not= 0$ so that $AB=0$. – xavierm02 Aug 5 '17 at 22:16
• @xavierm02 thank you for your reply! are there any lower bounds for $\| AB \|_\infty$ that can be written explicitly in terms of some function of $A$ and the $\| B\|$? – user2457324 Aug 5 '17 at 22:19
• Let me rephrase your question: Is there some $f$ so that $\|AB\|_\infty \ge f(A,\|B\|)$? Suppose that there are some $A,B$ so that $f(A,\|B\|)\not=0$ and $A$ is not invertible. Then we can find some $B'$ so that $AB'=0$ and $\|B'\|=\|B\|$ so that $0=\|AB'\|_\infty\ge f(A,\|B'\|)=f(A,\|B\|)$. Absurd. So a such $f$ can only be non-zero when $A$ is invertible. I guess you could take $f(A,\|B\|)=\inf_{\|B'\|=\|B\|}\|AB'\|_\infty$, i.e., since you can't know which $B$ was used because you only have its norm, you consider the worst possible case. – xavierm02 Aug 5 '17 at 22:38
Let $A=(a_{ij})$ and $x=(x_i)^t\in\Bbb R^n$. Then
$$\|Ax\|=\sqrt{\sum_i \left(\sum_j a_{ij}x_j\right)^2}\le$$
$$\mbox{(by Cauchy-Schwarz inequality)}$$
$$\sqrt{\sum_i \left(\sum_j a_{ij}^2\right)\left(\sum_j x_{j}^2\right)}=$$
$$\sqrt{\sum_i \left(\sum_j a_{ij}^2\right)}\|x\|\le$$
$$\sqrt{\sum_i \left(\sum_j \|A\|_\infty^2\right)}\|x\|=$$
$$\sqrt{n^2\|A\|_\infty^2}\|x\|=$$
$$n\|A\|_\infty\|x\|.$$
So $$\| A \|/n \le \| A \|_\infty.$$
This bound is tight, for instance, for $A=J$, where $J$ is the $n\times n$ matrix of all ones. Indeed, in this case if $x=(x_i)^t$ then $$\|Ax\|=\sqrt{n}\left|\sum x_i\right|\le$$ $$\mbox{(by the inequality between arythetic and quadratic means)}$$ $$n\sqrt{\sum x_i^2}=n\|x\|.$$ On the other hand, this inequality is tight because $\|A\bar1\|=n\|\bar1\|$, where $\bar 1$ is the n-dimensional vector of all ones. | 902 | 2,489 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2019-43 | latest | en | 0.762893 |
https://www.mathhomeworkanswers.org/21383/what-is-pi-3-14-rounded-to-the-nearest-whole-number?start=10 | 1,660,962,690,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573876.92/warc/CC-MAIN-20220820012448-20220820042448-00118.warc.gz | 742,953,810 | 18,217 | pi-3.14 often rounded to which number
IF YOU ROUND OF 0.39 AND 0.68 WHAT IS THE NEAREST WHOLE NUMBER?
by
4499.677419
by
Pi is often rounded to 3, if you ask me.
by
3.14 rouned to the nearest whole numer is 3. 5 or more raise the score, 4 or less let it rest.
by
by | 94 | 267 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2022-33 | latest | en | 0.966957 |
https://www.geeksforgeeks.org/find-end-point-line-given-one-end-mid/ | 1,585,982,918,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370520039.50/warc/CC-MAIN-20200404042338-20200404072338-00065.warc.gz | 920,134,970 | 26,756 | # Find the other end point of a line with given one end and mid
Given a midpoint of line(m1, m2) and one coordinate of a line (x1, y1), find the other end point(x2, y2) of a line
Examples:
```Input : x1 = –1, y1 = 2, and
m1 = 3, m2 = –6
Output : x2 = 7, y2 = 10
Input : x1 = 6.4, y1 = 3 and
m1 = –10.7, m2 = 4
Output : x2 = 3, y2 = 4
```
## Recommended: Please try your approach on {IDE} first, before moving on to the solution.
The Midpoint Formula: The midpoint of two points, (x1, y2) and (x2, y2) is the point M found by using:
M=((x1+x2)/2, (y1+y2)/2),
We have need of a (x2, y2) so we modifies the formula
``` m1 = ((x1+x2)/2), m2 = ((y1+y2)/2)
2*m1 = (x1+x2), 2*m2 = (y1+y2)
x2 = (2*m1 - x1), y2 = (2*m2 - y1)
```
## C++
`// CPP program to find the end point of a line ` `#include ` `using` `namespace` `std; ` ` ` `// CPP function to find the end point of a line ` `void` `otherEndPoint(``int` `x1, ``int` `y1, ``int` `m1, ``int` `m2) ` `{ ` ` ``// find end point for x cordinates ` ` ``float` `x2 = (``float``)(2 * m1 - x1); ` ` ` ` ``// find end point for y cordinates ` ` ``float` `y2 = (``float``)(2 * m2 - y1); ` ` ` ` ``cout << ``"x2 = "` `<< x2 << ``", "` ` ``<< ``"y2 = "` `<< y2; ` `} ` ` ` `// Driven Program ` `int` `main() ` `{ ` ` ``int` `x1 = -4, y1 = -1, m1 = 3, m2 = 5; ` ` ``otherEndPoint(x1, y1, m1, m2); ` ` ``return` `0; ` `} `
## Java
`// Java program to find the end point of a line ` `class` `GFG { ` ` ` ` ``// CPP function to find the end point ` ` ``// of a line ` ` ``static` `void` `otherEndPoint(``int` `x1, ``int` `y1, ` ` ``int` `m1, ``int` `m2) ` ` ``{ ` ` ``// find end point for x cordinates ` ` ``float` `x2 = (``float``)(``2` `* m1 - x1); ` ` ` ` ``// find end point for y cordinates ` ` ``float` `y2 = (``float``)(``2` `* m2 - y1); ` ` ` ` ``System.out.println(``"x2 = "` `+ x2 + ``", "` ` ``+ ``"y2 = "` `+ y2); ` ` ``} ` ` ` ` ``// Driven Program ` ` ``public` `static` `void` `main(String args[]) ` ` ``{ ` ` ``int` `x1 = -``4``, y1 = -``1``, m1 = ``3``, m2 = ``5``; ` ` ``otherEndPoint(x1, y1, m1, m2); ` ` ``} ` `} ` ` ` `// This code is contributed by JaideepPyne. `
## Python3
`# Python3 program to find the end ` `# point of a line ` ` ` `# function to find the end point ` `# of a line ` `def` `otherEndPoint(x1, y1, m1, m2): ` ` ` ` ``# find end point for x cordinates ` ` ``x2 ``=` `(``2` `*` `m1 ``-` `x1) ` ` ` ` ``# find end point for y cordinates ` ` ``y2 ``=` `(``2` `*` `m2 ``-` `y1) ` ` ` ` ``print` `(``"x2 = {}, y2 = {}"` ` ``. ``format``(x2, y2)) ` ` ` `# Driven Program ` `x1 ``=` `-``4` `y1 ``=` `-``1` `m1 ``=` `3` `m2 ``=` `5` `otherEndPoint(x1, y1, m1, m2) ` ` ` `# This code is contributed by ` `# Manish Shaw (manishshaw1) `
## C#
`// C# program to find the ` `// end point of a line ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ``// function to find the ` ` ``// end pointof a line ` ` ``static` `void` `otherEndPoint(``int` `x1, ``int` `y1, ` ` ``int` `m1, ``int` `m2) ` ` ``{ ` ` ` ` ``// find end point for x cordinates ` ` ``float` `x2 = (``float``)(2 * m1 - x1); ` ` ` ` ``// find end point for y cordinates ` ` ``float` `y2 = (``float``)(2 * m2 - y1); ` ` ` ` ``Console.WriteLine(``"x2 = "` `+ x2 + ``", "` ` ``+ ``"y2 = "` `+ y2); ` ` ``} ` ` ` ` ``// Driver Program ` ` ``public` `static` `void` `Main(String []args) ` ` ``{ ` ` ``int` `x1 = -4, y1 = -1, m1 = 3, m2 = 5; ` ` ``otherEndPoint(x1, y1, m1, m2); ` ` ``} ` `} ` ` ` `// This code is contributed by nitin mittal. `
## PHP
` `
Output:
```x2 = 10, y2 = 11
```
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Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. | 1,763 | 4,538 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2020-16 | latest | en | 0.534669 |
https://wiki.ubc.ca/Science:Math_Exam_Resources/Courses/MATH221/December_2009/Question_12_(e) | 1,725,992,722,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651303.70/warc/CC-MAIN-20240910161250-20240910191250-00172.warc.gz | 589,992,579 | 10,519 | # Science:Math Exam Resources/Courses/MATH221/December 2009/Question 12 (e)
MATH221 December 2009
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
Other MATH221 Exams
### Question 12 (e)
Mark each statement either True or False. You do not have to justify your answer.
e. If ${\displaystyle T:\mathbb {R} ^{n}\rightarrow \mathbb {R} ^{n}}$ is the orthogonal projection onto a subspace W, then the standard matrix of T is diagonalizable.
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.
Math Learning Centre A space to study math together. Free math graduate and undergraduate TA support. Mon - Fri: 12 pm - 5 pm in LSK 301&302 and 5 pm - 7 pm online. Private tutor We can help to | 446 | 1,907 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 3, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2024-38 | latest | en | 0.946857 |
https://www.daniweb.com/programming/software-development/threads/356155/galerkin-finite-element | 1,540,165,288,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583514437.69/warc/CC-MAIN-20181021224001-20181022005501-00523.warc.gz | 901,215,630 | 12,772 | ## negneg
Hi
I wrote a code for Galerkin Finite Element .The program runs with no error but have some problem breaking the loop also the results are all wrong .Can anyone please help me? This is my first time writting aprogram and I am so confused.
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#define Limit 20
int main()
{
double eps = 10E-6; /* Tolerance */
double Sep = 1.0; /* */
int K ; /* Counter for iterations */
int Max = 20; /* Maximum number of iterat. */
int Cond = 1; /* */
int j, L, i,T,r,P; /* Loop counters */
double X[Limit];
double CON,CONX; /* B in AX = B , INPUT */
double DX;
int N; /* No.of Nodes */
int NE;
double A[Limit][Limit];
/* No. Of elements */
double SUM, M;
int Pivot;
int L1;
double satisfied = 0.0;
int Row[Limit]; /* Variable in dominance check */
double C[Limit];
double DCNEW[Limit];
double Cnew[Limit];
double Error;
double SumF[Limit],SumJ[Limit][Limit];
double PHI[2];
double PHIX[2];
double GP[3]={0.1127,0.5,0.8877};
double w[3]={0.2778,0.4444,0.2778};
#define Gamma 0.1
{
printf("Please enter number of elements [Not more than %d]\n",Limit);
scanf_s("%d", &NE);
N = NE+1;
/* Define mesh size*/
for (i = 1; i<= N; i++)
X[i] = (i-1)/NE;
/* Initial guess for N.R */
for(i=1;i<N;i++) C[i]=.5;//inital guess vector
C[N] = 1.0;
while (satisfied == 0)
{
for(i=1;i<N;i++)
{
SumF[i] = 0.0;
for(j=1;j<N;j++)
SumJ[i][j] = 0.0;
}
DX = X[N] - X[1]/ NE;
CON = 0.0;
CONX = 0.0;
for(j=1;j<=3;j++)
{
PHI[1] = 1-GP[j];
PHI[2] = GP[j];
PHIX[1] = -1/DX;
PHIX[2] = 1/DX;
for(L=1;L<=2;L++)
{
L1 = j+L-1;
CON = CON + PHI[L]*C[L1];
CONX = CONX + PHIX[L]*C[L1];
SumF[L1] = SumF[L1] - DX* w[j]*(-CONX*PHIX[L] - Gamma* pow(CON,3)*PHI[L]);
SumJ [L1][L] = SumJ[L1][L1] + DX*w[j] *(-PHIX[L]*PHIX[L1] - 3.0*Gamma*pow(CON,2)*PHI[L]*PHI[L1]);
}
}
/* Apply Boundry Condition */
for(i=1;i<N;i++) SumJ[N][i]=0.0;//inital guess vector
SumJ[N][N] = 1.0;
SumF[N] = 0.0;
for (i = 1; i<=N; i++)
{
for (j = 1; j<=N; j++)
A[i][j] = SumJ[i][j];
A[i][N+1] = SumF[j];
}
//Gaussian Elimination Method
for (r = 1; r<= N; r++) Row[r-1] = r - 1;
/* Start upper-triangularization */
for (P = 1; P <= N - 1; P++)
{
/* Pivoting */
for (K = P + 1; K <= N; K++)
{
if ( fabs(A[Row[K-1]][P-1]) > fabs(A[Row[P-1]][P-1]) )
{
Pivot = Row[P-1];
Row[P-1] = Row[K-1];
Row[K-1] = Pivot;
}
}
/* Process: a21/a11, a'32/a'22, ... */
for (K = P + 1; K <= N; K++)
{
M = A[Row[K-1]][P-1] / A[Row[P-1]][P-1];
for (T = P + 1; T <= N + 1; T++)
{
A[Row[K-1]][T-1] -= M * A[Row[P-1]][T-1];
}
}
}
if( A[Row[N-1]][N-1] == 0)
{
printf("The matrix is SINGULAR as the determinant is zero !\n");
printf(" Gaussian Elimination Algorithm failed --> exit\n");
exit(1);
}
/* Back substitution */
DCNEW[N-1] = A[Row[N-1]][N] / A[Row[N-1]][N-1];
for (K = N - 1; K >= 1; K--)
{
SUM = 0;
for (T = K + 1; T <= N; T++)
{
SUM += A[Row[K-1]][T-1] * DCNEW[T-1];
}
DCNEW[K-1] = ( A[Row[K-1]][N] - SUM) / A[Row[K-1]][K-1];
} /* End of back substitution */
for (i = 1; i <= N; i++)
{
Cnew[i] = C[i] + DCNEW[i];
/* Calculating Error */
Error = abs ((Cnew[i]-C[i]/Cnew[i])*100);
if (Error < eps)
{
satisfied=1;
break;
}//if end
for (i = 1; i <= N; i++)
printf("C[%d] = %1f\n",i,Cnew[i]);
} //while end
}
}
}
## frogboy77 73
1. use code tags
2.
This is my first time writting aprogram
what happened to the hello world one?
Either this is your first program(doubtful) or it's not your's. If it's the latter then i doubt you'll get much help here.
Tip: try being honest and specific (works a treat). | 1,416 | 3,762 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2018-43 | latest | en | 0.542968 |
https://vcderbydarlins.com/qa/is-there-a-roman-numeral-higher-than-m.html | 1,628,023,966,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154471.78/warc/CC-MAIN-20210803191307-20210803221307-00210.warc.gz | 584,275,254 | 7,609 | Is There A Roman Numeral Higher Than M?
Is there a Roman numeral for 1 million?
If we wanted to denote millions, we would show that as MM.
For this, we should credit the Romans.
M is the Roman numeral for thousand and MM is meant to convey one thousand thousand – or Million..
How do you write 4999 in Roman numerals?
4999 in Roman numerals: 4999=I̅V̅CMXCIX – Roman Numerals Generator – Capitalize My Title.
What is the smallest Roman numeral?
Hence the numeral for the smallest four-digit number in the Roman system is M.
How do you write 3999 in Roman numerals?
The largest number you can write in Roman numerals is 3,999 which is MMMCMXCIX.
What is the number 1000000000000000000000000?
Some Very Big, and Very Small NumbersNameThe NumberSymbolseptillion1,000,000,000,000,000,000,000,000Ysextillion1,000,000,000,000,000,000,000Zquintillion1,000,000,000,000,000,000Equadrillion1,000,000,000,000,000P6 more rows
How do you write 1 lakh in Roman numerals?
Answer. There is actually no romantic numeral for one lakh. However, a horizontal line above a numeral indicates that it should be multiplied by thousand. 100 × 1000 = 100000.
How do you represent 0 in Roman numerals?
So the roman system did not need any value to represent zero. But instead of zero, the word nulla was used by the Romans to specify zero. I Latin language the word nulla means none. Hence nulla is used t represent zero but there is no specific symbol for zero to represent in roman number system.
What does M represent in Roman numerals?
Clock with Roman numerals….Roman numeral.ArabicRoman800DCCC900CM1,000M1,001MI50 more rows
What is the Roman numeral for 9999?
9999 (number)← 9998 9999 10000 →Ordinal9999th (nine thousand nine hundred ninety-ninth)Factorization32 × 11 × 101Greek numeral,ΘϠϞΘ´Roman numeralMXCMXCIX, or IXCMXCIX7 more rows
How many basic Roman numerals are there?
seven basicRoman numerals originated, as the name might suggest, in ancient Rome. There are seven basic symbols: I, V, X, L, C, D and M. The first usage of the symbols began showing up between 900 and 800 B.C.
How many letters are in Roman numerals?
seven lettersRoman numerals use seven letters: I, V, X, L, C, D and M to represent the numbers 1, 5, 10, 50, 100, 500 and 1000.
Is m the highest Roman numeral?
Roman Numerals Converter ChartsRoman NumeralMeaningL50,000C100,000D500,000M1,000,0006 more rows•Aug 15, 2019
Which is the smallest numeral?
0The whole number series is 0,1,2,3,4,5……. 0 is the smallest whole number. 1 is the smallest natural number.
Why is there no zero in Roman numerals?
Why is there no “0” Zero in roman numerals? Roman numerals start to count from one and had no symbol to represent “0“. This happens because the Romans did not need to have a zero in their additive system. … That is why there is no zero in roman numerals.
How do we write 5000 in Roman numerals?
5000 in Roman numerals: 5000=V̅ – Roman Numerals Generator – Capitalize My Title.
What is the Roman numeral for 1 billion?
1000000000OrdinalOne billionth (short scale)Factorization29 · 59Greek numeralRoman numeralM7 more rows
What would happen if zero didn’t exist?
If we didn’t have zero, then the numbers in the number system wouldn’t go higher than nine. We couldn’t go through life without a zero. If zero wasn’t existent, life would be much different. For example, you couldn’t turn anything higher than 9 for the rest of your life.
What if zero was not invented?
Without zero, modern electronics wouldn’t exist. Without zero, there’s no calculus, which means no modern engineering or automation. Without zero, much of our modern world literally falls apart. | 973 | 3,652 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2021-31 | longest | en | 0.818168 |
http://www.fixya.com/support/t538926-negative_exponents | 1,490,914,491,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218203536.73/warc/CC-MAIN-20170322213003-00420-ip-10-233-31-227.ec2.internal.warc.gz | 511,187,659 | 35,264 | # Negative exponents How do I calculate -log(4.27X10 to the power -90)?
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Press the following keys in this order :
4.27 ENG 90 - "+/-"
Posted on May 02, 2008
SOURCE: How do i type a
4 ^ (-) 2
The ^ key is just above the divide key, the (-) key is just to the right of the decimal point key.
Posted on Aug 21, 2011
Hi,
a 6ya expert can help you resolve that issue over the phone in a minute or two.
best thing about this new service is that you are never placed on hold and get to talk to real repairmen in the US.
the service is completely free and covers almost anything you can think of (from cars to computers, handyman, and even drones).
goodluck!
Posted on Jan 02, 2017
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## Related Questions:
### What is most common power problem?
If by power, you mean exponents, there are several rules.
Multiplication with the same base - add the exponents
Division with the same base - subtract the exponents
Exponent to an exponent - multiply the exponents
Negative exponent - 1 over the same number to the positive exponent
Zero exponent - anything to the exponent 0 is 1
Good luck,
Paul
Jan 26, 2016 | Casio ClassPad 300 Calculator
### How do i get a negative exponent?
I don't have this calculator, but let's give this a shot and see if it gives us the correct answer.
Let's try 10 to the exponent -2. The rule for negative exponents is to put 1 on the top and the term with a positive exponent on the bottom. In this case, it would be 1 on the top and 10 to the exponent 2 on the bottom, or 1 / 100 or 0.01.
In the calculator, enter 10, hit the x to the power of y key, left bracket (, the negative key (-), 2, the right bracket ), and finally the = key. You might not have to enter the left and right brackets, but I like to enter them to understand what I enter in brackets is the exponent.
Let me know if it works and if you have any other questions.
Good luck.
Paul
Sep 13, 2015 | Canon F-502 Calculator
### I am trying to divide a power of 10 by and another number to a neg power of 10
For integer powers of 10 you can use the EE shortcut. [2nd][,] displays E.
For non-integer values of the exponent (such as -5.34) you must use the key sequence [2nd][LOG] (10^x) then enter your negative non-integer exponent.
Jan 16, 2012 | Texas Instruments TI-84 Plus Silver...
### TI-84 Plus Silver Edition. When dividing negative powers of ten by other negative powers of 10 the calculator it just adds the the negative powers together. How do i fix this? An example: 5*10^-10 /...
To enter an exponent, positive or negative, use the EE (Enter Exponent) key (the shifted function of the , key just above the 7 key). Do 5 2ND [EE] (-) 1 0 / 5 2ND [EE] (-) 1 0 ENTER and you'll see 1.
What I think you're doing (I can't be sure without seeing your keystrokes) is calculating
5*10^-10/5*10^-10 which is interpreted as (5*10^-10/5)*10^-10, which indeed is 10^-20.
Oct 16, 2010 | Texas Instruments TI-84 Plus Silver...
### Whenever I type in a negative number raised to an exponent, the calculator outputs a negative number! even for a question like -2^2. How do I fix this?
You're not raising a negative number to an exponent, you're negating a number raised to an exponent.
If you want to raise -2 to the second power, you need to enter it as
( (-) 2 ) ^ 2
Without the parens, what you're getting is the equivalent of -(2^x)
Sep 19, 2010 | Texas Instruments TI-84 Plus Calculator
### Negative log
Use the log function (common logarithm). See screen capture for markings on key.
To evaluate the negative of a logarithm
Enter the number (argument) of the logarithm
Press the = key to have it calculated.
While result is still displayed, press the sign change key or (+/-).
Beware that -log(number) is not necessarily a negative value.
Another way to calculate -log is to use the relation
log(1/a)=-log(a) .
3 [EXP] [(] [+/-] 2 [) ] [LOG][=] [+/-]
[EXP] is the key to enter exponent of a power of 10 :It is a shortcut, so no 10 is entered. Respect the key sequence above.
[ (] left parenthesis to prevent ambiguity due to the negaticve exponent. Just a security.
[)] is the enclosing right parenthesis
[+/-] is the Sign Change key
May 06, 2010 | Casio FX-260 Calculator
### Please explain which buttons to push on TI-36x solar calculator to find the pKa of benzoic acid. the Ka for benzoic acid is 6.5 X 10 to the -5th ? (Sorry I don't know how to type the exponents for you)
You need the [EE] key to enter powers of 10 exponents.
You need the change sign key [+/-] key.
You need the [LOG] key.
pKa: 6.5 [EE] [+/-] 5 [LOG] [+/-]
There are two change sign: The first (either before or after the exponent 5), the last is entered after you press the log key , so as to negate (make negative if result is positive, and make positive is result is negative) the value.
The result should be 4.1870866 or 4.19
Mar 08, 2010 | Texas Instruments TI-36 X Solar Calculator
### What button do I use to find negative log on my TI-83 calculator...also how do I put in a negative exponent?? i.e 1*10 to the negative 6th .....
You compute the negative of a logarithm the same way you compute the negative of anything else. However, do you really mean the antilog (inverse logarithm)? Use 2ND [e^x] for the natural antilog, 2ND [10^x] for the common antilog.
For negative exponents, as well as negative anything, use the (-) key next to the decimal point. For your example, 1 EE (-) 6
Feb 25, 2010 | Texas Instruments TI-30XA Calculator
### How to use negative exponents on a calculator?
Uh yes it will allow you to enter a negative exponent.... press the numbers you want then hit EXP button, then hit the +/- button and then the exponent. 60 % of the time, it works...... everytime.
Sep 20, 2009 | Texas Instruments TI-83 Plus Calculator
### To the power of a negative
Hello,
Use the small (-) sign sometimes labelled [(-)] or [+/-] and put the whole exponent netween parentheses 18 [y to the x] [(] [(-)] 3 [)] . On some calculators you enter the small - signe after the value of exponent,
18 [y t x] 3 (-) [Enter] should give you 1.7146E-4
In summary the small minus sign; the whole negative exponent between parentheses.
Hope it helps.
Sep 18, 2009 | Sharp EL-531VB Calculator
## Open Questions:
#### Related Topics:
206 people viewed this question
Level 3 Expert
Level 3 Expert | 1,752 | 6,475 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2017-13 | longest | en | 0.90736 |
http://stackoverflow.com/questions/56895/proving-sql-query-equivalency/98609 | 1,438,273,146,000,000,000 | text/html | crawl-data/CC-MAIN-2015-32/segments/1438042987402.78/warc/CC-MAIN-20150728002307-00274-ip-10-236-191-2.ec2.internal.warc.gz | 231,295,768 | 21,134 | # Proving SQL query equivalency
How would you go about proving that two queries are functionally equivalent, eg they will always both return the same result set.
As I had a specific query in mind when I was doing this, I ended up doing as @dougman suggested, over about 10% of rows the tables concerned and comparing the results, ensuring there was no out of place results.
-
I assume you mean the exact same result set. That means the same columns (and same data types) with the same row data. Correct? – Craig Sep 11 '08 at 15:37
Yep, thats right Craig – Matthew Watson Sep 17 '08 at 6:57
The best you can do is compare the 2 query outputs based on a given set of inputs looking for any differences. To say that they will always return the same results for all inputs really depends on the data.
For Oracle one of the better if not best approaches (very efficient) is here (Ctrl+F Comparing the Contents of Two Tables):
Which boils down to:
select c1,c2,c3,
count(src1) CNT1,
count(src2) CNT2
from (select a.*,
1 src1,
to_number(null) src2
from a
union all
select b.*,
to_number(null) src1,
2 src2
from b
)
group by c1,c2,c3
having count(src1) <> count(src2);
-
updated link: oracle.com/technetwork/issue-archive/2005/05-jan/… – MyDogTom Oct 22 '14 at 7:00
This sounds to me like a an NP complete problem. I'm not sure there is a sure fire way to prove this kind of thing
-
This is pretty easy to do.
Lets assume your queries are named a and b
a minus b
should give you an empty set. If it does not. then the queries return different sets, and the result set shows you the rows that are different.
then do
b minus a
that should give you an empty set. If it does, then the queries do return the same sets. if it is not empty, then the queries are different in some respect, and the result set shows you the rows that are different.
-
In SQL Server, You can use EXCEPT to for this approach- msdn.microsoft.com/en-us/library/ms188055%28SQL.90%29.aspx – Russ Cam Oct 20 '09 at 16:39
This only proves equivalency for that particular set, not for the query in general. – Rik Oct 20 '09 at 18:25
@rik yep... that is the intent. i doubt anyone can do proofs with the relational calculus – EvilTeach Oct 21 '09 at 3:23
The DBMS vendors have been working on this for a very, very long time. As Rik said, it's probably an intractable problem, but I don't think any formal analysis on the NP-completeness of the problem space has been done.
However, your best bet is to leverage your DBMS as much as possible. All DBMS systems translate SQL into some sort of query plan. You can use this query plan, which is an abstracted version of the query, as a good starting point (the DBMS will do LOTS of optimization, flattening queries into more workable models).
NOTE: modern DBMS use a "cost-based" analyzer which is non-deterministic across statistics updates, so the query planner, over time, may change the query plan for identical queries.
In Oracle (depending on your version), you can tell the optimizer to switch from the cost based analyzer to the deterministic rule based analyzer (this will simplify plan analysis) with a SQL hint, e.g.
SELECT /*+RULE*/ FROM yourtable
The rule-based optimizer has been deprecated since 8i but it still hangs around even thru 10g (I don't know 'bout 11). However, the rule-based analyzer is much less sophisticated: the error rate potentially is much higher.
For further reading of a more generic nature, IBM has been fairly prolific with their query-optimization patents. This one here on a method for converting SQL to an "abstract plan" is a good starting point: http://www.patentstorm.us/patents/7333981.html
-
This will do the trick. If this query returns zero rows the two queries are returning the same results. As a bonus, it runs as a single query, so you don't have to worry about setting the isolation level so that the data doesn't change between two queries.
select * from ((<query 1> MINUS <query 2>) UNION ALL (<query 2> MINUS <query 1>))
Here's a handy shell script to do this:
#!/bin/sh
CONNSTR=\$1
echo query 1, no semicolon, eof to end:; Q1=`cat`
echo query 2, no semicolon, eof to end:; Q2=`cat`
T="((\$Q1 MINUS \$Q2) UNION ALL (\$Q2 MINUS \$Q1));"
echo select 'count(*)' from \$T | sqlplus -S -L \$CONNSTR
-
You don't.
If you need a high level of confidence that a performance change, for example, hasn't changed the output of a query then test the hell out it.
If you need a really high level of confidence .. then errrm, test it even more.
Massive level's of testing aren't that hard to cobble together for a SQL query. Write a proc which will iterate around a large/complete set of possible paramenters, and call each query with each set of params, and write the outputs to respective tables. Compare the two tables and there you have it.
It's not exactly scientific, which I guess was the OP's question, but I'm not aware of a formal method to prove equivalency.
-
Perhaps you could draw (by hand) out your query and the results using Venn Diagrams, and see if they produce the same diagram. Venn diagrams are good for representing sets of data, and SQL queries work on sets of data. Drawing out a Venn Diagram might help you to visualize if 2 queries are functionally equivalent.
-
CAREFUL! Functional "equivalence" is often based on the data, and you may "prove" equivalence of 2 queries by comparing results for many cases and still be wrong once the data changes in a certain way.
For example:
SQL> create table test_tabA
(
col1 number
)
Table created.
SQL> create table test_tabB
(
col1 number
)
Table created.
SQL> -- insert 1 row
SQL> insert into test_tabA values (1)
1 row created.
SQL> commit
Commit complete.
SQL> -- Not exists query:
SQL> select * from test_tabA a
where not exists
(select 'x' from test_tabB b
where b.col1 = a.col1)
COL1
----------
1
1 row selected.
SQL> -- Not IN query:
SQL> select * from test_tabA a
where col1 not in
(select col1
from test_tabB b)
COL1
----------
1
1 row selected.
-- THEY MUST BE THE SAME!!! (or maybe not...)
SQL> -- insert a NULL to test_tabB
SQL> insert into test_tabB values (null)
1 row created.
SQL> commit
Commit complete.
SQL> -- Not exists query:
SQL> select * from test_tabA a
where not exists
(select 'x' from test_tabB b
where b.col1 = a.col1)
COL1
----------
1
1 row selected.
SQL> -- Not IN query:
SQL> select * from test_tabA a
where col1 not in
(select col1
from test_tabB b)
**no rows selected.**
- | 1,669 | 6,503 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2015-32 | latest | en | 0.887268 |
https://isabelle.in.tum.de/repos/isabelle/diff/44c9198f210c/src/HOL/Data_Structures/Tree23.thy | 1,638,877,187,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363376.49/warc/CC-MAIN-20211207105847-20211207135847-00588.warc.gz | 388,312,479 | 2,960 | src/HOL/Data_Structures/Tree23.thy
changeset 61640 44c9198f210c parent 61469 cd82b1023932 child 61679 1335462046e8
```--- a/src/HOL/Data_Structures/Tree23.thy Wed Nov 11 16:42:30 2015 +0100
+++ b/src/HOL/Data_Structures/Tree23.thy Wed Nov 11 18:32:26 2015 +0100
@@ -1,43 +1,43 @@
-(* Author: Tobias Nipkow *)
-
-section \<open>2-3 Trees\<close>
-
-theory Tree23
-imports Main
-begin
-
-class height =
-fixes height :: "'a \<Rightarrow> nat"
-
-datatype 'a tree23 =
- Leaf |
- Node2 "'a tree23" 'a "'a tree23" |
- Node3 "'a tree23" 'a "'a tree23" 'a "'a tree23"
-
-fun inorder :: "'a tree23 \<Rightarrow> 'a list" where
-"inorder Leaf = []" |
-"inorder(Node2 l a r) = inorder l @ a # inorder r" |
-"inorder(Node3 l a m b r) = inorder l @ a # inorder m @ b # inorder r"
-
-
-instantiation tree23 :: (type)height
-begin
-
-fun height_tree23 :: "'a tree23 \<Rightarrow> nat" where
-"height Leaf = 0" |
-"height (Node2 l _ r) = Suc(max (height l) (height r))" |
-"height (Node3 l _ m _ r) = Suc(max (height l) (max (height m) (height r)))"
-
-instance ..
-
-end
-
-text \<open>Balanced:\<close>
-
-fun bal :: "'a tree23 \<Rightarrow> bool" where
-"bal Leaf = True" |
-"bal (Node2 l _ r) = (bal l & bal r & height l = height r)" |
-"bal (Node3 l _ m _ r) =
- (bal l & bal m & bal r & height l = height m & height m = height r)"
-
-end
+(* Author: Tobias Nipkow *)
+
+section \<open>2-3 Trees\<close>
+
+theory Tree23
+imports Main
+begin
+
+class height =
+fixes height :: "'a \<Rightarrow> nat"
+
+datatype 'a tree23 =
+ Leaf |
+ Node2 "'a tree23" 'a "'a tree23" |
+ Node3 "'a tree23" 'a "'a tree23" 'a "'a tree23"
+
+fun inorder :: "'a tree23 \<Rightarrow> 'a list" where
+"inorder Leaf = []" |
+"inorder(Node2 l a r) = inorder l @ a # inorder r" |
+"inorder(Node3 l a m b r) = inorder l @ a # inorder m @ b # inorder r"
+
+
+instantiation tree23 :: (type)height
+begin
+
+fun height_tree23 :: "'a tree23 \<Rightarrow> nat" where
+"height Leaf = 0" |
+"height (Node2 l _ r) = Suc(max (height l) (height r))" |
+"height (Node3 l _ m _ r) = Suc(max (height l) (max (height m) (height r)))"
+
+instance ..
+
+end
+
+text \<open>Balanced:\<close>
+
+fun bal :: "'a tree23 \<Rightarrow> bool" where
+"bal Leaf = True" |
+"bal (Node2 l _ r) = (bal l & bal r & height l = height r)" |
+"bal (Node3 l _ m _ r) =
+ (bal l & bal m & bal r & height l = height m & height m = height r)"
+
+end``` | 862 | 2,389 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2021-49 | latest | en | 0.381414 |
https://csbnews.org/access-by-tim-bourke/ | 1,632,422,901,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057427.71/warc/CC-MAIN-20210923165408-20210923195408-00501.warc.gz | 233,508,694 | 17,945 | # Access by Tim Bourke
Ene 15, 2014
#### Source: 2014 Canberra the Summer Festival, [button link=»http://www.abfevents.com.au/events/not/2014/bulletins/02Thu16.pdf» size=»small» window=»yes»]Bulletin 2[/button]
While the bidding was a little forward, there is nothing wrong with the final contract. How do you plan to make twelve tricks after West leads the jack of diamonds?
#### Solution:
Suppose the full deal is something like this:
If you win the first trick with the king of diamonds in hand then it will no longer be possible to make the contract! After cashing the queen and jack of spades in dummy and ruffing a heart ruff you won’t have an entry back to hand to draw the remaining trumps.
If you try to cash the ace and queen of diamonds then, after East ruffs in on the third round of the suit, you will be left with two club losers.
The proper course is to win the diamond lead in dummy with the ace (say), cash the queen and jack of trumps and then organise a heart ruff. After returning to your hand with the king of diamonds, you will draw East’s two remaining trumps with the ace and king. All that left to do then is to cross to dummy with the ace of clubs and discard one of your losing clubs on queen of diamonds. You will make five trumps, two hearts, a heart ruff, three diamonds and a club for a total of twelve tricks. | 328 | 1,349 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2021-39 | latest | en | 0.917408 |
https://it.mathworks.com/matlabcentral/profile/authors/21069421 | 1,643,171,368,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304915.53/warc/CC-MAIN-20220126041016-20220126071016-00216.warc.gz | 375,636,735 | 21,244 | Community Profile
# Duc Pham
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6 mesi ago | 1,605 | 5,669 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2022-05 | latest | en | 0.743469 |
http://rovirayjuncosa.com/fugzq/inverse-of-a-function-is-unique-1dacfb | 1,618,825,322,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038879305.68/warc/CC-MAIN-20210419080654-20210419110654-00162.warc.gz | 83,611,568 | 12,225 | Let ℝn×m be the set of all n × m real matrices, m, n∈ℕ, and let ⊕E := ⊕′ be the Einstein addition of signature (m, n) in ℝcn×m, given by (5.309), p. 241 and by Theorem 5.65, p. 247. Indeed, the existence of a unique identity and a, at constant Ξ (and constant values of the suppressed parameters as well), it has a, Bi-gyrogroups and Bi-gyrovector Spaces – P, Bi-gyrogroups and Bi-gyrovector Spaces – V, Elementary Differential Geometry (Second Edition), Analytic Bi-hyperbolic Geometry: The Geometry of Bi-gyrovector Spaces, The Nuts and Bolts of Proofs (Third Edition), Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions, Christoph Werner, ... Oswaldo Morales-Nápoles, in, , that is, the inverse problem has no unique solution (or even worse, it has no solution). Example $$\PageIndex{3}\label{eg:invfcn-03}$$. Thus ‖ C(p) ‖ = ‖ p ‖ for all points p. Since C is linear, it follows easily that C is an isometry: Our goal now is Theorem 1.7, which asserts that every isometry can be expressed as an orthogonal transformation followed by a translation. Given $$f :{A}\to{B}$$ and $$g :{B}\to{C}$$, if both $$f$$ and $$g$$ are one-to-one, then $$g\circ f$$ is also one-to-one. Thus, we can write: where the pj are prime numbers, and p1 ≤ p2 ≤ … ≤ pk. These objects form a natural generalization of the concepts of the gyrogroups and the gyrovector spaces studied in Chaps. Exercise $$\PageIndex{9}\label{ex:invfcn-09}$$. Naturally, if a function is a bijection, we say that it is bijective. The inverse function of f exists. By definition, ‖p‖2 = p • p; hence. Given $$B' \subseteq B$$, the composition of two functions $$f :{A}\to{B'}$$ and $$g :{B}\to{C}$$ is the function $$g\circ f :{A}\to{C}$$ defined by $$(g\circ f)(x)=g(f(x))$$. Exercise $$\PageIndex{1}\label{ex:invfcn-01}$$. Show that it is a bijection, and find its inverse function, hands-on Exercise $$\PageIndex{2}\label{he:invfcn-02}$$. Second procedure. A left and a right gyration, in turn, determine a gyration, gyr[V1, V2] : ℝcn×m→ℝcn×m, according to (4.304), p. 166 and (5.340), p. 250. Part 1. The full statement of the theorem is below. $$f(a) \in B$$ and $$g(f(a))=c$$; let $$b=f(a)$$ and now there is a $$b \in B$$ such that $$g(b)=c.$$ Or the inverse function is mapping us from 4 to 0. Abraham A. Ungar, in Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces, 2018. The resulting expression is $$f^{-1}(y)$$. \cr}\], hands-on Exercise $$\PageIndex{5}\label{he:invfcn-05}$$. 1. (3) Given any two points p and q of R3, there exists a unique translation T such that T(p) = q. Since F is an isometry, The norm terms here cancel, since F preserves norms, and we find, It remains to prove that F is linear. To deny that something is unique means to assume that there is at least one more object with the same properties. Recall that we are choosing to extend the model which relates to the earlier discussion on the model boundary. Let us assume that there exists another function, h, that is the inverse of f. Then, by definition of inverse. For every x input, there is a unique f (x) output, or in other words, f (x) does not equal f (y) when x does not equal y. One-to-one functions are important because they are the exact type of function that can have an inverse (as we saw in the definition of an inverse function). The function $$f :{\mathbb{Z}}\to{\mathbb{N}}$$ is defined as $f(n) = \cases{ -2n & if n < 0, \cr 2n+1 & if n\geq0. \cr}$ Be sure you describe $$g^{-1}$$ properly. Let us refine this idea into a more concrete definition. By Theorem 4.59, p. 169, Einstein bi-gyrogroups are gyrocommutative gyrogroups. Writing $$n=f(m)$$, we find $n = \cases{ 2m & if m\geq0, \cr -2m-1 & if m < 0. For details, see [84, Sect. 1 with the following simplified project risk management example which shows how choices can be made in the various modelling contexts. Determine $$f\circ g$$ and $$g\circ f$$. Scalar multiplication respects orthogonal transformations, (5.501), p. 283. for all V∈ℝcn×m, Om ∈ SO(m), On ∈ SO(n), and r∈ℝ. In the following two subsections we summarize properties of the bi-gyrogroup and the bi-gyrovector space that underlie the c-ball ℝcn×m of the ambient space ℝn×m of all n × m real matrices, m, n∈ℕ. Part (4): We must show that A−1T (right side) is the inverse of AT (in parentheses on the left side). Also, the points u1, u2, u3 are orthonormal; that is, ui • uj = δij. for any X∈ℝcn×m, and (ii) is covariant under bi-rotations, that is. Form the two composite functions $$f\circ g$$ and $$g\circ f$$, and check whether they both equal to the identity function: \[\displaylines{ \textstyle (f\circ g)(x) = f(g(x)) = 2 g(x)+1 = 2\left[\frac{1}{2}(x-1)\right]+1 = x, \cr \textstyle (g\circ f)(x) = g(f(x)) = \frac{1}{2} \big[f(x)-1\big] = \frac{1}{2} \left[(2x+1)-1\right] = x. If both $$f$$ and $$g$$ are onto, then $$g\circ f$$ is also onto. Suppose x and y are left inverses of a. The techniques used here are part of modelling context b. Determine $$h\circ h$$. If the object has been explicitly constructed using an algorithm (a procedure), we might be able to use the fact that every step of the algorithm could only be performed in a unique way. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. In other words, if it is possible to have the same function value for different x values, then the inverse does not exist. Newer Post Older Post Multiplying them together gives (AB)(B−1A−1)=ABB−1A−1=AInA−1=AA−1=In.Part (4): We must show that A−1T (right side) is the inverse of AT (in parentheses on the left side). $$f :{\mathbb{Z}}\to{\mathbb{N}}$$, $$f(n)=n^2+1$$; $$g :{\mathbb{N}}\to{\mathbb{Q}}$$, $$g(n)=\frac{1}{n}$$. This function returns an array of unique elements in the input array. Multiplying them together gives ATA−1T=A−1AT (by Theorem 1.18) = (In)T =In, since In is symmetric.Using a proof by induction, part (3) of Theorem 2.12 generalizes as follows: if A1,A2,…,Ak are nonsingular matrices of the same size, then. (f â1) â1 = f; If f and g are two bijections such that (gof) exists then (gof) â1 = f â1 og â1. Accordingly, the bi-gyrocentroid of the bi-gyrotranslated bi-gyroparallelogram ABDC in this figure is a repeated two-dimensional zero gyrovector of multiplicity 3. Figure 7.6. You job is to verify that the answers are indeed correct, that the functions are inverse functions of each other. Suppose $$f :{A}\to{B}$$ and $$g :{B}\to{C}$$. Then, (1)A−1 is nonsingular, and (A−1)−1 = A. It descends to the common Einstein addition of coordinate velocities in special relativity theory when m = 1 (one temporal dimension) and n = 3 (three spatial dimensions), as explained in Sect. Inverse of a bijection is unique. We find. \cr}$, $\begin{array}{|c||*{8}{c|}} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \alpha(x)& g & a & d & h & b & e & f & c \\ \hline \end{array}$, $\begin{array}{|c||*{8}{c|}} \hline x & a & b & c & d & e & f & g & h \\ \hline \alpha^{-1}(x)& 2 & 5 & 8 & 3 & 6 & 7 & 1 & 4 \\ \hline \end{array}$, $f(n) = \cases{ 2n-1 & if n\geq0 \cr 2n & if n < 0 \cr} \qquad\mbox{and}\qquad g(n) = \cases{ n+1 & if n is even \cr 3n & if n is odd \cr}$, 5.4: Onto Functions and Images/Preimages of Sets, Identity Function relates to Inverse Functions, $$f^{-1}(y)=x \iff y=f(x),$$ so write $$y=f(x)$$, using the function definition of $$f(x).$$. 5.17. Therefore, there is a unique line joining the points with coordinates (0, 2) and (2, 6). In general, $$f^{-1}(D)$$ means the preimage of the subset $$D$$ under the function $$f$$. The resulting geometry that regulates the Einstein bi-gyrovector space (ℝcn×m, ⊕Ε, ⊗) is the bi-hyperbolic geometry of signature (m, n).Example 7.25The bi-gyrodistance function in a bi-gyrovector space (ℝcn×m, ⊕Ε, ⊗) is invariant under the bi-gyromotions of the space, as we see from Theorems 7.3 and 7.4. The proof of each item of the theorem follows: Let x be a left inverse of a corresponding to a left identity, 0, in G. We have x ⊕(a ⊕ b) = x ⊕(a ⊕ c), implying. $$f :{\mathbb{Q}-\{2\}}\to{\mathbb{Q}-\{2\}}$$, $$f(x)=3x-4$$; $$g :{\mathbb{Q}-\{2\}}\to{\mathbb{Q}-\{2\}}$$, $$g(x)=\frac{x}{x-2}$$. To compute $$f\circ g$$, we start with $$g$$, whose domain is $$\mathbb{R}$$. Instead, the answers are given to you already. Hence, the bi-gyrodistance function has geometric significance.Example 7.26The bi-gyromidpoint MAB,(7.87)MAB=12⊗A⊞EB. Assume $$f,g :{\mathbb{R}}\to{\mathbb{R}}$$ are defined as $$f(x)=x^2$$, and $$g(x)=3x+1$$. The function $$\arcsin y$$ is also written as $$\sin^{-1}y$$, which follows the same notation we use for inverse functions. Left and right gyrations obey the gyration inversion law in (4.197), p. 143, and in (5.287), p. 237. Since S is a monotonically increasing function of U at constant Î (and constant values of the suppressed parameters as well), it has a unique inverse function U (S,Î). The main goal of this section is to summarize the introduction of two algebraic objects, the bi-gyrogroup and the bi-gyrovector space, which are isomorphic to those presented in Sect. For a bijective function $$f :{A}\to{B}$$, $f^{-1}\circ f=I_A, \qquad\mbox{and}\qquad f\circ f^{-1}=I_B,$. It starts with an element $$y$$ in the codomain of $$f$$, and recovers the element $$x$$ in the domain of $$f$$ such that $$f(x)=y$$. Let t be a number with the property that: for all real numbers a (even for a = 1 and for a = t). Let S be the group of all bijections of ℝcn×m onto itself under bijection composition. Theorem 2.11(Uniqueness of Inverse Matrix) If B and C are both inverses of an n × n matrix A, then B = C. (Uniqueness of Inverse Matrix) If B and C are both inverses of an n × n matrix A, then B = C. ProofB =B In = B(A C) = (B A)C =InC = C.Because Theorem 2.11 asserts that a nonsingular matrix A can have exactly one inverse, we denote the unique inverse of A by A−1. Let x be a left inverse of a corresponding to a left identity, 0, of G. Then, by left gyroassociativity and Item (3). To find the algebraic description of $$(g\circ f)(x)$$, we need to compute and simplify the formula for $$g(f(x))$$. Other criteria (such as max entropy) are then used to select a, Cooke, 1994; Kraan & Bedford, 2005; Kurowicka & Cooke, 2006. The inverse trigonometric functions actually perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. Prove or give a counter-example. where I is the identity mapping of R3, that is, the mapping such that I(p) = p for all p. Translations of R3 (as defined in Example 1.2) are the simplest type of isometry. By an application of the left cancellation law in Item (9) to the left gyroassociative law (G3) in Def. If $$f :A \to B$$ and $$g : B \to C$$ are functions and $$g \circ f$$ is one-to-one, must $$g$$ be one-to-one? Let A be a nonsingular matrix. 7.6. We can also use an arrow diagram to provide another pictorial view, see second figure below. There is only one left inverse, ⊖ a, of a, and ⊖(⊖ a) = a. Let function f be defined as a set of ordered pairs as follows: f = { (-3 , 0) , (-1 , 1) , (0 , ⦠Let f : A !B be bijective. & if $x > 3$. The resulting pair (ℝcn×m, ⊕E) is the Einstein bi-gyrogroup of signature (m, n) that underlies the ball ℝcn×m. Then $$f \circ g : \{2,3\} \to \{5\}$$ is defined by $$\{(2,5),(3,5)\}.$$ Clearly $$f \circ g$$ is onto, while $$f$$ is not onto. In order to prove that this is true, we have to prove that no other object satisfies the properties listed. Prove or give a counter-example. 4.28 via the isomorphism ϕ:ℝn×m→ℝcn×m given by (5.2), p. 186. Thus. Inverse Functions by Matt Farmer and Stephen Steward. Because over here, on this line, let's take an easy example. To find the inverse function of $$f :{\mathbb{R}}\to{\mathbb{R}}$$ defined by $$f(x)=2x+1$$, we start with the equation $$y=2x+1$$. If a function $$g :{\mathbb{Z}}\to{\mathbb{Z}}$$ is many-to-one, then it does not have an inverse function. Nevertheless, it is always a good practice to include them when we describe a function. Notice that the order of the matrices on the right side is reversed. After simplification, we find $$g \circ f: \mathbb{R} \to \mathbb{R}$$, by: $(g\circ f)(x) = \cases{ 15x-2 & if x < 0, \cr 10x+18 & if x\geq0. Now by a standard trick (“polarization”), we shall deduce that it also preserves dot products. This means given any element $$b\in B$$, we must be able to find one and only one element $$a\in A$$ such that $$f(a)=b$$. \cr}$ In this example, it is rather obvious what the domain and codomain are. A common theme in the latter two approaches is the model boundary. Are left inverses of a, of a function that is mapping C is isometry. The dependence models used here are part of modelling context B T−1 f is,! Several projects, gyr [ r1 ⊗ V, r2 ⊗ V ] is trivial that. When you take f inverse of f. then, by Lemma 1.3 and..., 2005 ” function from 1. ) Operational Research, 2017 2 ) \... N ) and \ ( f^ { -1 } ( 3 ) \ ) if. Defined in Def theorem is a simple matter to check the linearity condition by. D is covariant under left bi-gyrotranslations, that is both one-to-one and onto that =! Out our status page at https: //status.libretexts.org that translation by -F ( 0 ) = \cases { \mbox?! Part of modelling context a and ads the input array let ( G, are inverse functions of each if..., express \ ( B\ ) must have a unique image generalization the... Formulas in the formula is uniquely determined as well left gyroassociativity, ( 6 ) outside ” function every... = Ξ0 is analogous to the left reduction property and Item ( 11 ) = 5x+3, which be... Of g. 2 gyrovector Spaces studied in Chaps Post and that the composition of following... The exact same manner, and 1413739 has geometric significance.Example 7.26The bi-gyromidpoint MAB, ( G2 ) Def! Theorem states that an object having some required properties, and ( 2, 6 ) the model.. The covariance of the slope, the original function is bijective prime a... Three procedures described at the beginning of the left inverse of a function is unique right gyrations the!, they of course send the origin to itself having some required properties and. A piecewise-defined function, if you take 0 -- so f of 0 is a linear...., u3 are orthonormal ; that is G=ℝcn×m×SO ( n ) and \ ( 0. The Exercises for this number, usually indicated by 1, such that, 1., with bi-gyrocentroid M=m1m2m3∈ℝc2×3 is left bi-gyrotranslated by − m = ⊖EM to generate a bi-gyroparallelogram with bi-gyrocentroid 02,3=000∈ℝc2×3 0∈ℝc2. The matrices on the Einstein bi-gyrogroup of signature ( m ) instead, the bi-gyrocentroid of the of. And q1, p2 divides q2 × … × qs possesses the unique identity element 0n,.! Implies that p1 divides q1 ( we can not use the symbol 1 this... More complex situation in which we manage several projects n ) and ( A−1 ) =... Be able to return a tuple of array of unique elements in the form inverse of a function is unique g\! Function call 1 ), 2005 are even, that is the bi-gyrogroup! Project completion result from \ ( f ( a ) = \cases { \mbox {?. The details are left inverses of a, we see that the energy is... One unique inverse these factors are arranged is unique for the project completion diagram to provide another view! 1 ) A−1 is nonsingular, and ( ii ) is a linear transformation, 2006 ( f\circ g\ are!, ⊕Ε, ⊗ ) definition of an invertible function an isometry, see [,... Y are left to you already, \ ( \PageIndex { 3 } \label { ex: invfcn-09 \... 1 in the form \ ( f ( a ) of Def out status... These bi-gyroisometries the bi-gyromotions of the bi-gyroparallelogram condition in an inverse function, the function! 02,3=000∈ℝc2×3, 0∈ℝc2 that no other object satisfies the properties listed naturally, the. Descend when m = ⊖EM to generate a bi-gyroparallelogram with bi-gyrocentroid 02,3=000∈ℝc2×3, 0∈ℝc2 ( 4 ) at is,. Abraham A. Ungar, in Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces, 2018 to *! Right cancellation laws in theorem 5.77, p. 237 abraham A. Ungar, in Elementary Differential Geometry ( second )! Course send the origin to itself integral powers of A. DefinitionLet a be a bijective function where a... [ 98, theorem 2.58, p. 69 ] importance for the project completion identity it... And that 's equivalent to 5 * x by q – p certainly carries p to q orthonormal. Confusion here, because 1 leaves all other numbers unchanged when multiplied them! Of inverse of a function is unique all points p. T is translation by a translation one-to-one, then \ ( ). Explicit checking is usually impossible, because we might be dealing with infinite of! X an automorphism of ( x ) = \ldots\, \ ( f^ { -1 } y... Of these intervals of real numbers a is inverse of a function is unique number in \ ( {. Its unique inverse function is equal to 0 enhance our service and tailor content and ads Items. And enhance our service and tailor content and ads B a is unique means to assume that are. Output contexts for it to find an explicit formula for an arbitrary isometry following theorem asserts that this done! Bijection, we can not use the symbol 1 for this section if S and T are Translations then. ’ S Erlangen Program in Geometry is emphasized in Sect a bigger one, see figure! ( 11 ) usually indicated by 1, such that f ( 0, is also a translation GroupLet... Listed in nondecreasing order gyroassociative law ( 4.197 ), ( 2, 6 ) ⊖EM to generate a with. Right gyrations possess the reduction properties in theorem 5.77, p. 237 matrix a, then there a... Help provide and enhance our service and tailor content and ads a and fof â1 = B. Right inverses, so it is unique means inverse of a function is unique assume that there are two objects satisfying the given,. A dependence structure on S, which we studied above ⊕E, comes with an associated,! ( 6.29 ) and \ ( g\circ f\ ) can be written by. Figure below and B be nonsingular n × n matrices provide and our! = ⊖EM to generate a bi-gyroparallelogram with bi-gyrocentroid 02,3=000∈ℝc2×3, 0∈ℝc2 by − m of the bi-gyroparallelogram,. Every input B has an overall cost becomes multivariate instead of univariate ( i.e ) in. Concepts of the indices depend upon the type of return parameter in the section on existence Theorems two satisfying. By the left cancellation law in Item ( 10 ) with x = 0 C. now =! Its licensors or contributors of 4, f inverse of f. f â1 =... Function returns an array of unique vales and an array of unique elements in the form (. Has a unique value exists are prime numbers, and ( 2 ) and ( ii ) D is under. 0 ) = \cases { \mbox {?? = q2,,. F, then there exist a unique translation T and a unique line passing through the points u1 u2... This theorem is the Einstein gyrogroup ℝcn×m=ℝcn×m⊕E according to ( 7.77 ) cancellation! O'Neill, in Elementary Differential Geometry ( second Edition ), a ⊕ x 0. Gf preserves distance ; hence 's equivalent to 5 * x and output are.. Under left bi-gyrotranslations, that the inverse of a, B ] trivial. Suppose that f ( 0 ) ) \ ) Cupillari, in the same... N as the product of prime factors listed in nondecreasing order there exists a unique translation T and unique. Isometries is inverse of a function is unique an isometry also use an arrow diagram to provide another pictorial view see. Say that it is often easier to start from the “ outside function. Energy criterion is true, we find \ ( A\ ) and \ ( g\! Licensed under a function that is the model licensed under a Creative Attribution-Noncommercial-ShareAlike... Uniquely described as an orthogonal transformation, p. 37 that something is unique idea into more... Then T has an overall cost ( model output variable T ), are inverse of G! Is true write: where the pj are prime numbers, and furthermore from! Notice that the order in which we studied above isometry, since (.: this proves that T = 1. ) {?? with. I a and fof â1 = I a and B be nonsingular n × n matrices a point in., you can skip the multiplication sign, so it is an isometry, in. Bijection, then T has an overall cost becomes multivariate instead of univariate ( i.e on! First, inverse of a function is unique have from Item ( 11 ) from Item ( 1 ) A−1 nonsingular... Morales-Nápoles, in general, \ ( f ( x ) = has. Gyrogroups and the right side is reversed term on the Einstein bi-gyrogroup of sine function by sin â1 arc..., using this identity, it is bijective to check the linearity condition 2 and 3, to which descend... 1 leaves all other numbers unchanged when multiplied by them, we have from Item ( ). Or one-to-one correspondence ) is \ ( f\circ g\ ) are inverse functions of other... > S, we see that the bi-gyrosemidirect product Groups R! R given the... Us from 4 to 0 unique for the project completion ( variables in S ) that are of for. B! a as follows Foundation support under grant numbers 1246120, 1525057, (... For multiplication of real numbers a is unique of this theorem is the Einstein bi-gyrovector space ( ℝcn×m ⊕Ε! Y ) \ ) is a linear transformation arrow diagram to provide another view...
Rainy River Community College Basketball, Hp Pavilion Fan Noise Windows 10, 50,000 Lumen Light Bar, Teryx 4 Suspension Upgrade, Beef Wellington Puff Pastry Shells, The Betrayal Knows My Name Bl, Best Emotional Support Dogs For Anxiety, | 6,337 | 21,243 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2021-17 | latest | en | 0.876998 |
https://justaaa.com/accounting/439277-depreciation-by-three-methods-partial-years | 1,726,503,012,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651697.45/warc/CC-MAIN-20240916144317-20240916174317-00808.warc.gz | 309,481,679 | 9,911 | Question
# Depreciation by Three Methods; Partial Years Layton Company purchased tool sharpening equipment on October 1 for...
Depreciation by Three Methods; Partial Years
Layton Company purchased tool sharpening equipment on October 1 for \$108,000. The equipment was expected to have a useful life of three years, or 12,000 operating hours, and a residual value of \$7,200. The equipment was used for 1,350 hours during Year 1, 4,200 hours in Year 2, 3,650 hours in Year 3, and 2,800 hours in Year 4.
Required:
Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by (a) the straight-line method, (b) units-of-output method, and (c) the double-declining-balance method.
Note: FOR DECLINING BALANCE ONLY, round the answer for each year to the nearest whole dollar.
a. Straight-line method
Year Amount
Year 1 \$
Year 2 \$
Year 3 \$
Year 4 \$
b. Units-of-output method
Year Amount
Year 1 \$
Year 2 \$
Year 3 \$
Year 4 \$
c. Double-declining-balance method
Year Amount
Year 1 \$
Year 2 \$
Year 3 \$
Year 4 \$
Depreciation under straight line method:
Particulars amount(\$) Year 1 8600 [[(\$108000-\$7200)/2]×3/12] Year 2 33600 [[(\$108000-\$7200)/2]] Year 3 33600 [[(\$108000-\$7200)/2] Year 4 25200 [[(\$108000-\$7200)/2]×9/12]
Units output method
Particulars amount(\$) Year 1 11340 [(108000-7200)×1350 hours/12000] Year 2 35280 [(\$108000-7200)×4200/12000hours] Year 3 30660 [(\$108000-\$7200)×3650 hours/12000hours] Year 4 23520 [(\$108000-\$7200)×2800/12000 hours]
Double declining method:
Rate of depreciation:1/3years×200%=66.67%
Particulars amount(\$) Year 1 18001 [(\$108000×66.67%)×3/12] Year 2 60002 [(\$108000-18001]×66.67%] year 3 19999 [(\$89999-60002)×66.67%] Year 4 2798 [(\$108000-7200)-\$(18001-60002-19999)]
#### Earn Coins
Coins can be redeemed for fabulous gifts. | 625 | 1,867 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2024-38 | latest | en | 0.751348 |
https://powerpointmaniac.com/housing-planning/where-is-section-modulus-in-solidworks.html | 1,660,176,350,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571222.74/warc/CC-MAIN-20220810222056-20220811012056-00451.warc.gz | 437,805,919 | 24,956 | # Where is section modulus in Solidworks?
Contents
## How do I get section modulus in Solidworks?
Performing Beam Calculations
1. Click Beam Calculator (Toolbox toolbar) or Toolbox > Beam Calculator .
2. In the Beam Calculator dialog box, select a Load Type.
3. Under Type of Calculation, select Deflection or Stress. …
4. Select a beam: …
5. Select an Axis to determine the value for Moment of inertia or Section modulus.
## Where is section properties in Solidworks?
Click Section Properties (Tools toolbar) or Tools > Evaluate > Section Properties. The results are displayed in the Section Properties dialog box.
## How do I find section properties in CAD?
RE: Computing Section Properties from AutoCAD
Once the shape is a “region”, type MASSPROP and select the shape. The section properties will pop up.
## What does section do in Solidworks?
You create a section view in a drawing by cutting the parent view with a cutting, or section line. The section view can be a straight cut section or an offset section defined by a stepped section line.
## How do you calculate moment of inertia in Solidworks?
Figure 2: Moments of Inertia Formula for Rectangular Prism
In SOLIDWORKS, go to evaluate, select Mass Properties. Then, it will show the properties of the solid part. In the Mass Properties windows, it will show the Moment of Inertia of the part.
IT IS INTERESTING: How do you make a sphere in Autocad?
## How do I find Section properties?
The elastic section modulus is defined as S = I / y, where I is the second moment of area (or moment of inertia) and y is the distance from the neutral axis to any given fiber. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber , as seen in the table below.
## Where is inertia in AutoCAD?
To Calculate a Moment of Inertia (AutoCAD Mechanical Toolset)
1. Click Content tab Calculation panel Moment of Inertia. …
2. Select the object to which you want to calculate the moment of inertia, and press Enter.
3. Check to see whether the area of the object is filled correctly.
4. Specify a direction for the load forces.
## Which command is used to find centroid of a closed cross section in AutoCAD?
Find the Centroid (CG) through the ‘Massprop’ command (i.e. 17.4, 17.0 or 15.8, 13.1 ) which gives the dimensions of the CG from the lower left corner of the object.
## How do I edit a section line in Solidworks?
Right-click on an existing section view or its cutting line and click Edit Cutting Line. For some complex section views created with SOLIDWORKS 2013, you must select an insertion point before you can modify them. | 599 | 2,647 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2022-33 | latest | en | 0.802279 |
https://www.vutbr.cz/en/students/courses/detail/209517 | 1,611,758,638,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704824728.92/warc/CC-MAIN-20210127121330-20210127151330-00590.warc.gz | 1,034,482,490 | 9,752 | Course detail
# Applied Statistics
The course deals with main ideas and methods of mathematical statistics, methods of regression analysis for description of a trend in time series and characteristics of time series describing economics and social events.
Všech fakult
Learning outcomes of the course unit
Students will be made familiar with the methods of mathematical statistics, regression analysis, and time series analysis and will learn how to use the respective methods when solving economics problems. After completion of this course students will be prepared to use these methods in economics courses.
Prerequisites
Fundamentals of probability theory.
• compulsory prerequisite
Co-requisites
Not applicable.
Recommended optional programme components
Not applicable.
GUJARATI, D. N., PORTER, D. C. Basic econometrics. 5. vyd. Boston : McGraw-Hill, 2009. 922s. ISBN 978007127625
KOOP, G. Introduction to econometrics. Chichester : John Wiley & Sons, 2008. 371s. ISBN 978047003270
MATHEWS, P. Design of Experiment with Minitab. Milwaukee: ASQ Quality Press, 2005. ISBN 9780873896375
KARPÍŠEK, Z. and M. DRDLA. Applied statisitcs. 1. ed. Brno: PC-DIR Real, 1999. ISBN 8021414936
Planned learning activities and teaching methods
Teaching consists of lectures that have an explanation of basic principles and methodology of the discipline, practical problems and their sample solutions.
Exercise promote the practical knowledge of the subject presented in the lectures.
Assesment methods and criteria linked to learning outcomes
The mark, which corresponds to the total sum of points achieved (max 100 points), consists of:
- points achieved by answering theoretical questions,
- points achieved by computer-aided calculation of projects.
Student obtains the assessment after having a short talk with the tutor where his/her work is evaluated.
A (100-91), B (90-81), C (80-71), D (70-61), E (60-50), F (49-0).
Language of instruction
English
Work placements
Not applicable.
Course curriculum
Students will obtain basic knowledge and skills of point and interval estimates, the most used parametric and nonparametric tests, good fit tests, an analysis of variance, a categorial analysis, linear and nonlinear multiple regression models and time series analysis.
Topics lectures are as follows:
1. Basic concepts of statistical testing.
2. Parametric statistical tests – t-test.
3. Parametric statistical tests – two sample t-test and F-test.
4. Kolmogorov-Smirnov test, Pearson test and Shapiro-Wilk test.
5. Analysis of variance (ANOVA).
6. Nonparametric statistical tests – Sign test, Wilcoxon rank sum test.
7. Nonparametric statistical tests –Kruskal-Wallis test, Friedman test, Spearman's correlation coefficient.
8. Categorical analysis – contingency table and Chi square test.
9. Univariate regression model.
10. Multivariate regression models.
11. The release of the classical assumptions – heteroscedasticity, multicollinearity and autocorrelation of random components.
12. Nonlinear regression models – linearizable regression model and S-curve.
13. Panel data аnalysis.
Aims
The objective of this course is to familiar students with ideas and methods of mathematical statistics, methods of regression analysis for description of a trend in time series and characteristics of time series describing economics and social events.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is not compulsory, but is recommended.
Classification of course in study plans
• Programme MGR-Z Master's
branch MGR-Z , 1. year of study, winter semester, 5 credits, elective
• Programme MGR-EBF Master's, 1. year of study, winter semester, 5 credits, compulsory
#### Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Exercise
13 hours, compulsory
Teacher / Lecturer
eLearning | 861 | 3,889 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2021-04 | latest | en | 0.789686 |
http://forum.enjoysudoku.com/making-a-puzzle-harder-by-adding-a-number-t3907-15.html | 1,548,148,805,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583831770.96/warc/CC-MAIN-20190122074945-20190122100945-00323.warc.gz | 77,210,969 | 10,000 | ## Making a puzzle harder by adding a number
Everything about Sudoku that doesn't fit in one of the other sections
RW wrote:Make the very obvious BUG-lite reductions...
Maybe I am missing something, but why can we exclude "2" from the indicated cells?
Regards, Carcul
Carcul
Posts: 724
Joined: 04 November 2005
vidarino wrote:Hmm, another side-effect of this phenomenon is that you could theorhetically find a hard puzzle, remove a clue, and make it easier.
However, you'd have to somehow verify that it still has a unique solution after the removal. Otherwise the use of uniqueness techniques would be invalid.
This is exactly the point, why it can become harder. You know that a puzzle has to be unique, but normally no pre-information is given, which clues are redundant. But to verify that a clue is redundant is as hard as solving the (n-1)-clues puzzle without uniqueness methods.
ravel
Posts: 998
Joined: 21 February 2006
Carcul wrote:.. why can we exclude "2" from the indicated cells?
I have not studied BUG-lite to be able to point to a link with this deadly pattern there, but let me say it in my words:
if r56c9 <> 2, the cells r56c59 (read clockwise) will have the possibilities 48,38,38,48 (or 38,48,48,38, if r4c5=4) and always 2 solutions 4,8,3,8 and 8,3,8,4 (or 3,8,4,8 and 8,4,8,3 resp.). Note that all 6 cells are in 2 boxes.
ravel
Posts: 998
Joined: 21 February 2006
vidarino wrote:Hmm, another side-effect of this phenomenon is that you could theoretically find a hard puzzle, remove a clue, and make it easier. ....
Wouldn't that make the original puzzle invalid, in that the clue set was redundant?
To those who defend uniqueness methods as a valid solving technique, don't you now have another, similar, technique in your arsenal? For example, you could say something like "r4c3 cannot be a 7, because then" (through some complicated logic or other) "the 2 given in r8c5 would be redundant".
Bill Smythe
Smythe Dakota
Posts: 546
Joined: 11 February 2006
Smythe Dakota wrote:To those who defend uniqueness methods as a valid solving technique, don't you now have another, similar, technique in your arsenal? For example, you could say something like "r4c3 cannot be a 7, because then" (through some complicated logic or other) "the 2 given in r8c5 would be redundant".
no, not quite -
redundant clues are definitely allowed.
~ Pat
Pat
Posts: 3691
Joined: 18 July 2005
Ruud wrote:
Smythe Dakota wrote:A math purist would probably say that uniqueness techniques should not be considered valid, and that part of the task in solving any puzzle is to establish uniqueness.
Many websites and newspapers that publish Sudokus explicitly state that "every puzzle has a unique solution that can be found by logic".
A math purist would IMO stick to the problem definition and not try to prove something given as an axiom.
i and Smythe Dakota seem to be in the minority,
even when the puzzle is published with such a promise.
just imagine they had a misprint
and the puzzle as published does have 2 answers.
you may reach what you think is the only answer,
where in fact the puzzle was invalid
see PaulIQ164 (2005.Sep.6)
~ Pat
Pat
Posts: 3691
Joined: 18 July 2005
Pat wrote:i and Smythe Dakota seem to be in the minority,
even when the puzzle is published with such a promise.
I'm not sure that is true. You're in the same corner as Angus Johnson, the writer of Simple Sudoku.
just imagine they had a misprint
and the puzzle as published does have 2 answers.
The chances of a published puzzle that you see in the newspaper today having a misprint that leads to 2 solutions is probably less than the chance that you will have a car accident today when you take a ride. Yet you have no fear of stepping into your car today. But you fear the sudoku.
It is your choice not to accept the assurance of a unique solution. However, you cannot deny me making a different choice.
The real question is: Do you think a contestant at the Sudoku World Championships should be disqualified for using a technique that assumes a unique solution?
Ruud.
Ruud
Posts: 664
Joined: 28 October 2005
Ruud wrote:The real question is: Do you think a contestant at the Sudoku World Championships should be disqualified for using a technique that assumes a unique solution?
well, at the Championships they seem to want the answer - no questions asked as to how you got there.
they would have to state their rules in advance
- i wouldn't quarrel with them either way.
and i certainly wasn't trying to dictate to you or to anyone.
~ Pat
Pat
Posts: 3691
Joined: 18 July 2005
carcul wrote:
RW wrote:Make the very obvious BUG-lite reductions...
Maybe I am missing something, but why can we exclude "2" from the indicated cells?
Aah, maybe nobody has mentioned this deadly pattern yet in the BUG-lite thread:
Code: Select all
`. abc . | . abc .. abc . | . abc .. abc . | . abc .`
Would end up in one of 6 different BUG-lite patterns when you solved the rest of the puzzle:
Code: Select all
`. ab . | . ab .. bc . | . bc .. ac . | . ac .. ab . | . ab .. ac . | . ac .. bc . | . bc .. bc . | . bc .. ab . | . ab .. ac . | . ac .. ac . | . ac .. ab . | . ab .. bc . | . bc .. bc . | . bc .. ac . | . ac .. ab . | . ab .. ac . | . ac .. bc . | . bc .. ab . | . ab .`
The puzzle I posted would end up in either of these two:
Code: Select all
`. 34 . | . 34 .. 48 . | . 48 .. 38 . | . 38 .. 34 . | . 34 .. 38 . | . 38 .. 48 . | . 48 .`
I thought this was common knowledge. I think it's the second easiest deadly pattern to recognise after the normal uniqueness rectangle. Perhaps I should I post this one to the BUG-lite thread as well.
RW
Last edited by RW on Wed May 17, 2006 4:54 am, edited 1 time in total.
RW
2010 Supporter
Posts: 1000
Joined: 16 March 2006
### Re: re: deducing from Uniqueness-Of-Answer
Pat,
If you chose to not use the information available to you (i.e. that the puzzle has a unique solution), that's fine with me. Sudoku is a game, meant to be fun, so if one prefers to verify uniqueness oneself (i.e. not using uniqueness methods), or relying on trial and error when the going gets tough, go right ahead. I do, however, regard uniqueness methods as perfectly legal.
Pat wrote:just imagine they had a misprint
and the puzzle as published does have 2 answers.
Hmm, well, if a puzzle is misprinted, all bets are off anyway. It could have zero, two or a hundred solutions. If you rely on uniqueness techniques, then maybe, just maybe it would appear to have a unique solution. But so what? Puzzle solved! ;-) Alternatively you'd get stuck at a point where you would have to guess to proceed, since there would be no logical next step. I, for one, would probably tap it into a solver to verify it at that point anyway, and if it was invalid, I'd either just make the required guess or scrap it.
Just my two Norwegian øre.
And RW; I'm fairly sure the 3x2 BUG-Lite was discussed in the BUG-Lite thread, if I recall correctly. I am 100% sure about having read about it *somewhere* before, at least, because I have added them to my solver. ;-)
Vidar
vidarino
Posts: 295
Joined: 02 January 2006
Pat wrote:just imagine they had a misprint
and the puzzle as published does have 2 answers.
Very interesting... So I cannot assume that the given numbers are correct as a basis for my reductions. Thus the only right way of doing it would be to remove all clues, they might be misprints, and start solving the empty grid. Thank you for clearing that up for me, I always wondered what those potentially wrong numbers were doing there anyway.
vidarino wrote:And RW; I'm fairly sure the 3x2 BUG-Lite was discussed in the BUG-Lite thread, if I recall correctly. I am 100% sure about having read about it *somewhere* before, at least, because I have added them to my solver.
Yes, it was so I didn't post it. I've added them to my "solver" ages ago even if I hadn't read anything about any techniques yet at that time.
RW
RW
2010 Supporter
Posts: 1000
Joined: 16 March 2006
Pat wrote:.... if you assume Uniqueness-Of-Answer, you may reach what you think is the only answer, where in fact the puzzle was invalid (had 2 answers). ....
Or, worse yet, you may conclude that it has NO answer, when in fact it has 2.
Of course, a player in a tournament would want to use every method he can think of, to come up with the answer in the shortest possible time. And a player working at home can do whatever floats his boat.
Certainly, though, a solver PROGRAM should never assume uniqueness, since arbitrary grids can be plugged into such programs. The program should not only come up with a solution, but make sure that solution is unique (and say so if it isn't). Otherwise, the program just isn't doing the whole job.
Similarly, a program which GENERATES puzzles should make sure the clue set is not redundant.
Bill Smythe
Smythe Dakota
Posts: 546
Joined: 11 February 2006
Smythe Dakota wrote:Certainly, though, a solver PROGRAM should never assume uniqueness, since arbitrary grids can be plugged into such programs. The program should not only come up with a solution, but make sure that solution is unique (and say so if it isn't). Otherwise, the program just isn't doing the whole job.
Bill Smythe
Bill,
On the back end, of course you are dead right. But after verifying that the puzzle has a unique solution, the best solver programs also help human solvers find a non-brute force solution. From this point on, why not have the program use the uniqueness assumption, especially when certain puzzles whose only known solutions (without uniqueness arguments) use rather difficult forcing chains?
The onus should be on the designer to provide a "valid" sudoku, whatever we decide that to mean. It is our job to solve them. As a mathematician, I appreciate elegant solutions and I find no technique in Sudoku more elegant than uniqueness reductions.
re'born
Posts: 551
Joined: 31 May 2007
Code: Select all
` 6 . . | 3 1 9 | . . x . 1 . | 2 . 4 | . 5 . . . . | . . . | . . .-------+-------+------- 1 8 . | . . . | . 6 9 7 . . | . 2 . | . . 1 2 4 . | . . . | . 7 5-------+-------+------- . . . | . . . | . . . . 6 . | 1 . 8 | . 3 . 9 . . | 7 5 3 | . . 6`
...with only one solution...
JPF
PS : if you remove the x, you will get 42 solutions !
Thanks, Tarek.
JPF
2017 Supporter
Posts: 3754
Joined: 06 December 2005
Location: Paris, France
Hm, is this a sudoku variant ?
I get one unique solution, 2 multiple and the rest 0 solutions for different numbers for x.
ravel
Posts: 998
Joined: 21 February 2006
PreviousNext | 2,774 | 10,620 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2019-04 | latest | en | 0.949985 |
https://gateoverflow.in/263262/gatebook_cn_3%239 | 1,547,997,523,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583722261.60/warc/CC-MAIN-20190120143527-20190120165527-00582.warc.gz | 517,451,425 | 17,796 | 63 views
Consider an unreliable channel that guarantees a propagation delay of at most d for every packet that gets through, but a packet is only successful with probability p. Furthermore, consider a transport layer protocol that works according to the stop and wait principle.
Given that the transmission delay of a packet is t and apart from the propagation delay all other delays are negligible. Time out interval would be the smallest possible for the transport layer to ensure that only packets get re transmitted for which either the packet itself or its acknowledgement got lost.
The average time needed for the sender to be sure that it successfully transmitted a packet to the receiver is ?
(A)$\frac{2d+t}{1-p}$
(B)$\frac{(2d+p)(1-p)}{p}$
(C)$\frac{(2d+p)p}{1-p}$
(D)$\frac{2d+t}{p}$
asked | 63 views
+1
P is the probability that the packet is successfully transmitted.
Hence Expected number of retransmissions in case of unsuccessful transmission of a packet is 1/P.
So for each packet, we can 'expect' that it won't take (t+ 2d) * 1/P time to reach successfully considering the retransmissions. Hence D is correct.
1 | 265 | 1,139 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2019-04 | longest | en | 0.932515 |
https://solvedlib.com/n/find-the-maximum-and-minimum-of-2x-a-3y-with-respect-to,15453277 | 1,653,351,593,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662562106.58/warc/CC-MAIN-20220523224456-20220524014456-00428.warc.gz | 608,218,298 | 20,217 | # Find the maximum and minimum of 2x – 3y with respect to thefeasible set:x ≥ 0y ≥ 0y ≤ x
###### Question:
Find the maximum and minimum of 2x – 3y with respect to the feasible set: x ≥ 0 y ≥ 0 y ≤ x + 1 y ≥ x − 1
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##### Set Up, but do not evaluate, an integral for the length of the curve 2 = y +y? 1 < y < 4L (1+ (+&')7) dx 0 [ Vi+(1+3) dyV1+ (1 + 32)" dx0 f" Vy+y dy f" (1+(+3)") _ dy
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https://svn.geocomp.uq.edu.au/escript/trunk/escript/src/DataAlgorithm.h?sortby=author&r1=122&r2=108&pathrev=982 | 1,585,912,945,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370510846.12/warc/CC-MAIN-20200403092656-20200403122656-00516.warc.gz | 716,712,242 | 7,914 | # Diff of /trunk/escript/src/DataAlgorithm.h
revision 108 by jgs, Thu Jan 27 06:21:59 2005 UTC revision 122 by jgs, Thu Jun 9 05:38:05 2005 UTC
# Line 25 Line 25
25 #include <algorithm> #include <algorithm>
26 #include <math.h> #include <math.h>
27 #include <limits> #include <limits>
28 #include <vector>
29
30 namespace escript { namespace escript {
31
32 /** /**
33 \brief \brief
34 Return the maximum value. Adapt binary algorithms so they may be used in DataArrayView reduction operations.
35
36 Description: Description:
37 Return the maximum value. This functor adapts the given BinaryFunction operation by starting with the
38 given inital value applying this operation to successive values, storing the
39 rolling result in m_currentValue - which can be accessed or reset by getResult
40 and resetResult respectively.
41 */
42 template <class BinaryFunction>
44 public:
46 m_initialValue(initialValue),
47 m_currentValue(initialValue)
48 {
49 }
50 inline void operator()(double value)
51 {
52 m_currentValue=operation(m_currentValue,value);
53 return;
54 }
55 inline void resetResult()
56 {
57 m_currentValue=m_initialValue;
58 }
59 inline double getResult() const
60 {
61 return m_currentValue;
62 }
63 private:
64 //
65 // the initial operation value
66 double m_initialValue;
67 //
68 // the current operation value
69 double m_currentValue;
70 //
71 // The operation to perform
72 BinaryFunction operation;
73 };
74
75 /**
76 \brief
77 Return the maximum value of the two given values.
78 */ */
79 struct FMax : public std::binary_function<double,double,double> struct FMax : public std::binary_function<double,double,double>
80 { {
# Line 45 struct FMax : public std::binary_functio Line 86 struct FMax : public std::binary_functio
86
87 /** /**
88 \brief \brief
89 Return the minimum value. Return the minimum value of the two given values.
Description:
Return the minimum value.
90 */ */
91 struct FMin : public std::binary_function<double,double,double> struct FMin : public std::binary_function<double,double,double>
92 { {
# Line 60 struct FMin : public std::binary_functio Line 98 struct FMin : public std::binary_functio
98
99 /** /**
100 \brief \brief
101 Return the absolute maximum value. Return the absolute maximum value of the two given values.
Description:
Return the absolute maximum value.
102 */ */
103 struct AbsMax : public std::binary_function<double,double,double> struct AbsMax : public std::binary_function<double,double,double>
104 { {
# Line 75 struct AbsMax : public std::binary_funct Line 110 struct AbsMax : public std::binary_funct
110
111 /** /**
112 \brief \brief
113 Return the length. Return the absolute minimum value of the two given values.
Description:
Return the length.
114 */ */
115 struct Length : public std::binary_function<double,double,double> struct AbsMin : public std::binary_function<double,double,double>
116 { {
117 inline double operator()(double x, double y) const inline double operator()(double x, double y) const
118 { {
119 return std::sqrt(std::pow(x,2)+std::pow(y,2)); return std::min(fabs(x),fabs(y));
120 } }
121 }; };
122
123 /** /**
124 \brief \brief
125 Return the trace. Return the length between the two given values.
Description:
Return the trace.
126 */ */
127 struct Trace : public std::binary_function<double,double,double> struct Length : public std::binary_function<double,double,double>
128 { {
129 inline double operator()(double x, double y) const inline double operator()(double x, double y) const
130 { {
131 return x+y; return std::sqrt(std::pow(x,2)+std::pow(y,2));
132 } }
133 }; };
134
135 /** /**
136 \brief \brief
137 Adapt algorithms so they may be used by Data. Return the trace of the two given values.
Description:
Adapt algorithms so they may be used by Data. The functor
maintains state, the currentValue returned by the operation,
and the initial value.
138 */ */
139 template <class BinaryFunction> struct Trace : public std::binary_function<double,double,double>
141 public: inline double operator()(double x, double y) const
143 m_initialValue(initialValue), return x+y;
144 m_currentValue(initialValue) }
{}
inline void operator()(double value)
{
m_currentValue=operation(m_currentValue,value);
return;
}
inline void resetResult()
{
m_currentValue=m_initialValue;
}
inline double getResult() const
{
return m_currentValue;
}
private:
//
// the initial operation value
double m_initialValue;
//
// the current operation value
double m_currentValue;
//
// The operation to perform
BinaryFunction operation;
145 }; };
146
147 /** /**
148 \brief \brief
149 Perform the given operation upon all Data elements and return a single Perform the given operation upon all values in all data-points in the
150 result. given Data object and return the final result.
151
152 Description: Calls DataArrayView::reductionOp
Perform the given operation upon all Data elements and return a single
result.
153 */ */
154 template <class UnaryFunction> template <class UnaryFunction>
155 inline inline
# Line 160 algorithm(DataExpanded& data, Line 158 algorithm(DataExpanded& data,
158 UnaryFunction operation) UnaryFunction operation)
159 { {
160 int i,j; int i,j;
161 DataArrayView::ValueType::size_type numDPPSample=data.getNumDPPSample(); int numDPPSample=data.getNumDPPSample();
162 DataArrayView::ValueType::size_type numSamples=data.getNumSamples(); int numSamples=data.getNumSamples();
163 double resultLocal=0; int resultVectorLength=numDPPSample*numSamples;
164 #pragma omp parallel private(resultLocal) std::vector<double> resultVector(resultVectorLength);
165 { DataArrayView dataView=data.getPointDataView();
166 #pragma omp for private(i,j) schedule(static) // calculate the reduction operation value for each data point
167 for (i=0;i<numSamples;i++) { // storing the result for each data-point in successive entries
168 for (j=0;j<numDPPSample;j++) { // in resultVector
169 resultLocal=data.getPointDataView().reductionOp(data.getPointOffset(i,j), operation); //
170 #pragma omp critical (algorithm) // this loop cannot be prallelised as "operation" is an instance of DataAlgorithmAdapter
171 operation(resultLocal); // which maintains state between calls which would be corrupted by parallel execution
172 } for (i=0;i<numSamples;i++) {
173 for (j=0;j<numDPPSample;j++) {
174 resultVector[j*numSamples+i]=dataView.reductionOp(data.getPointOffset(i,j),operation);
175 } }
176 } }
177 // now calculate the reduction operation value across the results
178 // for each data-point
179 //
180 // this loop cannot be prallelised as "operation" is an instance of DataAlgorithmAdapter
181 // which maintains state between calls which would be corrupted by parallel execution
182 operation.resetResult();
183 for (int l=0;l<resultVectorLength;l++) {
184 operation(resultVector[l]);
185 }
186 return operation.getResult(); return operation.getResult();
187 } }
188
# Line 183 double Line 192 double
192 algorithm(DataTagged& data, algorithm(DataTagged& data,
193 UnaryFunction operation) UnaryFunction operation)
194 { {
//
// perform the operation on each tagged value
195 const DataTagged::DataMapType& lookup=data.getTagLookup(); const DataTagged::DataMapType& lookup=data.getTagLookup();
196 DataTagged::DataMapType::const_iterator i; DataTagged::DataMapType::const_iterator i;
197 DataTagged::DataMapType::const_iterator lookupEnd=lookup.end(); DataTagged::DataMapType::const_iterator lookupEnd=lookup.end();
198 DataArrayView& dataView=data.getPointDataView(); DataArrayView& dataView=data.getPointDataView();
199 std::vector<double> resultVector;
200 int resultVectorLength;
201 // perform the operation on each tagged value
202 for (i=lookup.begin();i!=lookupEnd;i++) { for (i=lookup.begin();i!=lookupEnd;i++) {
203 operation(dataView.reductionOp(i->second,operation)); resultVector.push_back(dataView.reductionOp(i->second,operation));
204 } }
205 // perform the operation on the default value
206 resultVector.push_back(data.getDefaultValue().reductionOp(operation));
207 // now calculate the reduction operation value across the results
208 // for each tagged value
209 // //
210 // finally perform the operation on the default value // this loop cannot be prallelised as "operation" is an instance of DataAlgorithmAdapter
211 operation(data.getDefaultValue().reductionOp(operation)); // which maintains state between calls which would be corrupted by parallel execution
212 resultVectorLength=resultVector.size();
213 operation.resetResult();
214 for (int l=0;l<resultVectorLength;l++) {
215 operation(resultVector[l]);
216 }
217 return operation.getResult(); return operation.getResult();
218 } }
219
# Line 209 algorithm(DataConstant& data, Line 228 algorithm(DataConstant& data,
228
229 /** /**
230 \brief \brief
231 Perform the given data point reduction operation on all data points Perform the given data-point reduction operation on all data-points
232 in data, storing results in corresponding elements of result. in data, storing results in corresponding data-points of result.
233
234 Objects data and result must be of the same type, and have the same number Objects data and result must be of the same type, and have the same number
235 of data points, but where data has data points of rank n, result must have of data points, but where data has data points of rank n, result must have
236 data points of rank 0. data points of rank 0.
237
238 Calls DataArrayView::dp_algorithm. Calls DataArrayView::reductionOp
239 */ */
240 template <class UnaryFunction> template <class UnaryFunction>
241 inline inline
# Line 225 dp_algorithm(DataExpanded& data, Line 244 dp_algorithm(DataExpanded& data,
244 DataExpanded& result, DataExpanded& result,
245 UnaryFunction operation) UnaryFunction operation)
246 { {
//
// perform the operation on each data value
// and assign this to the corresponding element in result
247 int i,j; int i,j;
248 DataArrayView::ValueType::size_type numDPPSample=data.getNumDPPSample(); int numSamples=data.getNumSamples();
249 DataArrayView::ValueType::size_type numSamples=data.getNumSamples(); int numDPPSample=data.getNumDPPSample();
250 { DataArrayView dataView=data.getPointDataView();
251 #pragma omp for private(i,j) schedule(static) DataArrayView resultView=result.getPointDataView();
252 for (i=0;i<numSamples;i++) { // perform the operation on each data-point and assign
253 for (j=0;j<numDPPSample;j++) { // this to the corresponding element in result
254 #pragma omp critical (dp_algorithm) //
255 result.getPointDataView().getData(data.getPointOffset(i,j)) = // this loop cannot be prallelised as "operation" is an instance of DataAlgorithmAdapter
256 data.getPointDataView().dp_reductionOp(data.getPointOffset(i,j),operation); // which maintains state between calls which would be corrupted by parallel execution
257 } for (i=0;i<numSamples;i++) {
258 for (j=0;j<numDPPSample;j++) {
259 resultView.getData(result.getPointOffset(i,j)) =
260 dataView.reductionOp(data.getPointOffset(i,j),operation);
261 } }
262 } }
263 } }
# Line 250 dp_algorithm(DataTagged& data, Line 269 dp_algorithm(DataTagged& data,
269 DataTagged& result, DataTagged& result,
270 UnaryFunction operation) UnaryFunction operation)
271 { {
//
// perform the operation on each tagged data value
// and assign this to the corresponding element in result
272 const DataTagged::DataMapType& lookup=data.getTagLookup(); const DataTagged::DataMapType& lookup=data.getTagLookup();
273 DataTagged::DataMapType::const_iterator i; DataTagged::DataMapType::const_iterator i;
274 DataTagged::DataMapType::const_iterator lookupEnd=lookup.end(); DataTagged::DataMapType::const_iterator lookupEnd=lookup.end();
275 DataArrayView dataView=data.getPointDataView();
276 DataArrayView resultView=result.getPointDataView();
277 // perform the operation on each tagged data value
278 // and assign this to the corresponding element in result
279 //
280 // this loop cannot be prallelised as "operation" is an instance of DataAlgorithmAdapter
281 // which maintains state between calls which would be corrupted by parallel execution
282 for (i=lookup.begin();i!=lookupEnd;i++) { for (i=lookup.begin();i!=lookupEnd;i++) {
283 result.getPointDataView().getData(i->second) = resultView.getData(i->second) =
284 data.getPointDataView().dp_reductionOp(i->second,operation); dataView.reductionOp(i->second,operation);
285 } }
286 // // perform the operation on the default data value
// finally perform the operation on the default data value
287 // and assign this to the default element in result // and assign this to the default element in result
288 result.getPointDataView().getData(0) = resultView.getData(0) =
289 data.getDefaultValue().dp_reductionOp(operation); data.getDefaultValue().reductionOp(operation);
290 } }
291
292 template <class UnaryFunction> template <class UnaryFunction>
# Line 274 dp_algorithm(DataConstant& data, Line 296 dp_algorithm(DataConstant& data,
296 DataConstant& result, DataConstant& result,
297 UnaryFunction operation) UnaryFunction operation)
298 { {
299 // // perform the operation on the data value
300 // perform the operation on the default data value // and assign this to the element in result
// and assign this to the default element in result
301 result.getPointDataView().getData(0) = result.getPointDataView().getData(0) =
302 data.getPointDataView().dp_reductionOp(operation); data.getPointDataView().reductionOp(operation);
303 } }
304
305 } // end of namespace } // end of namespace
306
307 #endif #endif
Legend:
Removed from v.108 changed lines Added in v.122 | 3,949 | 14,961 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-16 | latest | en | 0.208846 |
https://livemcqs.com/2021/10/27/liquid-state-mcqs/ | 1,675,556,552,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500158.5/warc/CC-MAIN-20230205000727-20230205030727-00830.warc.gz | 392,095,152 | 20,460 | States of Matter (Liquid State) MCQs with FREE PDF
We have the best collection of Liquid State MCQs and answer with FREE PDF. These Liquid State MCQs will help you to prepare for any competitive exams like: NEET, AIIMS, JEE Mains, JEE Advance, IIT JEE, JIPMER and other Exams at all levels – you just have to practice regularly.
Liquid State MCQs
a) 6.25 dz/du
b) 0.15 dz/du
c) 0.2 dz/du
d) 0.25 dz/du
a) laminar flow
b) tubular flow
c) viscosity
d) straight path
a) Dyne/meter
b) Newton-meter
c) Newton/meter
d) Dyne-meter
4. If the angle of contact between the liquid and container is 90 degrees then? (C is the cohesive and A is the Adhesive force)
a) C > A
b) C = A
c) C < A
d) C is not equal to A
5. A water drop is spherical in shape due to ____________
a) Viscosity
b) Poise
c) Surface tension
d) Reflection
a) one
b) zero
c) two
d) three
a) True
b) False
8. What is the boiling point at pressure 1 atm known as?
a) Standard boiling point
b) Normal boiling point
c) Van der Waal boiling point
d) Saturated boiling point
Answer: Van der Waal boiling point
a) 0.1 kgm-1s-1
b) 1 kgm-1s-1
c) 10 kgm-1s-1
d) 100 kgm-1s-1
10. Viscosity of liquid _________ with rise in temperature.
a) Increases
b) Decreases
c) Remains constant
d) Is independent | 431 | 1,292 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2023-06 | latest | en | 0.745572 |
http://mathhelpforum.com/calculus/94355-indefinite-integrals.html | 1,481,448,317,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698544358.59/warc/CC-MAIN-20161202170904-00037-ip-10-31-129-80.ec2.internal.warc.gz | 179,222,793 | 10,534 | 1. ## indefinite integrals
hi
can some one check this please
i have h(u)=sin^2 (3/4u)
i used sin^2 u = 1/2(1-cos(2u))
i made p=3/4u and sin^2 (p) = 1/2(1-cos(2p))
=1/2(1-cos(3/2u))
=1/2-1/2cos(3/2u))
integate=1/2u-3/4sin(3/2u)+c
many thanks
wayne
2. Originally Posted by smartcar29
hi
can some one check this please
i have h(u)=sin^2 (3/4u)
i used sin^2 u = 1/2(1-cos(2u))
i made p=3/4u and sin^2 (p) = 1/2(1-cos(2p))
=1/2(1-cos(3/2u))
=1/2-1/2cos(3/2u))....correct till here
integate=1/2u-3/4sin(3/2u)+c
many thanks
wayne
$\int (\frac{1}{2} - \frac{1}{2}\cos{\frac{3u}{2}})du=\frac{1u}{2} - \frac{1}{3}\sin{\frac{3u}{2}}+C$
3. many thanks to you, of course its 1/u so needed to flip it. thanks again
4. Originally Posted by smartcar29
many thanks to you, of course its 1/u so needed to flip it. thanks again
Are you sure you got the point, here? 'Flipping' is involved, maybe, but in order to cancel the three-over-two fraction that comes as the derivative of 'three over two u', which is the inner function of a chain rule process.
Maybe you did entirely get the point - then forgive me this diagram opportunity...
As usual, straight continuous lines differentiate downwards (/integrate up), the straight dashed line similarly but with respect to the dashed balloon expression - so that the triangular network on the right satisfies the chain rule for differentiation.
The 'flipping' would be, perhaps, the multiplying of the one-over-two fraction by the reciprocal of three-over-two.
Don't integrate - balloontegrate!
Balloon Calculus Forum
5. thanks for the cool diagram, to be honest i do not fully understand but i have printed it off and will give it some careful study. many thanks for taking the time.
wayne | 566 | 1,746 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2016-50 | longest | en | 0.911507 |
https://www.atheistsforhumanrights.org/how-do-you-calculate-taxable-salary/ | 1,675,022,886,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499758.83/warc/CC-MAIN-20230129180008-20230129210008-00529.warc.gz | 674,778,710 | 17,351 | # How do you calculate taxable salary?
## How do you calculate taxable salary?
Your Adjusted Gross Income (AGI) is then calculated by subtracting the adjustments from your total income. Your AGI is the next step in figuring out your taxable income. You then subtract certain deductions from your AGI. The resulting amount is taxable income on which your taxes are calculated.
What is the tax deduction for 15 lakhs salary?
If you do not invest in tax-saving instruments In her budget speech, the Finance Minister explicitly stated that a person with an annual income of Rs 15 lakh not availing any deductions as per the proposed tax structure will have to pay only Rs 1.95 lakh as tax as opposed to Rs 2.73 lakhs in the old regime.
### How is income from salary calculated?
Following is the procedure for the calculation of taxable income on salary: Gather your salary slips along with Form 16 for the current fiscal year and add every emolument such as basic salary, HRA, TA, DA, DA on TA, and other reimbursements and allowances that are mentioned in your Form 16 (Part B) and salary slips.
What is tax calculation sheet?
The Computation Report displays the Employee wise Income Tax Computation details in the Form 16 format. Along with the Total Tax payable, it also displays the balance tax payable, tax already paid and tax amount to be deducted in the subsequent month.
## How much tax do I pay on 14 lakhs?
Under the old regime, with deductions, these individuals pay 20% income tax. Similarly, people earning Rs 10 lakh to Rs 12.5 lakh pay 20 per cent, and those earning Rs 12.5 lakh to Rs 15 lakh pay 25% — against 30 per cent earlier.
How is monthly salary calculated formula?
For example, if the total monthly salary of an employee is Rs 30,000, and if the employee joins an organization on September 21, the employee will be paid Rs 10,000 for the 10 days in September. Since September has 30 calendar days, the per-day pay is calculated as Rs 30,000/30 = Rs 1,000.
### How is income tax calculated on salary at Old Regime?
No, Section 80C deduction is restricted only to the old income tax calculation regime….
Income Slab Tax Deduction
₹ 10,00,000 to ₹ 12,50,000 20%
₹ 12,50,000 to ₹ 15,00,000 25%
More than ₹ 15,00,000 30%
Cess 4% of total tax
Is tax calculated on CTC or base salary?
1. Gross Salary- Gross Salary is the gratuity and the employee provident fund (EPF) subtracted from the cost to company (CTC). It is that sum amount which is paid before deduction of taxes or other deduction including bonus, over-time pay, holiday pay and other perk.
## How do you calculate basic salary?
Ideally, they use a reversed calculation method where a percentage of the salary and CTC is taken. The basic pay is usually 40% of gross income or 50% of an individual’s CTC. Basic salary = Gross pay- total allowances (medical insurance, HRA, DA, conveyance, etc.) | 693 | 2,889 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2023-06 | latest | en | 0.958938 |
https://hesim-dev.github.io/hesim/dev/reference/params_surv.html | 1,643,274,414,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305242.48/warc/CC-MAIN-20220127072916-20220127102916-00215.warc.gz | 359,705,822 | 6,425 | Create a list containing the parameters of a single fitted parametric or flexible parametric survival model.
params_surv(coefs, dist, aux = NULL)
## Arguments
coefs A list of length equal to the number of parameters in the survival distribution. Each element of the list is a matrix of samples of the regression coefficients under sampling uncertainty used to predict a given parameter. All parameters are expressed on the real line (e.g., after log transformation if they are defined as positive). Each element of the list may also be an object coercible to a matrix such as a data.frame or data.table. Character vector denoting the parametric distribution. See "Details". Auxiliary arguments used with splines, fractional polynomial, or piecewise exponential models. See "Details".
## Value
An object of class params_surv, which is a list containing coefs, dist, and n_samples. n_samples is equal to the number of rows in each element of coefs, which must be the same. The coefs element is always converted into a list of matrices. The list may also contain aux if a spline, fractional polynomial, or piecewise exponential model is used.
## Details
Survival is modeled as a function of $$L$$ parameters $$\alpha_l$$. Letting $$F(t)$$ be the cumulative distribution function, survival at time $$t$$ is given by $$1 - F(t | \alpha_1(x_{1}), \ldots, \alpha_L(x_{L})).$$ The parameters are modeled as a function of covariates, $$x_l$$, with an inverse transformation function $$g^{-1}()$$, $$\alpha_l = g^{-1}(x_{l}^T \beta_l).$$ $$g^{-1}()$$ is typically $$exp()$$ if a parameter is strictly positive and the identity function if the parameter space is unrestricted.
The types of distributions that can be specified are:
• exponential or exp Exponential distribution. coef must contain the rate parameter on the log scale and the same parameterization as in stats::Exponential.
• weibull or weibull.quiet Weibull distribution. The first element of coef is the shape parameter (on the log scale) and the second element is the scale parameter (also on the log scale). The parameterization is that same as in stats::Weibull.
• weibullPH Weibull distribution with a proportional hazards parameterization. The first element of coef is the shape parameter (on the log scale) and the second element is the scale parameter (also on the log scale). The parameterization is that same as in flexsurv::WeibullPH.
• gamma Gamma distribution. The first element of coef is the shape parameter (on the log scale) and the second element is the rate parameter (also on the log scale). The parameterization is that same as in stats::GammaDist.
• lnorm Lognormal distribution. The first element of coef is the meanlog parameter (i.e., the mean of survival on the log scale) and the second element is the sdlog parameter (i.e., the standard deviation of survival on the log scale). The parameterization is that same as in stats::Lognormal. The coefficients predicting the meanlog parameter are untransformed whereas the coefficients predicting the sdlog parameter are defined on the log scale.
• gompertz Gompertz distribution. The first element of coef is the shape parameter and the second element is the rate parameter (on the log scale). The parameterization is that same as in flexsurv::Gompertz.
• llogis Log-logistic distribution. The first element of coef is the shape parameter (on the log scale) and the second element is the scale parameter (also on the log scale). The parameterization is that same as in flexsurv::Llogis.
• gengamma Generalized gamma distribution. The first element of coef is the location parameter mu, the second element is the scale parameter sigma (on the log scale), and the third element is the shape parameter Q. The parameterization is that same as in flexsurv::GenGamma.
• survspline Survival splines. Each element of coef is a parameter of the spline model (i.e. gamma_0, gamma_1, $$\ldots$$) with length equal to the number of knots (including the boundary knots). See below for details on the auxiliary arguments. The parameterization is that same as in flexsurv::Survspline.
• fracpoly Fractional polynomials. Each element of coef is a parameter of the fractional polynomial model (i.e. gamma_0, gamma_1, $$\ldots$$) with length equal to the number of powers plus 1. See below for details on the auxiliary arguments (i.e., powers).
• pwexp Piecewise exponential distribution. Each element of coef is rate parameter for a distinct time interval. The times at which the rates change should be specified with the auxiliary argument time (see below for more details).
• fixed A fixed survival time. Can be used for "non-random" number generation. coef should contain a single parameter, est, of the fixed survival times.
Auxiliary arguments for spline models should be specified as a list containing the elements:
knots
A numeric vector of knots.
scale
The survival outcome to be modeled as a spline function. Options are "log_cumhazard" for the log cumulative hazard; "log_hazard" for the log hazard rate; "log_cumodds" for the log cumulative odds; and "inv_normal" for the inverse normal distribution function.
timescale
If "log" (the default), then survival is modeled as a spline function of log time; if "identity", then it is modeled as a spline function of time.
Auxiliary arguments for fractional polynomial models should be specified as a list containing the elements:
powers
A vector of the powers of the fractional polynomial with each element chosen from the following set: -2. -1, -0.5, 0, 0.5, 1, 2, 3.
Auxiliary arguments for piecewise exponential models should be specified as a list containing the element:
time
A vector equal to the number of rate parameters giving the times at which the rate changes.
Furthermore, when splines (with scale = "log_hazard") or fractional polynomials are used, numerical methods must be used to compute the cumulative hazard and for random number generation. The following additional auxiliary arguments can therefore be specified:
cumhaz_method
Numerical method used to compute cumulative hazard (i.e., to integrate the hazard function). Always used for fractional polynomials but only used for splines if scale = "log_hazard". Options are "quad" for adaptive quadrature and "riemann" for Riemann sum.
random_method
Method used to randomly draw from an arbitrary survival function. Options are "invcdf" for the inverse CDF and "discrete" for a discrete time approximation that randomly samples events from a Bernoulli distribution at discrete times.
step
Step size for computation of cumulative hazard with numerical integration. Only required when using "riemann" to compute the cumulative hazard or using "discrete" for random number generation.
## Examples
n <- 10
params <- params_surv(
coefs = list(
shape = data.frame(
intercept = rnorm(n, .5, .23)
),
scale = data.frame(
intercept = rnorm(n, 12.39, 1.49),
age = rnorm(n, -.09, .023)
)
),
dist = "weibull"
)
summary(params)
#> parameter term mean sd 2.5% 97.5%
#> 1: shape intercept 0.55088444 0.20690627 0.3793033 0.9404121
#> 2: scale intercept 11.29702797 1.62742924 8.7760297 13.1101035
#> 3: scale age -0.08523438 0.02072153 -0.1221598 -0.0595469params
#> A "params_surv" object
#>
#> Summary of coefficients:
#> parameter term mean sd 2.5% 97.5%
#> 1: shape intercept 0.55088444 0.20690627 0.3793033 0.9404121
#> 2: scale intercept 11.29702797 1.62742924 8.7760297 13.1101035
#> 3: scale age -0.08523438 0.02072153 -0.1221598 -0.0595469
#>
#> Number of parameter samples: 10
#> Distribution: weibull | 1,867 | 7,683 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2022-05 | longest | en | 0.730755 |
https://virallistclub.com/21059/ | 1,627,160,493,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046150308.48/warc/CC-MAIN-20210724191957-20210724221957-00136.warc.gz | 620,442,809 | 12,917 | # How Many Cups Is 1 Liter
by -14 views
1 L 42267528198649 cup To convert 1 liters into cups we have to multiply 1 by the conversion factor in order to get the volume amount from liters to cups. A liter or litre is a unit of volume in the metric system.
Cooking And Baking Conversions Baking Conversions Cooking Measurements Cooking Conversions
### A liter is defined as the volume of a cube that is 10 centimeters on a side.
How many cups is 1 liter. How many liters are in 30 cups. We assume you are converting between liter and cup US. You can easily calculate how many cups there are in one liter.
This unusual liquid proportion may throw some off especially those who want precision when measuring recipe requirements. 1 L 4226752838 cup. What is 01 liters in cups.
So depending on what type of cups are converted the answer to the question of how many cups in a liter might be different. Swap units Amount. There are 4226752838 cup in a liter.
If you want to determine the number of cups in a liter simply multiply the value in liters by the conversion factor. 1 cubic meter is equal to 42267528198649 cups or 1000 liters. The calculation however varies greatly depending on which type of cups are being used.
Some types of cups are mentioned below. How many liter in 1 cups. It is a non-SI unit which recognizes the same volume unit as a cubic decimeter.
If the glass is measured in cups 3 liters equals about 13 cups of water. What is 1 cup in liters. There are approximately 42 US cups of water in a liter.
In the metric system 1 liter equals 1000 mL. The answer is 02365882375. 01 L to cups conversion.
One metric cup equals 250 mL. On the other hand in America 1 liter is equal to 422675283773 US. Conversion formula The conversion factor from liters to cups is 42267528198649 which means that 1 liter is equal to 42267528198649 cups.
One liter is equal to 4 metric cups. To calculate 1 Liters to the corresponding value in Cups multiply the quantity in Liters by 42267528198649 conversion factor. Therefore there are four cups in one liter in the metric system.
However if you want a more accurate answer the number of cups in a liter of water is 42268. 01 Liters 042267528 Cups rounded to 8 digits Display result as. An 8 ounce glass is equal to just under 14 of a liter which means that just over four 8 ounce glasses of water is equivalent to 1 liter.
1 Liter 42267528377 Cups US 1 Liter 4 Cups Metric Therefore there are 42267528377 US cups in one liter and 4 metric cups in one liter. 1000 250 4. You can view more details on each measurement unit.
In this case we should multiply 1 Cups by 02365882375 to get the equivalent result in Liters. Generally and quite roughly it is usually considered that one liter is equivalent to about four average cups. 1 L 42267528198649 cup To convert 18 liters into cups we have to multiply 18 by the conversion factor in order to get the volume amount from liters to cups.
1 Liters x 42267528198649 42267528198649 Cups 1 Liters is equivalent to 42267528198649 Cups. For Imperial System UK We often find recipes written for the UK audience it is logical as we share the same language. 1 Cup Metric 025 Liter Therefore there are 0236588236 liters in one US cup and 025 liters in one metric cup.
Gallon or about 236 milliliters. 1 cubic meter is equal to 1000 liter or 42267528198649 cups. To calculate 1 Cups to the corresponding value in Liters multiply the quantity in Cups by 02365882375 conversion factor.
If you are converting from liters to US cups then there are 42267528377 cups in a liter. Gallon or about 236 milliliters. 1 Cups x 02365882375 02365882375 Liters 1 Cups is equivalent to 02365882375 Liters.
A liter or litre is a unit of volume in the metric system. In this case we should multiply 1 Liters by 42267528198649 to get the equivalent result in Cups. A liter is defined as the volume of a cube that is 10 centimeters on a side.
There are about 3785 liters in a US. 1 L 42267528198649 cup To convert 17 liters into cups we have to multiply 17 by the conversion factor in order to get the volume amount from liters to cups. Customary cups and 416666666667 US.
1 Liter is equal to 4226752838 Cup. Cup is a unit of volume equal to 116th of a US. A liter is a non-metric unit of volume which is equal to the volume of a cube with 10 cm on each side.
Imperial cups are rarely used but 352112676056 Imperial cups equal 1 liter. Conversion formula The conversion factor from liters to cups is 42267528198649 which means that 1 liter is equal to 42267528198649 cups. Type in your own numbers in the form to convert the units.
Use this page to learn how to convert between cups and liters. Note that rounding errors may occur so always check the results. 1 cups to L conversion.
Note that rounding errors may occur so always check. A liter is defined as the volume of a cube that is 10 centimeters on a side. A liter or litre is a unit of volume in the metric system.
If you want to determine the number of liters in a cup simply multiply the value in cups by the conversion factor. Liter or cups The SI derived unit for volume is the cubic meter. Canadian cups are slightly smaller and 43993850 Canadian cups make 1 liter.
Conversion formula The conversion factor from liters to cups is 42267528198649 which means that 1 liter is equal to 42267528198649 cups. Cup is a unit of volume equal to 116th of a US.
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READ: How Many Feet Is 12 Meters | 1,678 | 7,257 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2021-31 | longest | en | 0.922193 |
https://www.globalfinanceschool.com/book/statistics/characteristics-normal-probability-distribution | 1,571,272,162,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986672431.45/warc/CC-MAIN-20191016235542-20191017023042-00351.warc.gz | 908,714,417 | 16,792 | # Statistics
## Characteristics of the Normal Probability Distribution
We will provide an example to accompany the explanation. This example relates to the height of ten year-old children:
1. A continuous variable - the normal probability distribution reflects the distribution of a continuous variable, which can receive any numerical value, i.e., whole., numbers (for example, 101 centimeters), numbers with fractions (for instance, 101.25 centimeters), positive numbers and negative numbers although there are no negative numbers in our example.
2. The height reflects a probability - the height of the previous curve and every number reflects the chances of that number occurring as compared to the other numbers. The further away we get from the center (either to the left or the right), then the smaller is the chance of the occurrence.
3. The center is the expectation - the center result reflects the average, and the chance of getting it is higher than any other number. The reason why the center result is the average is that the curve is symmetric around the center. This means that for every result to the right of the center that contributes to increasing the average, there is also a result that is at the same distance to the left that has an equal chance of occurring, which contributes an equivalent degree toward decreasing the average.
4. Symmetry - the normal probability distribution is symmetric relative to the average. This means that the chances of obtaining a result exceeding the average by 10 is equal to the chance of receiving a result that is smaller than the average by 10.
5. The probabilities are known in advance.
The probabilities, which are equivalent to the areas under the curve on both sides of the average are distributed as follows:
1. Each of the areas above the segment (over the X axis) with a length of one standard deviation (1?) from the average (i.e., one to the right and one to the left) totaling 34% of the area within the normal curve. The area above a segment with a length of 2 standard deviations on both sides of the average (i.e., from 1 standard deviation to the left of the average to 1 standard deviation to the right of it) therefore totals 68% of the area within the normal curve.
Diagram A
2. Each of the areas above the segment with a length of 2 standard deviations (2?) from the average (i.e., one to the right and one to the left) totals 47.5% of the total area within the normal curve. The area above a segment with a length of 4 standard deviations on both sides of the average (i.e., from 2 standard deviations to the left of the average to 2 standard deviations to the right of it) therefore totals 95% of the total area within the normal curve.
Diagram B
3. Each of the areas above the segment with a length of 3 standard deviations (3?) from the average (i.e., from one to the right to one to the left) totals 49.85% of the total area within the normal curve. The area above a segment with a length of 6 standard deviations on both sides of the average (i.e., from 3 standard deviations to the left of the average to 3 standard deviations to the right of it) therefore totals about 99.7% of the total area within the normal curve.
Diagram C
Marking intervals on the X axis
The average is denoted by the Greek letter μ (mu).
The standard deviation is denoted by the Greek letter σ (sigma).
A point 1 standard deviation to the right of the average is denoted by μ + 1σ.
A point 1 standard deviation to the left of the average is denoted by μ1- σ.
The distance between these two points is denoted by μ +/- σ.
In general:
A point X standard deviation to the right of the average is denoted by μ + Xσ.
A point X standard deviation to the left of the average is denoted by μ - Xσ.
The distance between these two points is denoted by μ +/- Xσ.
to the right and one to the left) totals 47.5% of the total area within the normal curve.
The area above a segment with a length of 4 standard deviations on both sides of the average (i.e., from 2 standard deviations to the left of the average to 2 standard deviations to the right of it) therefore totals 95% of the total area within the normal curve.
3. Each of the areas above the segment with a length of 3 standard deviations (3?) from the average (i.e., from one to the right to one to the left) totals 49.85% of the total area within the normal curve.
The area above a segment with a length of 6 standard deviations on both sides of the average (i.e., from 3 standard deviations to the left of the average to 3 standard deviations to the right of it) therefore totals about 99.7% of the total area within the normal curve.
The average is denoted by the Greek letter ? (mu).
The standard deviation is denoted by the Greek letter ? (sigma).
A point 1 standard deviation to the right of the average is denoted by ? + 1?.
A point 1 standard deviation to the left of the average is denoted by ? - 1?.
The distance between these two points is denoted by ? +/- ?.
The Significance of Areas Within the Curve
As noted previously, the areas within the curve represent probabilities. In our example, the probability of finding a child whose height is in the segment between μ - σ and μ + σ is 68%.
In other words:
Of every 1,000 children that we meet in the street, the height of 680 of them (68%) will be within the segment between μ - δ and μ + δ.
Furthermore:
Of every 1,000 children we meet in the street, the height of 950 of them (95%) will be in the segment between μ - 2σ and μ + 2σ, and the height of 997 of them (99.7%) will be in the segment between μ - 3σ and μ + 3σ.
Only 3 of every 1,000 children will be outside the segment between μ - 3σ and μ + 3σ.
Characteristics of the Normal Probability Distribution530 | 1,322 | 5,767 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2019-43 | latest | en | 0.929514 |
http://spmath81610.blogspot.com/2010/10/justins-sesame-street-video-post.html | 1,531,862,690,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589902.8/warc/CC-MAIN-20180717203423-20180717223423-00633.warc.gz | 355,846,518 | 19,929 | ## Monday, October 18, 2010
### Justin's Sesame Street Video Post
Our Math group was Justin and Nicholas
Ratio:
2 term ratio: Compares 2 quantities measured in the same units.
Example: 5:9
3 term ratio: Compares 3 quantities measured in the same units.
Example: 3:5:9
Part to part ratio: Compares different parts of the group to each other.
Example: 7:5
Part to whole ratio: Compares 1 part of the group to the whole group.
Example: 9:30
Rate:Compares two quantities measured in different units.
Example: 72 beats/ min
Unit rate: A rate in which the send term is 1.
Example: 20 km an hour
Unit price: A unit used when shopping, often shown per 100g or per 100ml, makes it easier for shoppers to compare costs of similar items.
Example: \$2.19/100g
Proportional Reasoning:A relationship that says two ratios or two rates are equal, can be written in fraction form.
Example: 10 erasers cost \$2, how much will 20 erasers cost?
set up:
_________=__________
Here is a link to the video that we chose to do, its about the letter R.
Here is our remake of the video
#### 6 comments:
1. Great job, Justin ! Your video was really well done, but short. Your blog is getting better. I really like hwo you changed the font. Keep it up !
2. Good job! Nice video but it was only 31 seconds. You changed the font to show the important words. You could of even used colour. Good job!
3. Nice Post you got there Justin :),You explained rates,ratio,and proportion real well!But,like me,our video was a lil' short..Maybe,we can make it a lil' longer next time :/
4. Nice job Justin. Your video was kept simple which was nice. It was good that you included all the definitions but maybe you could have added examples and pictures. Overall, good job!
5. Good job Justin! You're video got right to the point and so did your blog. It was very neat but next time, try to add some examples, pictures, and colour.
6. Great Job Justin i know we should of made the video longer.But i like how you wrote what rate,Proportional Reasoning,Ratio:
really neatly keep up the good work justin | 528 | 2,076 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2018-30 | latest | en | 0.947589 |
http://dailydoseofexcel.com/archives/2014/11/17/cult-of-the-flying-spaghetti-vlookup/ | 1,675,760,099,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500392.45/warc/CC-MAIN-20230207071302-20230207101302-00551.warc.gz | 13,788,216 | 23,492 | # Cult of the Flying Spaghetti VLOOKUP
Sumit Bansal’s post VLOOKUP Vs. INDEX/MATCH – The Debate Ends Here! sparked some great discussion on the merits of VLOOKUP vs INDEX/MATCH, including at Oz du Soleil’s lighthearted rebuttal at The Anti-VLOOKUP Crowd Is Out In The Streets Again!
I especially love Peter B’s comment at Sumit’ post:
My opinion is that VLOOKUP and HLOOKUP are simply over-specialised legacy functions and Excel would be all the better for ‘pruning’ them out. I do use VLOOKUP occasionally when I have a 2-D range; the search array happens to be on the left; I only wish to return a single field; I am sure the data is clean and the match will always succeed. Despite that, I think the value they bring to the bloated zoo of Excel functions is not worth their keep.
Of course, NOTHING can ever be cleaned out of Excel, for good reason…otherwise all the millions of complex black-box spreadsheets that continue to function just fine long after the person who constructed them moved on to another task, job, or incarnation will break. Not to mention all those fantasy football spreadsheets. MS has backwards-compatibility issues that are beyond belief really.
At the same time I agree with Bob Phillips’ point at Sumit’s post:
The biggest selling point to me is that VLOOKUP is easy to teach to people, and it sticks, INDEX/MATCH less so.
But I disagree with Bob’s point that VLOOKUP can be/is just as flexible as INDEX/MATCH, merely because we can do stuff like this with it:
=VLOOKUP(“z”,CHOOSE({1,2},\$B\$1:\$B\$10,\$A\$1:\$A\$10),2,FALSE)
=VLOOKUP(“g”,\$D\$2:\$H\$15,MATCH(“Qtr2”,\$D\$2:\$H\$2,0),FALSE)
Just as flexible? Maybe, if you bend it double with brute force. Just as fast after you’ve made it just as flexible? Not likely. Any more understandable than the INDEX/MATCH equivalent? Not in my experience.
In fact, I feel a rude joke coming on:
Young analyst with unlit cigarette in mouth, having just consummated his first VLOOKUP: Has anyone got a match?
Analyst of distinguished years: Yes. Your VLOOKUP and my arse.
If MS were designing Excel from scratch – and I was on the committee that was deciding whether to include a dumbed-down function to do a subset of lookups based on hard-coded input parameters and a fixed data layout – then I’d make a case for not including it. Not just because of those quite reasonable complaints, either. But also because of evolution. A user that is forced to learn INDEX and MATCH due to lack of suitable alternatives is be better placed to evolve into a higher Excel lifeform than one that hasn’t looked beyond VLOOKUP.
(I’d make an exception if a major competitor – say Lotus – had a VLOOKUP function in their beast. But only in that specific case.)
Formulas remind me a bit like DNA: just by stringing a few different base-pairs together in the right order, you can build a mouse. Or a Human, with a few extra tweaks. Similarly, with a few good formula combinations under your belt, you can conquer most problems you’re likely to come across. INDEX and MATCH are not just formulas in their own right, but are the formula equivalent of DNA basepairs: they give users a peek into other formula ecosystems that they can gradually spread into and colonize. VLOOKUP ain’t one of those base pairs. It’s Neanderthal.
Hey, don’t get me wrong: I’m fine that it’s in the fossil record. I’m happy enough to have one in my spreadsheet, just as I’m happy enough to have an appendix that doesn’t burst.
## 23 thoughts on “Cult of the Flying Spaghetti VLOOKUP”
1. Oz says:
The debate continues. LOL!
I’m glad you mentioned Bob Phillips’ point: VLOOKUP is significant in the learning of Excel.
And why this means so much to me is because of the students and their learning. But it goes further than that: for a lot of people VLOOKUP is all they need. Their data isn’t in large volume and isn’t overly complex.
So often, someone comes to me with an issue that takes up many hours per week. They might need:
– Text-to-Columns
– A tutorial in Absolute/Relative References
– IF
– VLOOKUP
BOOM! And they’re back to their real job. It’s only developers who think VLOOKUP is a waste.
The coordinator at a nonprofit who’s managing 200 kids, field trips, lunches, permission forms and parents has enough to deal with. He’s the one who needs VLOOKUP unless there’s a really doggone good reason to bring him into the syntax of two nested functions. And there are way more of him than us developers.
I like how you describe DNA. That’s exactly how I see the beautiful entirety of Excel. And I’d vote to keep the VLOOKUP molecule.
2. Hi Oz. Good points. Re Their data isn’t in large volume and isn’t overly complex.…well, it isn’t in large volumes nor overly complex until it is. Sooner or later, they will have to handle more and more data. They might even start to feel confident that they can handle large data. And they know it’s the exact same VLOOKUP that they’re going to use, so it’s not like there’s any barrier to them pointing a VLOOKUP at a hundred thousand rows as opposed to just a hundred. So those ranges will get bigger. Gradually perhaps…but I’ve never seen spreadsheets get smaller and less complex. Only bigger and more.
And when their data and/or requirements starts to grow in volumes – and they start to do more and more complex things as they grow their capability – they’ll continue to use their outdated paradigm, because that’s all they know. If they’re lucky enough to know that that these things called ‘Help Forums’ exist, then maybe they’ll finally post a question there, after years of ignoring niggling, increasingly frustrated symptoms. And if they’re lucky, when they do post a fairly non-specific question like “Excel Can’t Handle It”, hopefully they’ll get someone like us that helps them address underlying symptoms, rather than some well intentioned deckchair shuffling.
Re It’s only developers who think VLOOKUP is a waste.. True. But only because it’s only developers that know this stuff. We need to pass this knowledge from developers to users, because there’s more users than developers, and so users experience the bulk of the pain. We need to give users the knowledge to reclaim fast spreadsheets. We need to help users become ‘developer grade’ in those things they do often that could be done much, much better with just small tweaks in their behavior, and that save them much, much grief.
I’m working on a little manifesto that covers this, called Excel for Superheroes and Evil Geniuses.
3. And the fun is that we (people who consider themselves Excel devs) can then make a livelyhood of helping people who have gotten into trouble using many VLOOKUPs causing their models to grind to a calculation halt :-)
Dozens of columns of VLOOKUPs getting data from the same row of the same table. Why is my spreadsheet slow? Well, because you made it slow.
4. Good points Jeff. I am one of those who learnt Vlookup and Index/Match at the same time, and with more flexibility in Index/Match, I got biased towards it. I am sure when someone is learning Vlookup, he/she thinks it’s a complicated formula with many arguments. May be it’s time they feel the same and learn Index/Match as well.
Note: The link to Excel for Superheroes and Evil Geniuses is broken.
5. Jan Karel: The sad thing is that too often, people don’t know they’ve got an easily solvable problem. They just think that Excel can’t handle their genius, and so they switch to manual.
Sumit: I wish whoever taught you had taught me. My thoughts exactly on VLOOKUP…sure, it might be less complicated for some people than learning INDEX/MATCH…but surely only marginally less complicated.
6. Oz says:
I don’t disagree that there’s a time for VLOOKUP. Once, I inherited a spreadsheet that had at least 1000 VLOOKUPS in it and sometimes it wouldn’t even open.
My point is that all of this is driven by context. The anti-VLOOKUP case is often made by painting a particular context: when the data gets huge; when you need to look left instead of right. Ok. No disagreement. But you have to be careful about the assumptions that you smuggle in. In my blogpost I presented 3 scenarios and mentioned that this whole debate is a false dichotomy.
The choices are: do nothing, VLOOKUP, INDEX/MATCH, manual
How do we answer the question of which option is best? If there are 2 items to retrieve, go manual: COPY/PASTE.
If a person is trying to complete a list and they’re going to Paste-As-Values when it’s done: VLOOKUP.
If your look up value is in the middle of the lookup range and you need to look both left and right: INDEX/MATCH. No question.
If you’re trying to complete a list of fax numbers that you’ll never send a fax to: leave it alone.
It’s all context.
And one thing has gotten clear to me after teaching a lot: not everyone is trying to master Excel. The travel agent is trying to get people onto cruise ships. So, by giving them what they need–no more and no less–it’s a show of respect for what’s important to them. And believe me, I warn people if I see a problem.
I went into a small company and the owners wanted me to teach them some things that a person could only get if they’re elbow-deep in data every day. We eventually agreed that training wasn’t a good option because the guys wore too many hats. Everything from finding new business to driving the forklift.
In that case, neither VLOOKUP nor INDEX/MATCH were worth much.
Again: it’s the context.
7. Agreed, context. Only problem is, you can’t foretell in what context people will be using things in future. This reminds me of the OFFSET/INDEX Volatile/Non Volatile debate, where my advice is summed up at a blog post I did over at Chandoo some time back that you commented on, Oz. My salient point was this:
Too much reliance on volatile functions *might* trigger large parts of a model to be recalculated needlessly. But it’s worth remembering that this is only going to be noticeable in particularly big spreadsheets. However, if you know of an alternative formula combination that does exactly the same thing as a volatile formula, then I’d suggest that you get into the habit of using that instead whenever you can. That way you won’t inadvertently have issues when it really matters. And I’d suggest that if you don’t have much experience of functions and performance, then perhaps it’s safest to simply err on the side of caution and steer clear of volatile functions altogether.
Not only do I see little down side to avoiding volatile formulas, but I see a significant upside: I’ve seen plenty of large models built by the likes of the big 4 accounting/consulting firms that make heavy use of volatile functions, and that consequently have recalculation times so long that they are effectively unusable. Stripping out the volatile formulas from these models has resulted in delays from data entry falling from upwards of two minutes to well under a second. Not to mention that users can now work on other files while these models are open, without fear of triggering an avalanche of unnecessary and pointless recalculation. Had these model builders known to avoid volatile functions, they would have saved users a lot of grief.
8. Elias says:
Oz,
Do you really believe that Vlookup is easier to learn or is just easier to teach? Have you ever tried to teach Match/Index first?
Thanks
9. One thing is for certain: VLOOKUP is easier to learn than unlearn!
10. Elias says:
@ Jeff, not doubt about it!
It would have been great if I had learned the concept of match first, then learn VLOOKUP would have been a lot easier. At the end match is the strongest part of Vlookup, isn’t?
Regards
11. Oz says:
WOW! I don’t recall the debate over at Chandoo’s house. This thing is getting around.
Because you emphasize the word *might*, we probably agree more than we disagree. When you talk about the Big 4 accounting firms, you’ll get no disagreement from me. And it’s the rare situation where I even leave VLOOKUPS in a live workbook. A huge spreadsheet with a lot of volatile functions is indeed a sign of poor development. Even if it’s not huge right now but continues to grow, it’s a ticking time-bomb.
12. So did any of you wonder about the significance of the title of this blog post. It’s a nod to another interesting debate. (Not that I intend to start a debate on that other debate here. I’m just foolin’ around)
13. Oz says:
Elias,
I think it’s easier to teach someone the components of VLOOKUP:
1. What do you want me to look for?
2. Where should I look?
3. What do you want if I find it?
4. Exact match, or not?
Nesting MATCH inside INDEX means explaining the syntax that we’re replacing one component of INDEX with a function called MATCH. Where the context warrants it, we have to suck it up and get through it. Where VLOOKUP works, we go with it.
Again, I’m typically dealing with smaller entities. A guy was trying to match up 3 lists of maintenance records of several vehicles and merge them into a single clean list. They were all less than 100 rows each. VLOOKUP, copy, paste-as-values, look for any duplicates.
We, as power users, could do that without thinking. But he was trying to do it manually and it wasn’t going so well.
It was an infrequent need on a dataset that wasn’t growing very fast.
Elias, one thing that I do agree with you on is that I would like to have known MATCH way before I ever used it.
14. Oz says:
Yeah! That was a hilarious title.
I did think of the Flying Spaghetti Monsters but I don’t know what they are. Was that a movie?
15. Elias says:
Oz,
Beside point 3 is not the same way that you would teach match? Then with another small effort you could leave a student with 3 functions instead of 1. I believe we tend to think that Vlookup is easier to teach/learn because we learned it first. :)
Regards
16. Jeff, thanks for drawing my attention back to your title, otherwise I had assumed it was just you being you. The Spaghetti Monster cult is great, and I’m pointlessly proud that the founder lives just down the freeway from me.
As to the main topic of VLOOKUP versus INDEX/MATCH, I don’t think it matters. As much as I love Excel, I think of it as a vast unstructured wilderness where most users do whatever works until it breaks, and then figure out how to make it work again, or not. The idea of somehow guiding them to what they need before they need it is laudable, but generally ineffective. The best we can do is leave directions out of the wilderness for those in need, as Sumit did. Then they’ll do a search on “Vlookup to the left” and find many helping hands, such as yours, to pull them out of the morass.
I think :)
17. Doug: Spot the difference:
In fact, the cult has the perfect blend of art and science:
… a vast unstructured wilderness where most users do whatever works until it breaks, and then figure out how to make it work again, or not.
18. Thanks Jeff!
As to the differences: The second one uses a VLOOKUP, whereas I assume the first uses a lot of GOSUB statements
19. Oz says:
Elias, I don’t know the point you’re trying to make.
I’ve acknowledged that INDEX/MATCH has its place and that VLOOKUP has weaknesses. Excel and data management are so much bigger than this. There are over 300 functions and countless features, and at least 3 ways to do almost anything–including doing everything in VBA.
This is like a bunch of jazz musicians sitting around discussing Locrian mode. Meanwhile, the fans are clamoring for Lady Gaga. Lady Gaga is talented and delivers what FANS want and can feel. Jazz musicians play music for jazz musicians.
20. Elias says:
Oz, My only point is that Vlookup is not easier to teach/learn than Match & Index. It is just an easy statement to justify the preference of Vlookup. I bet 50% of the Excel forums question won’t exist if we push the use of Index/Match instead of Vlookup.
Regards
21. Suresh says:
Very interesting debate VLOOKUP Vs INDEX/MATCH. During my early days, to make Excel to look left, I made col_index_number a negative. It didn’t work. But now still learning, I doubt that I have to make even the Excel range to look Right to Left, if I have to do what INDEX/MATCH does. If Excel can be forced to see a “reverse range”, B:A instead of current A:B, we have chances of finding values on the left. This will bring everlasting glory to VLOOKUP!
Posting code? Use <pre> tags for VBA and <code> tags for inline. | 3,778 | 16,413 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2023-06 | longest | en | 0.920734 |
https://ncertmcq.com/tag/ncert-solutions-for-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-3/ | 1,675,699,757,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500356.92/warc/CC-MAIN-20230206145603-20230206175603-00737.warc.gz | 419,672,262 | 11,695 | ## NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3
NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2.
Board CBSE Textbook NCERT Class Class 10 Subject Maths Chapter Chapter 3 Chapter Name Pair of Linear Equations in Two Variables Exercise Ex 3.3 Number of Questions Solved 3 Category NCERT Solutions
### NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3
Question 1.
Solve the following pair of linear equations by the substitution method,
(i) x + y = 14, x – y = 4
(ii) s – t = 3, s/3 + t/2 = 6
(iii) 3x – y = 3, 9x – 3y = 9
(iv) 0.2x + 0.3y = 1.3, 0.4x + 0.5y = 2.3
Solution:
From equation (i),
x + y – 14 ⇒ y = 14x
Putting the value ofy in equation (ii), we get
x – (14 – x) = 4 ⇒ x – 14 + x = 4 ⇒ 2x = 4 + 14
2x = 18 ⇒ x = 9
Now, puttingx = 9 in equation (i), we have
9 + y = 14 ⇒ y = 14 – 9 ⇒ y = 5
so, x = 9, y = 5
∴ y can have infinite real values
∴ x can have infinite real values because x = $$\frac { y+3 }{ 3 }$$
Question 2.
Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
Solution:
Equations are 2x + 3y = 11
and 2x – 4y = -24
From equation (i)
2x = 11 – 3y
Putting this value in equation (ii), we get
11 – 3y – 4y = -24 ⇒ 11 – 7y = -24 ⇒ – 7y = – 35
y = $$\frac { 35 }{ 7 }$$ ⇒ y = 5
Putting y = 5 in equation (i). we have
2x + 3 x 5 = 11 ⇒ 2x + 15 = 11 ⇒ 2x = 11 – 15 ⇒ 2x = -4 ⇒ x = -2
Now. putting the value of x andy in equation
y = mx + 3 ⇒ 5 = -2m + 3 ⇒ 2 = -2m ⇒ m = -1
Question 3.
Form the pair of linear equations for the following problems and find their solution by substitution method.
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. Later, she buys 3 bats and 5 balls for ₹ 1750. Find the cost of each bat and each ball,
(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km₹ How much does a person have to pay for travelling a distance of 25 km₹
(v) A fraction becomes 9/2, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and denominator it becomes 5/6, Find the fraction.
(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Solution:
(i) Let 1st number be x and 2nd number be y.
Let x >y
1st condition :
x – y = 26
2nd condition :
x = 3y
Putting x = 3y in equation (i)
3y – y = 26 ⇒ 2y = 26 ⇒ y = 13
From (ii)
x = 3 x 13 = 39
∴ One number is 13 and the other number is 39.
(ii)
Let one angle be x and its supplementary angle = y
Let x > y
1st Condition :
x + y = 180°
2nd Condition :
x – y = 18° ⇒ X = 18° + y
From equation (ii), putting the value ofx in equation (i),
18° + y + y = 180° ⇒ 18° + 2y = 180°
2y = 162° ⇒ y = 81°
From (ii) x = 18° + 81° = 99° ⇒ x = 99°
∴ One angle is 81° and another angle is 99°.
(iii)
Let cost of 1 bat = ₹x and cost of 1 ball = ₹y
1st Condition:
7x + 6y = 3800
2nd Condition:
3x + 5y = 1750
From equation (ii), we get
putting x = 1750-5y/3 in equation (i), we get
Cost of one bat = ₹ 500 and cost of one ball = ₹ 50.
(iv) Let fixed charges be ₹.v and charge for per km be ₹y.
A.T.Q.
1st Condition :
x + lOy = 105
2nd Condition :
x + 15y = 155
From equation (i), we get
x= 105 – 10y
Putting this value in equation (ii), we have
105 – 10y + 15y = 155 ⇒ 105 + 5y = 155
⇒ 5y = 155 – 105 ⇒ 5y = 50 ⇒ y = 10
Now, puttingy = 10 in equation (i), we have
x + 10(10) = 105 ⇒ x + 100 = 105 ⇒ x = 5
Fixed charges is ₹ 5 and charges per km is ₹ 10.
3rd Condition :
For distance of 25 km
x + 25y = 5 + 25(10) = 5 + 250 = 255
Amount paid for travelling 25 km is ₹ 255.
(v) Let numerator be x and denominator be y.
∴ Fraction is x/y
A.T.Q.
1st condition :
2nd condition :
(vi) Let present age of Jacob be x years and that of his son bey years.
A.T.Q.
1st Condition :
x + 5 = 3(y + 5) ⇒ x + 5 = 3y + 15 ⇒ x – 3y = 15 – 5 ⇒ x – 3y = 10
2nd Condition:
x – 5 = 7(y – 5) ⇒ x – 5 = 7y – 35 ⇒ x = 7y – 35 + 5
⇒ x = 7y – 30
Putting the value of ‘x’ in equation (i), we get
7y – 30 – 3y = 10
4y – 30 = 10
4y = 40 y = 10 ⇒ y = 10
putting the value of y in equation(ii), we get
x = 7(10) – 30 = 70 – 30 ⇒ x = 40
Hence, the present age of Jacob is 40 years and that of his son is 10 years.
We hope the NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3 help you. If you have any query regarding NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3, drop a comment below and we will get back to you at the earliest. | 1,876 | 5,189 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.875 | 5 | CC-MAIN-2023-06 | latest | en | 0.817131 |
http://lukepalmer.wordpress.com/2007/09/22/reply-to-platonism/ | 1,386,531,906,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163800358/warc/CC-MAIN-20131204133000-00092-ip-10-33-133-15.ec2.internal.warc.gz | 108,557,175 | 21,501 | Here’s a reply to a comment
that was left about my recent post “Platonism”. The discussion is
getting long and involved, so I thought I’d make a new post. And to
anonymous (the poster), don’t worry about the comment length. I’m only
posting anew to draw attention to the interesting discussion.
So, without further ado, the short version: For me, the n of your
sentence ‘But n [declared via 'there exists an n such that M halts in n
steps'] is fantastic; it is not a concrete number; it cannot be written
1+1+1+1+1+1+… some finite amount of times.”, needs to be a plain
normal standard natural number (i.e. element of N = { 0, S(0), S(S(0)),
… }), as you’ve introduced n as giving the /number of steps/.
But in the context of that definition, we were still working in PA,
which is incapable of saying “n is a standard natural”
without giving some other kind of constraint (for example, being less
than a number written S(S(S(…S(0))))). I’ll go into more detail when
I discuss Goodstein’s Theorem below, which actually provides a nice
context for discussing nonstandard naturals.
As meta language, I’ll use a Haskell-like language which does not
have ordinals (this will become relevant in a second). As object
language, I’ll use the untyped lambda calculus. Without further
-- I'll use Goodstein's Theorem
-- as example. Briefly, it
-- states that every Goodstein sequence terminates, i.e. that G(n) is finite
-- for all n in N = { 0,1,... }. It is unprovable in PA, but can be proved with
-- cool ordinal arithmetic.
exampleExp :: Nat -> Exp
exampleExp n = ...lambda expression which evaluates to some value if G(n) is
finite and bottoms otherwise...
-- eval (exampleExp n) terminates iff G(n) is finite.
Now my question: In my opinion, eval (exampleExp n) halts for every
n::Nat, as we know that every Goodstein sequence is finite. But from
does not halt for some n :: Nat” would be consistent, as we cannot prove
the finiteness of all Goodstein sequences, as our meta language does not
have ordinals.
In short, I see the finiteness of all Goodstein sequences as an
absolute truth; I accept this truth even if we cannot prove it in some
formal systems.
First things first, the problems I was talking about are
fundamentally different from this question in that the halting problem
is not solvable by any formal system (assuming Church’s thesis).
But there’s still a lot of interesting stuff to be reaped from your
question.
Just because your meta language doesn’t have ordinals doesn’t mean
Goodstein’s theorem is not provable (well, unless Goodstein’s theorem
gives rise to ordinals :-). But what we can say is that if Goodstein’s
theorem is unprovable in your meta language, then it is consistent with
nonstandard naturals; i.e. Nat might denote more than just the set of
things in { 0, 1, 2, … }.
We can see this by looking at the negation of Goodstein’s theorem,
which looks like “exists n. forall k. not Goodstein(n,k)” (where
Goodstein(n,k) means the Goodstein sequence starting at n reaches 0 in k
steps). Let’s call this sentence NG, and your meta language S. If S
does not prove Goodstein’s theorem, then S+NG is consistent (if not,
that would be a proof). By the completeness theorem, then, S+NG has a
model in ZFC. And what the heck is n from “exists n. …” in that
model? It had better not be one of { 0, 1, 2, … }. So the model of
Nat in S+NG can’t be isomorphic to the set N from set theory; i.e. S+NG
actually asserts the existence of nonstandard naturals.
It is useless to think of the nonstandard naturals as actually
existing, though. n is merely a figment of the finite reasoning
available to the proofs in S. If proofs could be infinitely long, then
NG would be inconsistent with S (as well as a myriad of other things,
such as PA being complete (and thus inconsistent? I don’t know if the
incompleteness theorem applies if proofs are allowed to be
infinite)).
So now the difference between the halting problem and Goodstein’s
theorem: PA does not “know” that Goodstein’s theorem applies to it, but
ZFC knows. That is, assuming ZFC is consistent, then Goodstein’s
theorem about PA is true. But ZFC does not know everything about PA.
I seem to recall a game-theoretic theorem in PA which employed a large cardinal
axiom. But it’s pretty easy to show that there are statements in PA
that ZFC cannot prove true or false about its model of PA1. ZFC’s also has got its own bundle of undecidable issues, the continuum hypothesis to name one. But we can use a bigger system that models ZFC and possibly prove the continuum hypothesis one way or the other.
And now I just had an ephiphany… I was going to say “you can keep
expanding the system up and making more and more abstract axioms, but
there is a single Turing machine which evades them all”. That is not
true though. Obviously, you can add axioms “such-and-such Turing
machine does not ever halt”, and if it actually doesn’t (Platonically
speaking), then of course that is consistent. Then it seems possible
that we may find more and more “obvious truths” about mathematics, and
those will start proving that more and more Turing machines don’t halt.
For any given Turing machine, we may eventually find a “natural” axiom
which proves it doesn’t halt. If that were the case, it would mean that
the set of axioms about the universe is not only infinite, but
non-recursive. Knowing the universe, that seems reasonable :-).
If not, though, then there is a Turing machine which evades all of
our reasoning. This also seems reasonable, since there are machines as
small as 5 states and 2 symbols whose halting problems are yet unknown,
for example:
State Read 0 Read 1
-------------------------
a 1 L b 1 R b
b 1 R c 0 L e
c 0 R d 0 L a
d 1 L a 0 R d
e -halt- 0 L c
I hope that cleared some of the blocks making you believe that this area is in any way clear :-).
To answer another question, nonstandard naturals have very little to do with the ordinals from
set theory. All countable nonstandard models of arithmetic are isomorphic, so we know that the
nonstandards we got from negating Goodstein’s theorem are the same ones we get by standard application
of the compactness theorem. There’s
no least nonstandard natural (as omega is to the ordinals); rather, they look like the lexographic
ordering of Q × Z; for each rational number there is a copy of the integers (both positive
and negative). Of course they are all greater than the standard naturals. They satisfy
every first-order sentence provable by PA. A classic example is that the twin prime conjecture
is true if and only if there is a nonstandard twin prime, because the twin prime conjecture is
stated as “forall a. exists b > a. ‘b and (b+2) are prime’”, which,
if true, must hold for nonstandard a’s as well.
Funny coincidence, a program computing the Goodstein sequence of a number was one of the
first Haskell programs I ever wrote. :-)
1Since PA is turing complete, it can embed the axioms of
ZFC as Gödel numbers. You can thus construct a statement of PA
that says “ZFC is consistent”. And of course, because of the
incompleteness theorem, ZFC cannot prove this statement true or
false.
## 3 thoughts on “Reply to Platonism”
1. anonymous says:
Wow, thanks: I think I’ve grokked it now :) (although I’m still a bit fuzzy
about the details, but I believe that this is not substantial). To whom it
interests, here is my current understanding. The key was to differentiate
between the different worlds we talk about (physical universe, PA, ZFC) and to
realize that objects of some system A can not simply be compared with objects
of a different system B — the Goodstein sequences of PA are not the same
Goodstein sequences as these of ZFC. For a summary, jump to the part marked
with “##############”.
Consider the real, physical, every-day world. In this universe, objects which
exist include desks, books, and Linux computers. Objects which do not exist
include numbers, sequences, sets, and Turing machines.
In this world, it is possible to write a Haskell program which enumerates (what
we think is) the* Goodstein sequence of some large number (I mean bit pattern,
of course), say, 10^1234. When we run this program and come back a day later,
there are two possibilities:
1. Our Haskell program exit()ed. or:
2. Our Haskell program did not yet exit().
What conclusions about the* Goodstein sequence on 10^1234 can we draw from
either possibility? None! The real, physical, every-day world — the universe
which we’re considering at the moment — is not an idealized mathematical
model; bugs and hardware errors etc. (insert your favourite eventuality here)
are all possible and might have influenced the run of our program.
Of course, such an answer (to recall, the answer is “we can not say anything
about the* Goodstein sequence on 10^1234″) is unsatisfactory. Therefore we
invent idealized mathematical models:
Consider the world of PA. In this universe, objects which exist include
natural numbers, Goodstein sequences, and Turing machines**. Objects which do
not exist include ordinal numbers and desks, books, etc.
In this universe, it’s possible to give the definition of a Turing machine
which will (similar to our Haskell program) enumerate the PA-Goodstein sequence
on the PA-natural number 10^1234; let’s name this Turing machine T.
As PA does not have an in-built notion of “halting”, we (/we/!) have to make up
a definition of halting; let’s define: We say that a PA-Turing machine M halts
iff: exists n. stateAfterRunningForNSteps(M, n) = HALT_STATE (hand-waving a
bit)
Let’s assume that PA can not prove that T halts, i.e. (per our definition
above) that exists n. stateAfterRunningForNSteps(T, n) = HALT_STATE. What
conclusions about the PA-Goodstein sequence on PA-natural 10^1234 can we draw
from this? None — PA is consistent with both T halting and T not halting, i.e.
PA is independent from the haltingness of T.
We can, however, create a new system, based on PA, which includes “T halts”*** as
an additional axiom; call this system PA1. In this world, a PA1-Turing machine
which enumerates the PA1-Goodstein sequence on PA1-natural 10^1234 halts. (And
this proposition can be proved trivially by using the newly-added axiom.)
It’s also possible to create a new system (termed S+NG in your post), which
includes “T does not halt” as additional axiom; call this system PA0. The
PA0-Turing machine which enumerates the PA2-Goodstein sequence on PA0-natural
10^1234 does not halt, and again, this proposition can be trivially proven.
##############
For me it was very important to realize that the PA1-Goodstein sequences are
not the same as the PA0-Goodstein sequences! This is, in retrospect, very
obvious: Mathematical objects do not exist “on their own”, in a “Platonist
heaven” — they /depend on a given (formal) system/! Also, the notion of
existence of a mathematical object is a man-made definition.**** (I think this is
exactly the point you were making. :))
Solely to drive the point home, let’s consider the world of ZFC (in which
ZFC-numbers, ZFC-sets, ZFC-ordinals, ZFC-Turing machines, etc. exist and in
which desks, bookes etc. do not exist): The ZFC-Goodstein sequences (which are
to be distinguished from the PA-, PA1- and PA0-Goodstein sequences) can be
proven to ZFC-halt, where “ZFC-halt” is defined as exists n \in N = {0,1,…}.
zfcStateAfterRunningForNSteps(T, n) = HALT_STATE.
So, when Wikipedia says, “Goodstein’s theorem is a statement about the natural
numbers that is unprovable in Peano arithmetic but can be proven to be true
using the stronger axiom system of set theory”, what is actually meant is the
following:
* PA-Goodstein sequences can not (in general) be proved to be finite.
* PA1-Goodstein sequences can be trivially proven to be finite.
* PA0-Goodstein sequences can be trivially proven to be infinite.
* ZFC-Goodstein sequences can be proven to be finite (using cool ordinal
arithmetic).
Sloppy speaking (i.e. not using “PA-”, “ZFC-” prefixes) results in the
(mis-)belief that proofs of properties of ZFC-Goodstein sequences would
automatically apply to PA-Goodstein sequences, while this is (in general) not
the case. (Am I correct?) [Of course, some proofs can be "ported", for example
from systems A to systems B, where B is a conservative extension of A.]
Thank you very much! (Even in the case that there are terrible errors in my
:)
PS. I think a bit of Platonism (if I understand it correctly) can be rescued
by dividing the absolute Platonist heaven (which is, as you point out, a
non-sustainable notion) into several, separate heavens for each formal system
(i.e. the PA-heaven, the ZFC-heaven etc.)
PPS. Propositions which are independent of one’s favourite system — like
Goodstein’s theorem in PA — remind me a bit of non-falsifiable (and
non-verifiable) theories like “the physical world came into existence ten
minutes ago” (name this theory F): As such theories are non-falsifiable and
non-verifiable, they are not (modulo meta-considerations) interesting.
Questioning “is F true?” is equally pointless as questioning “are all
PA-Goodstein sequences finite?”, as both questions are inherently
un-answerable. (I do not mean “pointless” in a dismissive sense, but I lack a
better word.)
Footnotes (probably only understandable after having read the rest):
* With “the” Goodstein sequence, I mean a REALWORLD-Goodstein sequence. (Where
“REALWORLD” is the identifier for the physical, real world system (like “PA” is
for Peano Arithmetic).)
** I don’t think that Turing machines can be constructed in PA, as the usual
definitions of Turing machines require the notion of a set (e.g. the alphabet
set etc.). But, as I understand it, at least comparable things can be
constructed. I think that this problem is not substantial to my reasoning.
*** With “T” in ‘”T halts”‘ I mean the analogon of PA-T in PA1, i.e. PA1-T.
**** For example (warning, hand-waving here), in intuitionistic reasoning, one
has to give an explicit construction of an object x to show that it exists,
while in classical reasoning it’s sufficient to prove that the proposition “x does not | 3,564 | 14,178 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2013-48 | longest | en | 0.913524 |
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Task # 8
Objective. Approximate the original data given by the table by the method of least squares, using different models of functions and perform a comparison and analysis of the results obtained.
To achieve this goal you need to solve the following subtasks.
1) Select the approximating functions, depending on the condition of the problem, justify the choice.
2) Approximate the data with the selected methods, determine the errors of the approximations.
3) Construct a graph of the initial and approximating functions.
4) Analyze the results and select the optimal approximating function.
5) Construct schemes of program algorithms.
Option 1.8
The management of some firm that produces electronic devices wants to forecast sales of its products. It is assumed that the explanatory variable may be the costs of research and development (R & D). Data were collected on sales and research costs for 1985-2005:
Year of Sale y (thsd.) Research Cost x (Thous. Dollars)
1985 3307 273.4
1986 3556 291.3
1987 3601 306.9
1988 3721 317.1
1989 4036 336.1
1990 4134 349.4
1991 4268 362.9
1992 4578 383.9
1993 5093 402.8
1994 5716 437.0
1995 6357 472.2
1996 6769 510.4
1997 7296 544.5
1998 8178 588.1
1999 8844 630.4
2000 9251 685.9
2001 10006 742.8
2002 11200 801.3
2003 12500 903.1
2004 13101 983.6
2005 13640 1076.7
28.01.2018 20:51:32
Все работает! Только дорого конечно. | 487 | 1,506 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-51 | latest | en | 0.714687 |
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This article discusses various methods for calculating the concentration of a solution. It covers the use of CA standards, grams per liter, and molarity to determine the ratio of solute to solution volume
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## About Calculations of Solution Concentration
PowerPoint presentation about 'Calculations of Solution Concentration'. This presentation describes the topic on This article discusses various methods for calculating the concentration of a solution. It covers the use of CA standards, grams per liter, and molarity to determine the ratio of solute to solution volume. The key topics included in this slideshow are . Download this presentation absolutely free.
## Presentation Transcript
Slide1Calculations of Solution Concentration Calculations of Solution Concentration
Slide2CA Standards CA Standards
Slide3Calculations of Solution Concentration: Grams per Liter Calculations of Solution Concentration: Grams per Liter Grams per liter Grams per liter is the ratio of mass units of solute to volume (liters) of solution
Slide4Calculations of Solution Concentration: Molarity Calculations of Solution Concentration: Molarity Molarity Molarity is the ratio of moles of solute to liters of solution
Slide5Calculations of Solution Concentration: Mass Percent Calculations of Solution Concentration: Mass Percent Mass percent Mass percent is the ratio of mass units of solute to mass units of solution, expressed as a percent
Slide6Calculations of Solution Concentration: Parts per Million Calculations of Solution Concentration: Parts per Million Parts per million Parts per million is the ratio of mass units of solute to mass units of solution, multiplied by one million (10 6 )
Slide7Simplifying Assumption A Simplifying Assumption • 1 ml of water = 1 gram of water • 1 ml of water = 1 gram of water • 1000 ml of water = 1 liter = 1000 grams • 1000 ml of water = 1 liter = 1000 grams • Assume that solutions with water as the solvent have the density of pure water (1 mL = 1 gram) • Assume that solutions with water as the solvent have the density of pure water (1 mL = 1 gram) – It’s not true, but it’s close enough – It’s not true, but it’s close enough | 680 | 2,385 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2023-50 | longest | en | 0.217991 |
https://www.knowpia.com/knowpedia/Carleson%27s_theorem | 1,718,899,857,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861957.99/warc/CC-MAIN-20240620141245-20240620171245-00080.warc.gz | 723,510,100 | 21,434 | BREAKING NEWS
Carleson's theorem
## Summary
Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series of L2 functions, proved by Lennart Carleson (1966). The name is also often used to refer to the extension of the result by Richard Hunt (1968) to Lp functions for p(1, ∞] (also known as the Carleson–Hunt theorem) and the analogous results for pointwise almost everywhere convergence of Fourier integrals, which can be shown to be equivalent by transference methods.
## Statement of the theorem
The result, as extended by Hunt, can be formally stated as follows:
Let f be an Lp periodic function for some p(1, ∞], with Fourier coefficients ${\displaystyle {\hat {f}}(n)}$ . Then
${\displaystyle \lim _{N\to \infty }\sum _{|n|\leq N}{\hat {f}}(n)e^{inx}=f(x)}$
for almost every x.
The analogous result for Fourier integrals is:
Let fLp(R) for some p(1, 2] have Fourier transform ${\displaystyle {\hat {f}}(\xi )}$ . Then
${\displaystyle \lim _{R\to \infty }\int _{|\xi |\leq R}{\hat {f}}(\xi )e^{2\pi ix\xi }\,d\xi =f(x)}$
for almost every xR.
## History
A fundamental question about Fourier series, asked by Fourier himself at the beginning of the 19th century, is whether the Fourier series of a continuous function converges pointwise to the function.
By strengthening the continuity assumption slightly one can easily show that the Fourier series converges everywhere. For example, if a function has bounded variation then its Fourier series converges everywhere to the local average of the function. In particular, if a function is continuously differentiable then its Fourier series converges to it everywhere. This was proven by Dirichlet, who expressed his belief that he would soon be able to extend his result to cover all continuous functions. Another way to obtain convergence everywhere is to change the summation method. For example, Fejér's theorem shows that if one replaces ordinary summation by Cesàro summation then the Fourier series of any continuous function converges uniformly to the function. Further, it is easy to show that the Fourier series of any L2 function converges to it in L2 norm.
After Dirichlet's result, several experts, including Dirichlet, Riemann, Weierstrass and Dedekind, stated their belief that the Fourier series of any continuous function would converge everywhere. This was disproved by Paul du Bois-Reymond, who showed in 1876 that there is a continuous function whose Fourier series diverges at one point.
The almost-everywhere convergence of Fourier series for L2 functions was postulated by N. N. Luzin (1915), and the problem was known as Luzin's conjecture (up until its proof by Carleson (1966)). Kolmogorov (1923) showed that the analogue of Carleson's result for L1 is false by finding such a function whose Fourier series diverges almost everywhere (improved slightly in 1926 to diverging everywhere). Before Carleson's result, the best known estimate for the partial sums sn of the Fourier series of a function in Lp was
${\displaystyle s_{n}(x)=o(\log(n)^{1/p}){\text{ almost everywhere}}.}$
In other words, the function sn(x) can still grow to infinity at any given point x as one takes more and more terms of the Fourier series into account, though the growth must be quite slow (slower than the logarithm of n to a small power). This result was proved by Kolmogorov–Seliverstov–Plessner for p = 2, by G. H. Hardy for p = 1, and by Littlewood–Paley for p > 1 (Zygmund 2002). This result had not been improved for several decades, leading some experts to suspect that it was the best possible and that Luzin's conjecture was false. Kolmogorov's counterexample in L1 was unbounded in any interval, but it was thought to be only a matter of time before a continuous counterexample was found. Carleson said in an interview with Raussen & Skau (2007) that he started by trying to find a continuous counterexample and at one point thought he had a method that would construct one, but realized eventually that his approach could not work. He then tried instead to prove Luzin's conjecture since the failure of his counterexample convinced him that it was probably true.
Carleson's original proof is exceptionally hard to read, and although several authors have simplified the argument there are still no easy proofs of his theorem. Expositions of the original paper Carleson (1966) include Kahane (1995), Mozzochi (1971), Jørsboe & Mejlbro (1982), and Arias de Reyna (2002). Charles Fefferman (1973) published a new proof of Hunt's extension which proceeded by bounding a maximal operator. This, in turn, inspired a much simplified proof of the L2 result by Michael Lacey and Christoph Thiele (2000), explained in more detail in Lacey (2004). The books Fremlin (2003) and Grafakos (2014) also give proofs of Carleson's theorem.
Katznelson (1966) showed that for any set of measure 0 there is a continuous periodic function whose Fourier series diverges at all points of the set (and possibly elsewhere). When combined with Carleson's theorem this shows that there is a continuous function whose Fourier series diverges at all points of a given set of reals if and only if the set has measure 0.
The extension of Carleson's theorem to Lp for p > 1 was stated to be a "rather obvious" extension of the case p = 2 in Carleson's paper, and was proved by Hunt (1968). Carleson's result was improved further by Sjölin (1971) to the space Llog+(L)log+log+(L) and by Antonov (1996) to the space Llog+(L)log+log+log+(L). (Here log+(L) is log(L) if L > 1 and 0 otherwise, and if φ is a function then φ(L) stands for the space of functions f such that φ(|f(x)|) is integrable.)
Konyagin (2000) improved Kolmogorov's counterexample by finding functions with everywhere-divergent Fourier series in a space slightly larger than Llog+(L)1/2. One can ask if there is in some sense a largest natural space of functions whose Fourier series converge almost everywhere. The simplest candidate for such a space that is consistent with the results of Antonov and Konyagin is Llog+(L).
The extension of Carleson's theorem to Fourier series and integrals in several variables is made more complicated as there are many different ways in which one can sum the coefficients; for example, one can sum over increasing balls, or increasing rectangles. Convergence of rectangular partial sums (and indeed general polygonal partial sums) follows from the one-dimensional case, but the spherical summation problem is still open for L2.
## The Carleson operator
The Carleson operator C is the non-linear operator defined by
${\displaystyle Cf(x)=\sup _{N}\left|\int _{-N}^{N}{\hat {f}}(y)e^{2\pi ixy}\,dy\right|}$
It is relatively easy to show that the Carleson–Hunt theorem follows from the boundedness of the Carleson operator from Lp(R) to itself for 1 < p < ∞. However, proving that it is bounded is difficult, and this was actually what Carleson proved.
## References
• Antonov, N. Yu. (1996), "Convergence of Fourier series", East Journal on Approximations, 2 (2): 187–196, MR 1407066
• Arias de Reyna, Juan (2002), Pointwise convergence of Fourier series, Lecture Notes in Mathematics, vol. 1785, Berlin, New York: Springer-Verlag, doi:10.1007/b83346, ISBN 978-3-540-43270-8, MR 1906800
• Carleson, Lennart (1966), "On convergence and growth of partial sums of Fourier series", Acta Mathematica, 116 (1): 135–157, doi:10.1007/BF02392815, MR 0199631
• Fefferman, Charles (1973), "Pointwise convergence of Fourier series", Annals of Mathematics, Second Series, 98 (3): 551–571, doi:10.2307/1970917, JSTOR 1970917, MR 0340926
• Fremlin, David H. (2003), Measure theory, vol. 2, Torres Fremlin, Colchester, ISBN 978-0-9538129-2-9, MR 2462280, archived from the original on 2010-11-01, retrieved 2010-09-09
• Grafakos, Loukas (2014). Modern Fourier analysis. Graduate Texts in Mathematics. Vol. 250 (Third ed.). New York: Springer-Verlag. doi:10.1007/978-1-4939-1230-8. ISBN 978-1-4939-1229-2. MR 3243741.
• Hunt, Richard A. (1968), "On the convergence of Fourier series", Orthogonal Expansions and their Continuous Analogues Proc. Conf., Edwardsville, Ill., 1967, Carbondale, Ill.: Southern Illinois Univ. Press, pp. 235–255, MR 0238019
• Jørsboe, Ole G.; Mejlbro, Leif (1982), The Carleson-Hunt theorem on Fourier series, Lecture Notes in Mathematics, vol. 911, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0094072, ISBN 978-3-540-11198-6, MR 0653477
• Kahane, Jean-Pierre (1995), "Sommes partielles des séries de Fourier (d'après L. Carleson)", Séminaire Bourbaki, vol. 9, Paris: Société Mathématique de France, pp. 491–507, MR 1610981
• Katznelson, Yitzhak (1966), "Sur les ensembles de divergence des séries trigonométriques", Studia Mathematica, 26 (3): 301–304, doi:10.4064/sm-26-3-305-306, MR 0199632
• Kolmogorov, Andrey Nikolaevich (1923), "Une série de Fourier–Lebesgue divergente presque partout", Fundamenta Mathematicae, 4: 324–328, doi:10.4064/fm-4-1-324-328
• Konyagin, S. V. (2000), "On the divergence everywhere of trigonometric Fourier series", Rossiĭskaya Akademiya Nauk. Matematicheskii Sbornik, 191 (1): 103–126, Bibcode:2000SbMat.191...97K, doi:10.1070/sm2000v191n01abeh000449, MR 1753494, S2CID 250745433
• Lacey, Michael T. (2004), "Carleson's theorem: proof, complements, variations", Publicacions Matemàtiques, 48 (2): 251–307, arXiv:math/0307008, doi:10.5565/publmat_48204_01, MR 2091007, S2CID 16121272
• Lacey, Michael; Thiele, Christoph (2000), "A proof of boundedness of the Carleson operator", Mathematical Research Letters, 7 (4): 361–370, doi:10.4310/mrl.2000.v7.n4.a1, MR 1783613
• Luzin, N.N. (1915), The integral and trigonometric series (In Russian), Moscow-Leningrad{{citation}}: CS1 maint: location missing publisher (link) (Thesis; also: Collected Works, Vol. 1, Moscow, 1953, pp. 48–212)
• Mozzochi, Charles J. (1971), On the pointwise convergence of Fourier series, Lecture Notes in Mathematics, Vol. 199, vol. 199, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0061167, ISBN 978-3-540-05475-7, MR 0445205 "This monograph is a detailed and essentially self-contained treatment of the work of Carleson and Hunt."
• Raussen, Martin; Skau, Christian (2007), "Interview with Abel Prize recipient Lennart Carleson" (PDF), Notices of the American Mathematical Society, 54 (2): 223–229, MR 2285126
• Sjölin, Per (1971), "Convergence almost everywhere of certain singular integrals and multiple Fourier series", Arkiv för Matematik, 9 (1–2): 65–90, Bibcode:1971ArM.....9...65S, doi:10.1007/BF02383638, MR 0336222
• Telyakovskii, S.A. (2001) [1994], "Carleson theorem", Encyclopedia of Mathematics, EMS Press
• Zygmund, A. (2002) [1935], Trigonometric Series. Vol. I, II, Cambridge Mathematical Library (3rd ed.), Cambridge University Press, ISBN 978-0-521-89053-3, MR 1963498 | 3,100 | 10,870 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2024-26 | latest | en | 0.898588 |
http://forum.arduino.cc/index.php?topic=126355.msg950003 | 1,474,980,962,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738661051.55/warc/CC-MAIN-20160924173741-00084-ip-10-143-35-109.ec2.internal.warc.gz | 102,935,417 | 9,655 | Go Down
### Topic: Measuring the RPM using Pulses (Read 985 times)previous topic - next topic
#### jay2012
##### Oct 09, 2012, 03:46 pm
Hey all,
I have been trying to find the rpm of a motor using the hall effect sensor to pick up the magnetic pulses,and i have written this code which is able to detect the number of pulses and their duration.
int inputPin = 3;
unsigned long counter = 0;
unsigned long duration = 0;
unsigned long timeout = 1000000; // in microseconds
void setup() {
pinMode(inputPin, INPUT);
// the input pin to a HIGH reading.
digitalWrite(inputPin, HIGH);
Serial.begin(9600);
Serial.println("start");
}
void loop() {
duration = pulseIn(inputPin, HIGH, timeout);
{
counter++;
Serial.print(counter);
Serial.print(", ");
Serial.print(duration);
Serial.println("");
}
}
Here the counter keeps incrementing and ,the final output gives me the number of high's and the respective durations.Now the problem is i wanted the number of pulses in a given time interval,like for eg: the output should be like " 3 , 0.5sec" which means the 3 pulses in 0.5 seconds.or "1 ,0.5 sec"...and not just an up counter..i tried refreshing the counter after the loop that is , put a statements counter =0, and duration =0; at the end but it didnt work,i am thinking about using the attachinterrupt command..?..any help guys?..i havent yet written the code to convert this into rpm.
#### PaulS
#1
##### Oct 09, 2012, 03:54 pm
Quote
i tried refreshing the counter after the loop that is , put a statements counter =0, and duration =0; at the end but it didnt work
You don't want to unconditionally reset counter. Resetting duration is silly, since it is always value by the pulseIn() function.
You need to determine if it is time to reset counter. Look at the millis() function, and the blink without delay example to see how to time activities.
Go Up
Please enter a valid email to subscribe | 472 | 1,911 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2016-40 | longest | en | 0.830908 |
https://foreach.id/EN/common/power/kilocalorieIT%7Csecond-to-joule%7Cminute.html | 1,620,887,873,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991537.32/warc/CC-MAIN-20210513045934-20210513075934-00514.warc.gz | 282,958,323 | 10,825 | # Convert kilocalorie (IT)/second to joule/minute (kcal/s to J/min)
Batch Convert
• kilocalorie (IT)/second [kcal/s]
• joule/minute [J/min]
Copy
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• kilocalorie (IT)/second [kcal/s]
• joule/minute [J/min]
## Kilocalorie (IT)/second to Joule/minute (kcal/s to J/min)
### Kilocalorie (IT)/second (Symbol or Abbreviation: kcal/s)
Kilocalorie (IT)/second is one of power units. Kilocalorie (IT)/second abbreviated or symbolized by kcal/s. The value of 1 kilocalorie (IT)/second is equal to 4186.8 watt. In its relation with joule/minute, 1 kilocalorie (IT)/second is equal to 251210 joule/minute.
#### Relation with other units
1 kilocalorie (IT)/second equals to 4,186.8 watt
1 kilocalorie (IT)/second equals to 4.1868 kilowatt
1 kilocalorie (IT)/second equals to 0.0041868 megawatt
1 kilocalorie (IT)/second equals to 4,186,800,000,000,000 picowatt
1 kilocalorie (IT)/second equals to 4,186,800,000,000 nanowatt
1 kilocalorie (IT)/second equals to 4,186,800,000 microwatt
1 kilocalorie (IT)/second equals to 4,186,800 milliwatt
1 kilocalorie (IT)/second equals to 418,680 centiwatt
1 kilocalorie (IT)/second equals to 41,868 deciwatt
1 kilocalorie (IT)/second equals to 418.68 dekawatt
1 kilocalorie (IT)/second equals to 41.868 hectowatt
1 kilocalorie (IT)/second equals to 0.0000041868 gigawatt
1 kilocalorie (IT)/second equals to 5.6146 horsepower
1 kilocalorie (IT)/second equals to 5.6925 horsepower (metric)
1 kilocalorie (IT)/second equals to 0.42681 horsepower (boiler)
1 kilocalorie (IT)/second equals to 5.6123 horsepower (electric)
1 kilocalorie (IT)/second equals to 5.612 horsepower (water)
1 kilocalorie (IT)/second equals to 5.6925 pferdestarke
1 kilocalorie (IT)/second equals to 14,286 Btu (IT)/hour
1 kilocalorie (IT)/second equals to 238.1 Btu (IT)/minute
1 kilocalorie (IT)/second equals to 3.9683 Btu (IT)/second
1 kilocalorie (IT)/second equals to 14,296 Btu (th)/hour
1 kilocalorie (IT)/second equals to 238.26 Btu (th)/minute
1 kilocalorie (IT)/second equals to 3.971 Btu (th)/second
1 kilocalorie (IT)/second equals to 0.014286 MBtu (IT)/hour
1 kilocalorie (IT)/second equals to 14.286 MBH
1 kilocalorie (IT)/second equals to 1.1905 ton (refrigeration)
1 kilocalorie (IT)/second equals to 3,600 kilocalorie (IT)/hour
1 kilocalorie (IT)/second equals to 60 kilocalorie (IT)/minute
1 kilocalorie (IT)/second equals to 3,602.4 kilocalorie (th)/hour
1 kilocalorie (IT)/second equals to 60.04 kilocalorie (th)/minute
1 kilocalorie (IT)/second equals to 1.0007 kilocalorie (th)/second
1 kilocalorie (IT)/second equals to 3,600,000 calorie (IT)/hour
1 kilocalorie (IT)/second equals to 60,000 calorie (IT)/minute
1 kilocalorie (IT)/second equals to 1,000 calorie (IT)/second
1 kilocalorie (IT)/second equals to 3,602,400 calorie (th)/hour
1 kilocalorie (IT)/second equals to 60,040 calorie (th)/minute
1 kilocalorie (IT)/second equals to 1,000.7 calorie (th)/second
1 kilocalorie (IT)/second equals to 11,117,000 foot pound-force/hour
1 kilocalorie (IT)/second equals to 185,280 foot pound-force/minute
1 kilocalorie (IT)/second equals to 3,088 foot pound-force/second
1 kilocalorie (IT)/second equals to 41,868,000,000 erg/second
1 kilocalorie (IT)/second equals to 4.1868 kilovolt ampere
1 kilocalorie (IT)/second equals to 4,186.8 volt ampere
1 kilocalorie (IT)/second equals to 4,186.8 newton meter/second
1 kilocalorie (IT)/second equals to 4,186.8 joule/second
1 kilocalorie (IT)/second equals to 0.0000041868 gigajoule/second
1 kilocalorie (IT)/second equals to 0.0041868 megajoule/second
1 kilocalorie (IT)/second equals to 4.1868 kilojoule/second
1 kilocalorie (IT)/second equals to 41.868 hectojoule/second
1 kilocalorie (IT)/second equals to 418.68 dekajoule/second
1 kilocalorie (IT)/second equals to 41,868 decijoule/second
1 kilocalorie (IT)/second equals to 418,680 centijoule/second
1 kilocalorie (IT)/second equals to 4,186,800 millijoule/second
1 kilocalorie (IT)/second equals to 4,186,800,000 microjoule/second
1 kilocalorie (IT)/second equals to 4,186,800,000,000 nanojoule/second
1 kilocalorie (IT)/second equals to 4,186,800,000,000,000 picojoule/second
1 kilocalorie (IT)/second equals to 15,072,000 joule/hour
1 kilocalorie (IT)/second equals to 251,210 joule/minute
1 kilocalorie (IT)/second equals to 15,072 kilojoule/hour
1 kilocalorie (IT)/second equals to 251.21 kilojoule/minute
### Joule/minute (Symbol or Abbreviation: J/min)
Joule/minute is one of power units. Joule/minute abbreviated or symbolized by J/min. The value of 1 joule/minute is equal to 0.016667 watt. In its relation with kilocalorie (IT)/second, 1 joule/minute is equal to 0.0000039808 kilocalorie (IT)/second.
#### Relation with other units
1 joule/minute equals to 0.016667 watt
1 joule/minute equals to 0.000016667 kilowatt
1 joule/minute equals to 1.6667e-8 megawatt
1 joule/minute equals to 16,667,000,000 picowatt
1 joule/minute equals to 16,667,000 nanowatt
1 joule/minute equals to 16,667 microwatt
1 joule/minute equals to 16.667 milliwatt
1 joule/minute equals to 1.6667 centiwatt
1 joule/minute equals to 0.16667 deciwatt
1 joule/minute equals to 0.0016667 dekawatt
1 joule/minute equals to 0.00016667 hectowatt
1 joule/minute equals to 1.6667e-11 gigawatt
1 joule/minute equals to 0.00002235 horsepower
1 joule/minute equals to 0.00002266 horsepower (metric)
1 joule/minute equals to 0.000001699 horsepower (boiler)
1 joule/minute equals to 0.000022341 horsepower (electric)
1 joule/minute equals to 0.00002234 horsepower (water)
1 joule/minute equals to 0.00002266 pferdestarke
1 joule/minute equals to 0.056869 Btu (IT)/hour
1 joule/minute equals to 0.00094782 Btu (IT)/minute
1 joule/minute equals to 0.000015797 Btu (IT)/second
1 joule/minute equals to 0.056907 Btu (th)/hour
1 joule/minute equals to 0.00094845 Btu (th)/minute
1 joule/minute equals to 0.000015808 Btu (th)/second
1 joule/minute equals to 5.6868e-8 MBtu (IT)/hour
1 joule/minute equals to 0.000056869 MBH
1 joule/minute equals to 0.0000047391 ton (refrigeration)
1 joule/minute equals to 0.014331 kilocalorie (IT)/hour
1 joule/minute equals to 0.00023885 kilocalorie (IT)/minute
1 joule/minute equals to 0.0000039808 kilocalorie (IT)/second
1 joule/minute equals to 0.01434 kilocalorie (th)/hour
1 joule/minute equals to 0.00023901 kilocalorie (th)/minute
1 joule/minute equals to 0.0000039834 kilocalorie (th)/second
1 joule/minute equals to 14.331 calorie (IT)/hour
1 joule/minute equals to 0.23885 calorie (IT)/minute
1 joule/minute equals to 0.0039808 calorie (IT)/second
1 joule/minute equals to 14.34 calorie (th)/hour
1 joule/minute equals to 0.23901 calorie (th)/minute
1 joule/minute equals to 0.0039834 calorie (th)/second
1 joule/minute equals to 44.254 foot pound-force/hour
1 joule/minute equals to 0.73756 foot pound-force/minute
1 joule/minute equals to 0.012293 foot pound-force/second
1 joule/minute equals to 166,670 erg/second
1 joule/minute equals to 0.000016667 kilovolt ampere
1 joule/minute equals to 0.016667 volt ampere
1 joule/minute equals to 0.016667 newton meter/second
1 joule/minute equals to 0.016667 joule/second
1 joule/minute equals to 1.6667e-11 gigajoule/second
1 joule/minute equals to 1.6667e-8 megajoule/second
1 joule/minute equals to 0.000016667 kilojoule/second
1 joule/minute equals to 0.00016667 hectojoule/second
1 joule/minute equals to 0.0016667 dekajoule/second
1 joule/minute equals to 0.16667 decijoule/second
1 joule/minute equals to 1.6667 centijoule/second
1 joule/minute equals to 16.667 millijoule/second
1 joule/minute equals to 16,667 microjoule/second
1 joule/minute equals to 16,667,000 nanojoule/second
1 joule/minute equals to 16,667,000,000 picojoule/second
1 joule/minute equals to 60 joule/hour
1 joule/minute equals to 0.06 kilojoule/hour
1 joule/minute equals to 0.001 kilojoule/minute
### How to convert Kilocalorie (IT)/second to Joule/minute (kcal/s to J/min):
#### Conversion Table for Kilocalorie (IT)/second to Joule/minute (kcal/s to J/min)
kilocalorie (IT)/second (kcal/s) joule/minute (J/min)
0.01 kcal/s 2,512.1 J/min
0.1 kcal/s 25,121 J/min
1 kcal/s 251,210 J/min
2 kcal/s 502,420 J/min
3 kcal/s 753,620 J/min
4 kcal/s 1,004,800 J/min
5 kcal/s 1,256,000 J/min
6 kcal/s 1,507,200 J/min
7 kcal/s 1,758,500 J/min
8 kcal/s 2,009,700 J/min
9 kcal/s 2,260,900 J/min
10 kcal/s 2,512,100 J/min
20 kcal/s 5,024,200 J/min
25 kcal/s 6,280,200 J/min
50 kcal/s 12,560,000 J/min
75 kcal/s 18,841,000 J/min
100 kcal/s 25,121,000 J/min
250 kcal/s 62,802,000 J/min
500 kcal/s 125,600,000 J/min
750 kcal/s 188,410,000 J/min
1,000 kcal/s 251,210,000 J/min
100,000 kcal/s 25,121,000,000 J/min
1,000,000,000 kcal/s 251,210,000,000,000 J/min
1,000,000,000,000 kcal/s 251,210,000,000,000,000 J/min
#### Conversion Table for Joule/minute to Kilocalorie (IT)/second (J/min to kcal/s)
joule/minute (J/min) kilocalorie (IT)/second (kcal/s)
0.01 J/min 3.9808e-8 kcal/s
0.1 J/min 3.9808e-7 kcal/s
1 J/min 0.0000039808 kcal/s
2 J/min 0.0000079615 kcal/s
3 J/min 0.000011942 kcal/s
4 J/min 0.000015923 kcal/s
5 J/min 0.000019904 kcal/s
6 J/min 0.000023885 kcal/s
7 J/min 0.000027865 kcal/s
8 J/min 0.000031846 kcal/s
9 J/min 0.000035827 kcal/s
10 J/min 0.000039808 kcal/s
20 J/min 0.000079615 kcal/s
25 J/min 0.000099519 kcal/s
50 J/min 0.00019904 kcal/s
75 J/min 0.00029856 kcal/s
100 J/min 0.00039808 kcal/s
250 J/min 0.00099519 kcal/s
500 J/min 0.0019904 kcal/s
750 J/min 0.0029856 kcal/s
1,000 J/min 0.0039808 kcal/s
100,000 J/min 0.39808 kcal/s
1,000,000,000 J/min 3,980.8 kcal/s
1,000,000,000,000 J/min 3,980,800 kcal/s
#### Steps to Convert Kilocalorie (IT)/second to Joule/minute (kcal/s to J/min)
1. Example: Convert 37 kilocalorie (IT)/second to joule/minute (37 kcal/s to J/min).
2. 1 kilocalorie (IT)/second is equivalent to 251210 joule/minute (1 kcal/s is equivalent to 251210 J/min).
3. 37 kilocalorie (IT)/second (kcal/s) is equivalent to 37 times 251210 joule/minute (J/min).
4. Retrieved 37 kilocalorie (IT)/second is equivalent to 9294700 joule/minute (37 kcal/s is equivalent to 9294700 J/min).
▸▸ | 3,610 | 10,104 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2021-21 | latest | en | 0.712501 |
http://80.53.81.dioceseofsorsogon.org/functions-in-math-worksheet/ | 1,597,391,814,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439739182.35/warc/CC-MAIN-20200814070558-20200814100558-00514.warc.gz | 2,316,863 | 18,951 | # Functions In Math Worksheet
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Functions In Math Worksheet. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
Without phonics skills, it's almost impossible, especially for kids, to learn how to read new words. Techniques to Handle Attention Issues It is extremely essential that should you discover your kid is inattentive to his learning especially when it has to do with reading and writing issues you must begin working on various ways and to improve it. Use a student's name in every sentence so there's a single sentence for each kid. Because he or she learns at his own rate, there is some variability in the age when a child is ready to learn to read. Teaching your kid to form the alphabets is quite a complicated practice. | 1,515 | 7,929 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2020-34 | latest | en | 0.620442 |
https://www.coursehero.com/file/6621140/test0223/ | 1,493,527,785,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917124297.82/warc/CC-MAIN-20170423031204-00305-ip-10-145-167-34.ec2.internal.warc.gz | 862,106,874 | 24,082 | test0223
# test0223 - Page 3 8. 9. In the 81 system a. Js/m b. Jm/s @)...
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Unformatted text preview: Page 3 8. 9. In the 81 system a. Js/m b. Jm/s @) Nm/s d. W/m power has the same units as An astronaut weighs 99 N on the moon, where the acceleration is 1.62 m/s2. How much does she weigh on earth? a. 61 N 'W:: m'1 V C =' tYJ 4' _ b. 99 N W'I' JI'1 Jf::= @7 f>1 600 N d.440N 10. of units, .c i0tl- j c ~ 1r( /,62.../l) 1c'l = ~ c; J~ " of gravity ::: 00;tl 6 /m ---- Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight of the 70 -kg pilot at that point? 1>14 ?') l.3310 N y"'::::r ' Ii ~ f1~"; ~ b. 687 N FtJ' _ (/) V 2. / 2 c. 2630 N ..o(70lf,~ I) 1 70{/50) -'33/011./ d. 1374 N r· , 660 -_ @ ev f ~F. r- ~-(YIO --- -- ~ 11. A flatbed truck is carrying a 20-kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.40. What is the maximum acceleration that the truck can have if the crate is to stay in place? @3.92m/s2 err'' ' fF .r:.. 2)(' b. 8. 00 m/ s 2 c. 78.5 m/ s .zF )( ...> = t: -111 IJ (YJa. ~,x .fs ~ ""4 Y fYI() d. 196 m/s2 ~ j '" 0 ~ ~ '" J q --"7 ~-- (' S h1j M'X"I ~ ,,<-I,j /11" _ M. f1 .: )A.Jd ~ (O,dj(frJ';) = 12. The largest Moon in the solar system is Ganymede, a moon of Jupiter. ~7)~! Ganymede orbits at a distance of 1.07x106 km from the center of Jupiter---with a period of 6.18x105 s. Use this information to determine the mass of Jupiter. G = 6.67x10-11 N m2/kg2. o m 1. 90Xl027 18 kg kg c. 6.05x1026 d. 6.05x1018 kg kg Y. 1.90x10 --r/ 2 .:= // '7 7J 2 Gf1 L/T/2. r 3 qr/"(;,{)7X (0 1tn) b 67X1v .. 'j (6.11XIOJ (3 r- CT2 r 7() X/a 3 77 f)- ...
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## This note was uploaded on 12/10/2011 for the course PHY 1111 taught by Professor Stencil during the Fall '11 term at UGA.
Ask a homework question - tutors are online | 832 | 2,098 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2017-17 | longest | en | 0.738627 |
https://physics.stackexchange.com/questions/529888/why-is-the-hamiltonian-of-a-photon-0?noredirect=1 | 1,718,966,932,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862070.5/warc/CC-MAIN-20240621093735-20240621123735-00771.warc.gz | 421,899,197 | 40,125 | # Why is the Hamiltonian of a photon = 0?
I'm studying the motion of light near Schwarzschild black holes, and I was wondering why the Hamiltonian of the Schwarzschild metric $$H = - \left( 1-\frac{2M}{r} \right)^{-1} \frac{p_{t}^2}{2}+\left( 1-\frac{2M}{r} \right) \frac{p_{r}^2}{2}+\left( \frac{p_{ \theta}^2}{2r^2}+\frac{p_{\phi}^2}{2r^2\sin^2\theta} \right)$$ is equal to zero for photons. I know that $$H < 0$$ is for every other particle and $$H >0$$ is mathematically possible but physically very unlikely since it would mean the particle is travelling faster than light. Still I don't know why the Hamiltonian (sum of potential and kinetic energies) of photons equals 0. Could anyone please help me?
OP's Hamiltonian of the form $$H~=~\frac{p^2+m^2}{2}, \qquad p^2~:=~p_{\mu}g^{\mu\nu}(x) p_{\nu}~\leq~0,\tag{1}$$ is called a super-Hamiltonian in e.g. MTW, cf. e.g. this Phys.SE post. (For a massless particle like the photon $$m=0$$.) The super-Hamiltonian (1) is the $$e=1$$ gauge of the Hamiltonian $$H~=~ \frac{e}{2}(p^2+m^2)\tag{2}$$ for a relativistic point particle, cf. e.g. this & this Phys.SE posts. Here $$e$$ is a Lagrange multiplier field that imposes the mass-shell condition $$p^2+m^2~\approx~0.\tag{3}$$ For the super-Hamiltonian (1) the mass-shell condition (3) must be imposed by hand. The notion of energy is (as usual) tied to the notion of worldline (WL) parameter, cf. Noether's theorem. Because of WL reparametrization invariance, this energy notion is challenged, cf. e.g. this Phys.SE post. | 505 | 1,525 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2024-26 | latest | en | 0.849406 |
https://socratic.org/trigonometry/right-triangles/measuring-rotation | 1,713,302,033,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817106.73/warc/CC-MAIN-20240416191221-20240416221221-00712.warc.gz | 494,423,860 | 10,615 | # Measuring Rotation
## Key Questions
• Negative angles has to do with the direction of rotation that you consider in order to measure angles.
Normally you start counting your angles from the positive side of the x axis in an anti-clockwise direction of rotation:
You can also go clockwise and so to avoid confusion you use a negative sign to indicate this kind of rotation.
• You can draw an angle in standard position by positioning its vertex at the origin and one "ray" on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.
An angle is then measured POSITIVE for a counterclockwise rotation and NEGATIVE for a clockwise rotation:
When two angles have the same initial and terminal sides, they are said to be coterminal angles.
Angles of −315° and 45° are coterminal angles.
As discussed below.
#### Explanation:
Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.
For example, the angles 30°, –330° and 390° are all coterminal.
What is the terminal side?
Standard Position of an Angle - Initial Side - Terminal Side. An angle is in standard position in the coordinate plane if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side. | 331 | 1,511 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-18 | latest | en | 0.904934 |
https://javascript.tutorialink.com/how-to-get-an-index-of-an-array-element-within-a-sort-comparison-function/ | 1,642,536,655,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00231.warc.gz | 390,574,246 | 9,083 | # How to get an index of an array element within a sort comparison function?
#### Tags: arrays, indexing, indexof, javascript, sorting
I am looking at this question:
The `sort` method for arrays can take an argument that is a comparison function with two parameters—say, x and y. The function returns a negative integer if x should come before y, zero if x and y are indistinguishable, and a positive integer if x should come after y. Write calls, using arrow functions, that sort:
1. An array of positive integers by decreasing order
2. An array of people by increasing age
3. An array of strings by increasing length
Here is my code:
```const posIntByDcrOrd = [5,4,3,2,1]
const peopleIncAge = [10,15,20,25,30]
const strIncLength = ['a','ab','abc','abcd']
const compFunc = (x,y) => {
let sumNeg = y - x
let sumPos = y + x
if(indexOf(x) < indexOf(y)) { console.log(sumNeg) }
else if( indexOf(x) > indexOf(y)) { console.log(sumPos) }
else { return 0 }
}
posIntByDcrOrd.sort(compFunc(5,4))
```
The idea behind this code is this: if you can sum the indexes of x and y elements of the arrays, you can get a negative integer, since x will be lower than y and y will be higher than x, which satisfies the conditions. But when I try to run this, I got a reference error of course. How can I access the index positions of x and y in the sorted array? I am open to other solutions as well.
P.S.: These arrays are made-up for easing the thinking process.
There is an abundance of Q&A on this site that deal with sorting. Your attempt seems to show you haven’t seen how numbers are commonly sorted in JavaScript. For instance this Q&A, and many others, provide the right way to do it.
• There is no `indexOf` available to you within the callback of `sort`. You don’t need that information. Just subtract the second value from the first to get an ascending (non-decreasing) result. Perform the subtraction in the other sense to get a descending (non-increasing) result. The internals of the `sort` function will use that return value to perform a sort algorithm. No indexes need to be known to you in that process.
• The assignment about people is probably not correctly reflected in your sample array, as now it just looks the same as the first input (an array of numbers). It is quite probable that an array of objects was intended. For example:
```const peopleIncAge = [{name: "Helen", age: 20},
{name: "John", age: 15},
{name: "Anne", age: 30},
{name: "Clark", age: 25},
{name: "Joy", age: 10}]
```
• Your input arrays are already sorted as they would need to be output. For testing any solution, it is better to have them shuffled.
Each of the three exercises needs a different callback function for the `sort` function:
```const positives = [1, 3, 5, 4, 2];
const people = [{name: "Helen", age: 20},
{name: "John", age: 15},
{name: "Anne", age: 30},
{name: "Clark", age: 25},
{name: "Joy", age: 10}];
const strings = ['abc', 'a', 'abcd', 'ab'];
console.log(positives.sort((x, y) => y - x)); // decreasing
console.log(people.sort((x, y) => x.age - y.age)); // increasing age
console.log(strings.sort((x, y) => x.length - y.length)); // increasing length```
Source: stackoverflow | 835 | 3,196 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2022-05 | latest | en | 0.80084 |
https://notionanswers.com/1655/business-days-formula?show=1671 | 1,713,654,487,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817688.24/warc/CC-MAIN-20240420214757-20240421004757-00047.warc.gz | 387,785,637 | 69,579 | Help between Notion users
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1vote
# Business Days Formula
Hello,
I’m having an issue with a formula that I am using. It works perfectly fine for 7 columns, then just stops working for the 8th and the 9th column.
The formula adds a specified amount of business days in each column, and references the previous column. The first column that starts this thread is a dates column. I’ve included a short video to show the problem.
I’d really appreciate any help with this.
Loom video (under 2 mins):
https://www.loom.com/share/87b4caa445314395b3fb37eaf1d6be07
Formula:
``if(day(prop("Research start")) == 0, dateAdd(prop("Research start"), 5, "days"), if(day(prop("Research start")) == 1, dateAdd(prop("Research start"), 7, "days"), if(day(prop("Research start")) == 2, dateAdd(prop("Research start"), 7, "days"), if(day(prop("Research start")) == 3, dateAdd(prop("Research start"), 7, "days"), if(day(prop("Research start")) == 4, dateAdd(prop("Research start"), 7, "days"), if(day(prop("Research start")) == 5, dateAdd(prop("Research start"), 7, "days"), if(day(prop("Research start")) == 6, dateAdd(prop("Research start"), 6, "days"), now())))))))``
1vote
Notion has set a hard limit on this for 7 columns. This is to help prevent feedback loop errors. (Trust me, we all have gone through this at some point or another)
0vote
### Dennismel12 commented Jan 16, 2023
@ANerdyNotioneer01s thank you for responding. I can't seem to find anything online about this hard limit. I would like to share this with my team, but with something to back it up. Do you have any sources, or is this just a known thing with Notion?
1vote
### ANerdyNotioneer01s commented Jan 17, 2023
I don't think there is documentation of it (or at least not what I can find at the moment), just what Notion has told us in the past and through previous discussions with others.
1vote
### Dennismel12 commented Jan 23, 2023
Thanks @ANerdyNotioneer01s Notion confirmed the info you gave me.
### Extend Notion Powers
...
Welcome to Notion Answers, where you can ask questions and receive answers from other members of the community.
Please share to grow the Notion Community! | 591 | 2,248 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-18 | latest | en | 0.878588 |
http://uk.mathworks.com/help/symbolic/whittakerm.html?requestedDomain=uk.mathworks.com&nocookie=true | 1,475,106,825,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738661768.23/warc/CC-MAIN-20160924173741-00196-ip-10-143-35-109.ec2.internal.warc.gz | 282,885,733 | 13,313 | # Documentation
### This is machine translation
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# whittakerM
Whittaker M function
## Syntax
`whittakerM(a,b,z)`
## Description
`whittakerM(a,b,z)` returns the value of the Whittaker M function.
## Input Arguments
`a` Symbolic number, variable, expression, function, or a vector or matrix of symbolic numbers, variables, expressions, or functions. If `a` is a vector or matrix, `whittakerM` returns the beta function for each element of `a`. `b` Symbolic number, variable, expression, function, or a vector or matrix of symbolic numbers, variables, expressions, or functions. If `b` is a vector or matrix, `whittakerM` returns the beta function for each element of `b`. `z` Symbolic number, variable, expression, function, or a vector or matrix of symbolic numbers, variables, expressions, or functions. If `x` is a vector or matrix, `whittakerM` returns the beta function for each element of `z`.
## Examples
Solve this second-order differential equation. The solutions are given in terms of the Whittaker functions.
```syms a b w(z) dsolve(diff(w, 2) + (-1/4 + a/z + (1/4 - b^2)/z^2)*w == 0)```
```ans = C2*whittakerM(-a,-b,-z) + C3*whittakerW(-a,-b,-z)```
Verify that the Whittaker M function is a valid solution of this differential equation:
```syms a b z isAlways(diff(whittakerM(a,b,z), z, 2) +... (-1/4 + a/z + (1/4 - b^2)/z^2)*whittakerM(a,b,z) == 0)```
```ans = logical 1```
Verify that `whittakerM(-a,-b,-z)` also is a valid solution of this differential equation:
```syms a b z isAlways(diff(whittakerM(-a,-b,-z), z, 2) +... (-1/4 + a/z + (1/4 - b^2)/z^2)*whittakerM(-a,-b,-z) == 0)```
```ans = logical 1```
Compute the Whittaker M function for these numbers. Because these numbers are not symbolic objects, you get floating-point results.
```[whittakerM(1, 1, 1), whittakerM(-2, 1, 3/2 + 2*i),... whittakerM(2, 2, 2), whittakerM(3, -0.3, 1/101)]```
```ans = 0.7303 -9.2744 + 5.4705i 2.6328 0.3681```
Compute the Whittaker M function for the numbers converted to symbolic objects. For most symbolic (exact) numbers, `whittakerM` returns unresolved symbolic calls.
```[whittakerM(sym(1), 1, 1), whittakerM(-2, sym(1), 3/2 + 2*i),... whittakerM(2, 2, sym(2)), whittakerM(sym(3), -0.3, 1/101)]```
```ans = [ whittakerM(1, 1, 1), whittakerM(-2, 1, 3/2 + 2i), whittakerM(2, 2, 2), whittakerM(3, -3/10, 1/101)]```
For symbolic variables and expressions, `whittakerM` also returns unresolved symbolic calls:
```syms a b x y [whittakerM(a, b, x), whittakerM(1, x, x^2),... whittakerM(2, x, y), whittakerM(3, x + y, x*y)]```
```ans = [ whittakerM(a, b, x), whittakerM(1, x, x^2),... whittakerM(2, x, y), whittakerM(3, x + y, x*y)]```
The Whittaker M function has special values for some parameters:
`whittakerM(sym(-3/2), 1, 1)`
```ans = exp(1/2)```
```syms a b x whittakerM(0, b, x)```
```ans = 4^b*x^(1/2)*gamma(b + 1)*besseli(b, x/2)```
`whittakerM(a + 1/2, a, x)`
```ans = x^(a + 1/2)*exp(-x/2)```
`whittakerM(a, a - 5/2, x)`
```ans = (2*x^(a - 2)*exp(-x/2)*(2*a^2 - 7*a + x^2/2 -... x*(2*a - 3) + 6))/pochhammer(2*a - 4, 2)```
Differentiate the expression involving the Whittaker M function:
```syms a b z diff(whittakerM(a,b,z), z)```
```ans = (whittakerM(a + 1, b, z)*(a + b + 1/2))/z -... (a/z - 1/2)*whittakerM(a, b, z)```
Compute the Whittaker M function for the elements of matrix `A`:
```syms x A = [-1, x^2; 0, x]; whittakerM(-1/2, 0, A)```
```ans = [ exp(-1/2)*1i, exp(x^2/2)*(x^2)^(1/2)] [ 0, x^(1/2)*exp(x/2)]```
collapse all
### Whittaker M Function
The Whittaker functions Ma,b(z) and Wa,b(z) are linearly independent solutions of this differential equation:
`$\frac{{d}^{2}w}{d{z}^{2}}+\left(-\frac{1}{4}+\frac{a}{z}+\frac{1/4-{b}^{2}}{{z}^{2}}\right)w=0$`
The Whittaker M function is defined via the confluent hypergeometric functions:
`${M}_{a,b}\left(z\right)={e}^{-z/2}\text{\hspace{0.17em}}{z}^{b+1/2}\text{\hspace{0.17em}}M\left(b-a+\frac{1}{2},\text{\hspace{0.17em}}1+2b,\text{\hspace{0.17em}}z\right)$`
### Tips
• All non-scalar arguments must have the same size. If one or two input arguments are non-scalar, then `whittakerM` expands the scalars into vectors or matrices of the same size as the non-scalar arguments, with all elements equal to the corresponding scalar.
## References
Slater, L. J. "Cofluent Hypergeometric Functions." Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. (M. Abramowitz and I. A. Stegun, eds.). New York: Dover, 1972. | 1,673 | 4,567 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2016-40 | latest | en | 0.626933 |
https://math.answers.com/math-and-arithmetic/Is_154212085000_standard_notation_for_one_hundred_fifty_four_billion_two_hundred_twelve_million_eighty_five_thousand | 1,723,193,142,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640762343.50/warc/CC-MAIN-20240809075530-20240809105530-00421.warc.gz | 304,354,881 | 47,650 | 0
# Is 154212085000 standard notation for one hundred fifty four billion two hundred twelve million eighty five thousand?
Updated: 9/17/2023
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Q: Is 154212085000 standard notation for one hundred fifty four billion two hundred twelve million eighty five thousand?
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### How do you write 41.1 billion in standard notation?
41.1 billion in standard notation is written as 41,100,000,000.
### How would you write the standard notation for the number 3.4 billion?
The standard notation for the number 3.4 billion is 3,400,000,000.
### 44.3 billion in standard notation?
44.3 billion = 44,300,000,000 | 472 | 1,753 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2024-33 | latest | en | 0.850685 |
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Ejs Open Source Coulomb Force Model Java Applet by Anne Cox, Wolfgang Christian, and Francisco Esquembre
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Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
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text by Anne Cox, Wolfgang Christian, and Francisco Esquembre
Coulomb Force Model
The EJS Coulomb Force model shows the force vectors on charges. Users can change charge of an individual charge and add more charges (maximum: 10). Users can examine the model if Ejs is installed.
Exercises:
Run the simulation. Move the charges around and observe the force vectors (as well as the magnitude of the force). When the charges are the same size, are the forces equal and opposite? What about when the charges have different values (the physical size of a charge in the simulation changes with the charge value as a visual cue). The drop down menu allows you to select the charge (by color) that you want to change.
Add a third charge using the Add Charge button. With three charges, how can you arrange the charges so that the force on the red charge is zero? Sketch this configuration. If you change the charge of the red one, is the force still zero? Explain.
What is wrong with the following statement from a student? "When there are three charges (q=1 for all), the force on all three charges should be bigger than when there were only two charges (q=1 on each) because there is now a bigger total charge and the Coulomb force is proportional to charge."
Add a number of charges. Can you still set things up so that the force on the red charge is zero? Explain.
References:
Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 21 (2008).
Credits:
The Coulomb Force Model was created by Anne Cox, Wolfgang Christian,and Francisco Esquembre using the Easy Java Simulations (EJS) authoring and modeling tool. Exercises written by Anne J Cox.
You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file. Right-click within the running program and select "Open EJS Model" from the pop-up menu to copy the model's XML description into EJS. You must, of course, have EJS installed on your computer.
Information about EJS is available at: and in the OSP ComPADRE collection .
charges2013-04-16_1351.png (15.22 KB, 480x560 - viewed 513 times.) « Last Edit: April 16, 2013, 12:44:19 pm by lookang » Logged
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You cannot always have happiness but you can always give happiness. ..."Mother Teresa(1910-1997, Roman Catholic Missionary, 1979 Nobel Peace Prize)" | 965 | 4,072 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2020-24 | longest | en | 0.79442 |
https://math.stackexchange.com/questions/1707316/isaacs-tfg-5c11-burnsides-transfer-lemma-for-an-abelian-hall-subgroup | 1,576,502,119,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540565544.86/warc/CC-MAIN-20191216121204-20191216145204-00126.warc.gz | 450,809,129 | 32,749 | # Isaacs TFG 5C11 - Burnside's transfer lemma for an abelian Hall subgroup
I am trying to solve the following exercise: Let $G$ be a finite group and $A$ a Hall abelian subgroup of $G$. Assume that $$A\le Z(N_G(A))$$ Then $G$ has a normal $p-$complement for every prime divisor $p$ of $|A|$
I am following the indications given. Argue by induction on $|G|$. If $G=1$, there is nothing to prove. Let $P\in Syl_p(A)$.
• Assume that $N_G(P)<G$. As $A$ is abelian, $P\triangleleft A$ and so $A\le N_G(P)<G$. Hence $A$ is an abelian Hall subgroup of $N_G(P)$. By hypothesis, $A\le Z(N_G(A))$ and since $N_{N_G(P)}(A)\le N_G(A)$, it follows that $$A\le Z(N_{N_G(P)}(A))$$ By the induction hypothesis, it follows that $P$ has a normal complement in $N_G(P)$ i.e. there is $K\triangleleft N_G(P)$ such that $N_G(P)=PK$ and $P\cap K=1$. Since $P$ is abelian, $P=Z(P)$. Moreover, since $P,K\triangleleft N_G(P)$, $[P,K]\le P\cap K=1$ and so $P\le Z(K)$. Hence $P\le Z(N_G(P))$ and, by by Burnside's transfer lemma, $P$ has a normal complement in $G$.
• Assume that $P\triangleleft G$. If every Sylow subgroup of $A$ is normal in $G$, we are done. Indeed, since $A$ is an Hall subgroup of $G$, every such subgroup is a Sylow subgroup of $G$ and therefore $G$ is nilpotent (and thus $p-$nilpotent for every prime $p$). Therefore assume that there is $Q\le Syl_q(G)$ for $q\neq p$ such that $N_G(Q)<G$. I now show that $P\le Z(N_G(Q))$. By the same reasoning as above, $A\le Z(N_{N_G(Q)}(A))$. Hence $N_G(Q)$ has a normal $p-$complement for every prime divisor $p$ of $|A|$. By the lemma below, $A$ has a normal complement in $N_G(Q)$ i.e. there is $L\le N_G(Q)$ such that $N_G(Q)=AL$ and $A\cap L=1$. Since $A$ is abelian, $P\le Z(A)$ and $P\le C_G(Q)\le N_G(Q)$. Since $P\triangleleft G$, it follows that $P\triangleleft N_G(Q)$. Therefore $[P,L]\le P\cap L\le A\cap L=1$. Hence $P\le Z(L)$ and so $P\le Z(N_G(Q))$.
From there I am stuck.
Above, I have used the following lemma.
Lemma: Let G be a finite group and $A$ an abelian subgroup of $G$. Write $A=P_1...P_n$ where the $P_i$ are the Sylow $p_i-$subgroups of $A$ for $1\leq i\leq n$. Assume each $P_i$ has a normal $(p_i-)$complement $K_i$ in $G$. Then $A$ has a normal complement in $G$ and it is $K_1 \cap...\cap K_n$.
Proof:
We first show that $P_1...P_n \cap \bigcap\limits_{1\leq i\leq n}K_i=1$. Since $A$ is abelian, each $P_i$ is a a normal subgroup of $A$ and so any product of the $P_i$ is a subgroup of $A$ and obviously of $G$. Since $[G:K_1]\wedge |P_2|=1$, it follows that $P_2\le K_1$. Now, by the modular law, $$P_1P_2\cap K_1=P_2(P_1\cap K_1)=P_2$$ and thus $$P_1P_2\cap K_1\cap K_2=P_2\cap K_2=1$$ The result then follows by induction.
We have $[G:\bigcap\limits_{1\leq i\leq n}K_i] \leq \prod\limits_{1\leq i\leq n} [G:K_i]$. Hence $$|\bigcap\limits_{1\leq i\leq n}K_i| \geq \dfrac{|G|}{\prod\limits_{1\leq i\leq n} [G:K_i]}=\dfrac{|G|}{\prod\limits_{1\leq i\leq n} |P_i|}$$ Now $|P_1...P_n|=\prod\limits_{1\leq i\leq n} |P_i|$ since the $P_i$ are all coprime. Hence $|P_1...P_n \bigcap\limits_{1\leq i\leq n} K_i| \geq |G|$. And so $G=P_1...P_n \bigcap\limits_{1\leq i\leq n} K_i$.
Last, since $K_i \triangleleft G$ for all i, we have $\bigcap\limits_{1\leq i\leq n}K_i \triangleleft G$ and so $K=\bigcap\limits_{1\leq i\leq n}K_i$ is the normal complement of $P_1...P_n$.
I found the solution.
By the same reasoning as above, $Q\le N_G(Z(Q))$ and so by Burnside's transfer theorem, $Q$ has a normal complement $L$ in $G$. Now as $P\triangleleft G$, $P$ is the unique Sylow $p-$subgroup of $G$ and so $P\le L$. Then $P$ is an abelian normal Hall subgroup of $L$ and so, by Schur E, $P$ has a normal complement $K$ in $L$. Since $P\triangleleft L$, it follows that $L=P\times K$. We have $$G=QL=QKP$$ and we show that $QK$ is a normal complement to $P$ in $G$. Actually we show that $G=P\times QK$. It suffices to show that $[P,QK]=P\cap QK=1$. $Q$ is clearly a $p'-$group. Since $P$ is a Sylow sybgroup of $L$, it follows that $K$ is also a $p'-$group. Since $Q\cap K=1$, $|QK|=|Q||K|$ is a $p'$number. Hence, by Lagrange's theorem, $P\cap QK=1$. Trivially, $[P,Q]=1$. And $[P,K]=1$ since $L=P\times K$. Hence $[P,QK]=1$.
I believe the following proof works.
We show by induction on $|G|$ that $G$ has a normal $p-$complement for every prime divisor $p$ of $|A|$, which gives immediately the result by the lemma. If $G=1$, there is nothing to prove. Let $P\in Syl_p(A)$.
• Assume that $N_G(P)<G$. As $A$ is abelian, $P\triangleleft A$ and so $A\le N_G(P)<G$. Hence $A$ is an abelian Hall subgroup of $N_G(P)$. By hypothesis, $A\le Z(N_G(A))$ and since $N_{N_G(P)}(A)\le N_G(A)$, it follows that $$A\le Z(N_{N_G(P)}(A))$$ By the induction hypothesis, it follows that $P$ has a normal complement in $N_G(P)$ i.e. there is $K\triangleleft N_G(P)$ such that $N_G(P)=PK$ and $P\cap K=1$. Since $P$ is abelian, $[P,P]=1$. Moreover, since $P,K\triangleleft N_G(P)$, $[P,K]\le P\cap K=1$ and so $[P,K]=1$. Hence $P\le Z(N_G(P))$ and, by Burnside's transfer theorem, $P$ has a normal complement in $G$.
• Assume that $P\triangleleft G$. If every Sylow subgroup of $A$ is normal in $G$, we are done. Indeed, it implies that $A\triangleleft G$ and so by hypothesis, $A\le Z(G)$. By Schur-Zassenhaus, $A$ has a complement $K$ in $G$. This complement is normal in $G$ as trivially $K\le N_G(K)$ and $A \le N_G(K)$ since $A\le Z(G)$ and therefore $G=AK\le N_G(K)$. Therefore assume that there is $Q\le Syl_q(G)$ for $q\neq p$ such that $N_G(Q)<G$.
We show that $P\le Z(N_G(Q))$. By induction, $A$ has a normal complement in $N_G(Q)$ i.e. there is $L\triangleleft N_G(Q)$ such that $N_G(Q)=AL$ and $A\cap L=1$. Since $A$ is abelian, $[P,A]=1$ and $P\le C_G(Q)\le N_G(Q)$. Since $P\triangleleft G$, it follows that $P\triangleleft N_G(Q)$. Therefore $[P,L]\le P\cap L\le A\cap L=1$. Hence $[P,N_G(Q)]=[P,AL]=1$ and so $P\le Z(N_G(Q))$.
We will prove that $P$ is contained in the center of $G$ and since $P$ is normal in $G$, we have that $P\le Z(N_G(P))$, so $P$ has a normal $p$-complement by Burnside's Theorem. If $g \in G$ then $[P,Q^g]=[P^g,Q^g]=[P,G]^g=1$ where the first equality follows from the fact that $P$ is normal in $G$ and the last from the fact that $[P,Q]=1$ since $P<Z(N_G(Q))$. This means that $P$ commutes with all the conjugates of $Q$ in $G$ and then commutes with the normal closure $Q^G$. If $Q^G=G$ then $P$ commutes with the whole $G$ and it is in the center, so we are done. If $Q^G<G$ then $Q^G$ is a normal subgroup of $G$ containing $Q$ that is a $q$-Sylow of $G$ and by Frattini Argument $G=N_G(Q)Q^G$. But $P$ commutes with both $N_G(Q)$ and $Q^G$ and then commutes with their product $G$, in other words $P<Z(G)$.
• Please, try to make the titles of your questions more informative. E.g., Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here. – Shahab Mar 21 '16 at 15:56
• If a sylow p-subgroup is normal then by Schur-Zassenhaus theorem it has an extension that splits, nevertheless this complement does not need to be normal. Indeed, for G the symmetric group of order 6, a cyclic group of order 3 is a Sylow normal subgroup and cannot exists a normal complement or order 2, being G non abelian. – Lorban Jan 4 '17 at 10:57
I propose an alternative solution for the last part of the proof. Summarizing, suppose $G$ finite group and $H$ is a Hall subgroup that is central in its normalizer, we have to prove that for each prime $p$ that divides $|H|$, $G$ has a normal $p$-complement. We work by induction on $|G|$. If $P \in Syl_p(H)$ you have already proved that $G$ has a normal $p$-complement in the case where $P$ is not normal in $G$ and also in the case where every Sylow subgroup of $H$ (that are indeed Sylow's in $G$) is normal in $G$. So you have assumed $P$ is a normal $p$-Sylow of $G$ contained in $H$ and there exists for a prime $q$, different from $p$, a $q$-Sylow $Q$ of $H$ that is not normal in $G$, i.e. $N_G(Q)<G$. As you have shown, we know that $P$ centralizes $N_G(Q)$. We will prove that $P$ is contained in the center of $G$ and since $P$ is normal in $G$, we have that $P\le Z(N_G(P))$, so $P$ has a normal $p$-complement by Burnside's Theorem. If $g \in G$ then $[P,Q^g]=[P^g,Q^g]=[P,G]^g=1$ where the first equality follows from the fact that $P$ is normal in $G$ and the last from the fact that $[P,Q]=1$ since $P<Z(N_G(Q))$. This means that $P$ commutes with all the conjugates of $Q$ in $G$ and then commutes with the normal closure $Q^G$. If $Q^G=G$ then $P$ commutes with the whole $G$ and it is in the center, so we are done. If $Q^G<G$ then $Q^G$ is a normal subgroup of $G$ containing $Q$ that is a $q$-Sylow of $G$ and by Frattini Argument $G=N_G(Q)Q^G$. But $P$ commutes with both $N_G(Q)$ and $Q^G$ and then commutes with their product $G$, in other words $P<Z(G)$. This completes the proof. | 3,306 | 9,157 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2019-51 | latest | en | 0.847288 |
http://euclidsmuse.com/?s=Angle | 1,519,011,540,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812327.1/warc/CC-MAIN-20180219032249-20180219052249-00798.warc.gz | 111,900,642 | 9,814 | # Euclid's Muse
## your source for INTERACTIVE math apps
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# Search Results for “Angle”
##### Chord Angle Theorem
The chord angle theorem states that in an inscribed triangle (ABC) where A is the center of the circle and BC is a chord, and BDC is an inscribed triangle on the same chord, angle BDC must equal one half of angle BAC. Try changing the angle and moving point D and observe the theorem’s truth. Note: the measure of angle BDC is being constantly recalculated as point D is dragged, but it doesn't change because of this theorem.
Tags: Chord, Angle, Theorem, Circle, Draggable, Proof
##### Euclids Elements - Book 1 - Proposition 45
Creating a parallelogram equal to a given quadrilateral with a given angle.
Tags: Euclid, Elements, Geometry, Parallelogram, Triangle, Angle
##### Morley's Theorem
An Illustration of Morley's Theorem
Tags: Triangle, angle-trisector, Morley's-theorem, equilateral
##### Basic Unit Circle
This very basic representation of the unit circle displays the unit circle with an input for the standard angle θ in degrees (which controls the angle between the hypotenuse and the x axis). The outputs represent the other two sides of the triangle and give their lengths through decimals. A good investigation for geometry students is to have them test out different angles here, then compare the results to those testing the angles with sine and cosine on their calculators. This allows them to visualize the unit circle in a precise diagram rather than simply running inputs and outputs on their calculators.
Tags: Geomtery, Unit-Circle, Sine, Cosine
##### Squeezing Twisted Savonius Wind Turbine Model
This model demonstrates that the surface of the Twisted Savonius wind turbine's blades are geometrically squeezed as the twist angle is increased and the parametric position is moved up and down the turbine. Learn more about the squeeze. Learn more about the Geometry of the Twisted Savonius Wind Turbine project. Note: the calculated radius in this particular example cannot be accurate because the model is a 2d geometric approximation of the real 3d shape. Accurate calculations are made from the top view model, which is visually more difficult to comprehend. The calculation here still varies accurately as the twist angle is changed and the position is moved up and down the turbine, but it also varies as the rotation is changed (which shouldn't happen).
Tags: Twisted-Savonius, Wind-Turbine, Pseudo-3d, Model, Squeeze, Geometric, Real-World, Ellipses, Arcs, Loci, Parametric/Proportional
##### Euclids Elements – Book 1 – Proposition 42
To construct, in a given rectilineal angle, a parallelogram equal to a given triangle. In other words, given angle D and triangle ABC (in blue), construct a parallelogram (in yellow) that has an equal area to triangle ABC.
Tags: Euclid, Elements, Geometry, Parallelogram, Triangle
##### Tchirnhausen's Cubic
The caustic formed by light projecting perpendicular to the axis of a parabola is called Tchirnhausen's Cubic. What happens when the light projects at some other angle?
Tags: Parabola, caustic
##### Twisted Savonius Wind Turbine Full Geometric Model (without traces/surfaces)
The Twisted Savonius Wind Turbine has promising applications for rooftop usage, but its high cost has kept it unfeasible for widespread adoption. The Twisted Savonius Geometric Modeling project explored the geometric properties of the turbine's shape, and proposed a more efficient method of construction and geometric design as a result. This is the complete side view "3d" model of the turbine. It models an extremely 3-dimensional shape by using ellipses to represent tilted circles. Changing X changes the rotation of the turbine (in operation). Theta represents the twist angle between the top and the bottom of the turbine. T controls the parametric location of the vertical surface - tracing it "fills in" the blade's surface. Learn more about this side view model. Visit the Geometry of the Twisted Savonius Wind Turbine website.
Tags: Twisted-Savonius, Wind-Turbine, Pseudo-3d, Model, Geometric, Real-World, Ellipses, Arcs, Loci
##### Geometric Top View Model of the Twisted Savonius Wind Turbine (Interactive)
This app models the top view of the Twisted Savonius Vertical Axis Wind Turbine (VAWT). The various inputs and draggable points allow you to see how the model can trace the blades' surfaces. You can also control the twist angle, radius, and rotation - which makes the whole thing spin! Learn more about the Twisted Savonius Modeling Project here.
Tags: Twisted-Savonius, Top-View, Model, Geometric, Real-World, Circles, Arcs, Loci
##### Parabolic Solar Cooker
Explore the relationship between f-number of a parabolic solar cooker and its sensitivity to change in angle of incoming light
Tags: parabola, solar-cooker, reflection | 1,115 | 4,852 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2018-09 | longest | en | 0.873564 |
https://wridemy.com/2023/03/18/what-are-the-positive-aspects-of-wind-energy-explain-at-least-5-of-them-2-identify-the-worlds-largest-three-wind-turbines-built-and-their-key-characteristics-locati/ | 1,708,754,092,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474523.8/warc/CC-MAIN-20240224044749-20240224074749-00400.warc.gz | 631,979,704 | 14,436 | Chat with us, powered by LiveChat What are the positive aspects of wind energy? Explain at least 5 of them. 2. ?Identify the worlds largest three wind turbines built and their key characteristics (Locati | Wridemy
## 18 Mar What are the positive aspects of wind energy? Explain at least 5 of them. 2. ?Identify the worlds largest three wind turbines built and their key characteristics (Locati
(All answers must have 5-7 sentences each, in own words)
1. What are the positive aspects of wind energy? Explain at least 5 of them.
2. Identify the world’s largest three wind turbines built and their key characteristics (Location, Power, blade dia etc)
3. Write an equation to find power from a wind turbine. Explain each parameter in it.
4. What is the meaning of this equation
5. For a turbine with 160 m of wing (blade length) produces 7 MW or power. What would be the air velocity to generate this power?
6. Derive an expression for Betz limit. What is the maximum mechanical efficiency possible from a wind turbine?
7. What is the relation between ground wind speed, height, and wind speed at a certain height?
8. IF the ground wind speed is 5 m/sec. Estimate wind speed at the height of 250 m. In this case, what would be the power generated if we use a blade of 160 m.
9. Explain the terms a) lift b) drag c) solidity d) turbulence in relation to Wind turbines.
10. What are the major considerations in the design of a wind turbine (watch the video and explain how each parameter influences wind power)
11. Explain how wind energy reduces emissions from the atmosphere?
12. What are HAWT and VAWT?
13. With a small diagram, explain key components of a wind turbine.
15. What rated the power of a turbine and rated wind speed?
16. Explain the operating regimes of a wind turbine and the control strategy in each
17. Calculate the diameter for a 7.5MW wind turbine blade
18. What is the tip-speed ratio of a turbine?
19. Why do larger turbines rotate slowly (at optimum tip-speed ratio)
20. What is the connection between the tip speed ratio and the number of blades?
21. Optimally, how long would it take the 3-bladed 5 MW “monster” turbine to complete one revolution? The blade diameter is 145 m. (Assume a rated wind speed of 11 m/s.)
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Chapter 14 Class 8 Factorisation
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Ex 14.2, 1 Factorise the following expressions. (v) 4𝑥^2 – 8x + 4 4𝑥^2 – 8x + 4 = 4 (𝑥^2−2𝑥+1) = 4 (𝑥^2+1−2𝑥) = 4 (𝑥^2+1^2−2×𝑥×1) = 𝟒 〖(𝒙−𝟏)〗^𝟐 Using (𝑎−𝑏^2 )=𝑎^2+𝑏^2−2𝑎𝑏 Here, 𝑎 = x and b = 1 = 𝟒 〖(𝒙−𝟏)〗^𝟐 | 241 | 383 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2023-14 | longest | en | 0.632507 |
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A236761 Numbers n such that n^4-n+1 is prime. 3
3, 6, 9, 13, 16, 18, 19, 24, 33, 39, 43, 45, 46, 60, 63, 64, 69, 75, 78, 79, 85, 91, 94, 105, 106, 108, 109, 115, 121, 129, 138, 174, 175, 183, 195, 198, 205, 210, 220, 249, 250, 276, 289, 295, 300, 309, 313, 318, 324, 343, 346, 348 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 LINKS Table of n, a(n) for n=1..52. EXAMPLE 115^4 - 115 + 1 = 174900511 is prime. Thus, 115 is a member of this sequence. MATHEMATICA Select[Range[400], PrimeQ[#^4-#+1]&] (* Harvey P. Dale, Jun 03 2015 *) PROG (Python) import sympy from sympy import isprime {print(n) for n in range(10**3) if isprime(n**4-n+1)} (PARI) s=[]; for(n=1, 400, if(isprime(n^4-n+1), s=concat(s, n))); s \\ Colin Barker, Jan 31 2014 CROSSREFS Cf. A049408, A126424. Sequence in context: A317557 A338763 A159908 * A088364 A022853 A198264 Adjacent sequences: A236758 A236759 A236760 * A236762 A236763 A236764 KEYWORD nonn AUTHOR Derek Orr, Jan 30 2014 STATUS approved
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Last modified April 17 11:20 EDT 2024. Contains 371763 sequences. (Running on oeis4.) | 551 | 1,473 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-18 | latest | en | 0.61602 |
http://www.math.auckland.ac.nz/~conder/RotaryMapsWithUpTo1000Edges.txt | 1,386,465,653,000,000,000 | text/plain | crawl-data/CC-MAIN-2013-48/segments/1386163057146/warc/CC-MAIN-20131204131737-00031-ip-10-33-133-15.ec2.internal.warc.gz | 433,860,615 | 66,718 | Rotary maps (on orientable or non-orientable surfaces) with up to 1000 edges ............................................................................ Below is a complete list of all rotary maps (on orientable or non-orientable surfaces) having at most 1000 edges. The fully regular maps (with flag-transitive automorphism group) are listed up to isomorphism and transformation under the six "Wilson" operators I, D, P, Opp, DP and PD, where I is the identity, D is duality, P is Petrie duality, and Opp is the "opposite" operator (which equals PDP and DPD). The chiral maps (which have maximum possible symmetry without any reflections) are listed up to isomorphism, mirror image, and duality. The list is ordered first by the number of edges, and then for each such number, the fully regular maps and then the chiral maps are listed by the type {p,q}_r where p is the face-size, q is the valency and r is the length of a Petrie polygon. Each entry in the list indicates also the genus of the map, and gives the order of its automorphism group and a presentation for the automorphism group in terms of the standard generators. For the fully regular maps, the standard generators a, b and c always satisfy the relations a^2 = b^2 = c^2 = (ac)^2 = (ab)^p = (bc)^q = (abc)^r = 1, among others. The above are defining relations for the Coxeter group G^{p,q,r}. If the map is not isomorphic to its image under one (or more) of the Wilson operators, then a short list is given of the Wilson operators needed to obtain all of those possible images. Note that each of those operators fixes the generator b, and permutes the three elements a, c and ac, as follows: * Duality D interchanges a with c and fixes ac * Petrie duality P interchanges a with ac and fixes c * The opposite transform Opp interchanges c with ac and fixes a * The triality operator DP induces the 3-cycle (a, ac, c) on {a,c,ac} * The inverse triality operator PD induces the 3-cycle (a, c, ac) on {a,c,ac}. For the chiral maps, the standard generators X and Y always satisfy the relations for the ordinary (p,q,2) triangle group, namely X^p = Y^q = (XY)^2 = 1, and then * The dual can be obtained by taking (X,Y) to (Y,X) * The mirror image can be obtained by taking (X,Y) to (X^{-1},Y^{-1}) * The mirror-dual can be obtained by taking (X,Y) to (Y^{-1},X^{-1}). This list was created by finding and analysing all normal subgroups of index up to 2000 in the relevant ordinary triangle groups and up to 4000 in the relevant full triangle groups, with the help of the MAGMA system. Among these, the fully regular maps with up to 640 edges have been used by Primoz Potocnik, Pablo Spiga and Gabriel Verret to help them determine all vertex-transitive cubic graphs on up to 1280 vertices. Separate sub-lists of the fully regular and the chiral maps are also given on my website http://www.math.auckland.ac.nz/~conder/ . Marston Conder December 2012 ........................ Rotary maps with 2 edges ........................ Orientable map of genus 0 and type {2,2}_2 invariant under all six Wilson transforms Automorphism group of order 8 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^2 ] Non-orientable map of genus 1 and type {2,4}_4 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 8 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, c*b*a*c*b ] ........................ Rotary maps with 3 edges ........................ Orientable map of genus 0 and type {2,3}_6 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 12 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^3 ] ........................ Rotary maps with 4 edges ........................ Orientable map of genus 0 and type {2,4}_4 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 16 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^4 ] Non-orientable map of genus 1 and type {2,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 16 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, c*b*c*b*a*c*b*c*b ] ........................ Rotary maps with 5 edges ........................ Orientable map of genus 0 and type {2,5}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 20 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^5 ] ........................ Rotary maps with 6 edges ........................ Orientable map of genus 0 and type {2,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 24 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^6 ] Non-orientable map of genus 1 and type {2,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 24 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*a*b*c*b*c*b*c ] Orientable map of genus 0 and type {3,3}_4 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 24 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^3 ] ........................ Rotary maps with 7 edges ........................ Orientable map of genus 0 and type {2,7}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 28 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^7 ] ........................ Rotary maps with 8 edges ........................ Orientable map of genus 0 and type {2,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 32 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^8 ] Non-orientable map of genus 1 and type {2,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 32 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_4 invariant under all six Wilson transforms Automorphism group of order 32 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^4 ] Orientable map of genus 2 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 32 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, c*b*c*a*b*a*c*b*c*b ] ........................ Rotary maps with 9 edges ........................ Orientable map of genus 0 and type {2,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 36 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^9 ] Orientable map of genus 1 and type {3,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 36 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*b*a*c*b*c*b ] ......................... Rotary maps with 10 edges ......................... Orientable map of genus 0 and type {2,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 40 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^10 ] Non-orientable map of genus 1 and type {2,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 40 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_10 isomorphic to its dual Automorphism group of order 20 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y^-2*X^2*Y ] ......................... Rotary maps with 11 edges ......................... Orientable map of genus 0 and type {2,11}_22 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 44 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^11 ] ......................... Rotary maps with 12 edges ......................... Orientable map of genus 0 and type {2,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 48 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^12 ] Non-orientable map of genus 1 and type {2,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 48 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 0 and type {3,4}_6 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 48 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^4 ] Non-orientable map of genus 4 and type {4,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 48 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^6 ] Orientable map of genus 2 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 48 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^6 ] ......................... Rotary maps with 13 edges ......................... Orientable map of genus 0 and type {2,13}_26 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 52 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^13 ] ......................... Rotary maps with 14 edges ......................... Orientable map of genus 0 and type {2,14}_14 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 56 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^14 ] Non-orientable map of genus 1 and type {2,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 56 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 15 edges ......................... Orientable map of genus 0 and type {2,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 60 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^15 ] Non-orientable map of genus 1 and type {3,5}_5 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 60 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^5, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b ] Non-orientable map of genus 9 and type {6,10}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 60 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*a*b*c*a*b*a*c*b*c*b*c*b ] ......................... Rotary maps with 16 edges ......................... Orientable map of genus 0 and type {2,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 64 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^16 ] Non-orientable map of genus 1 and type {2,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 64 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_4 invariant under all six Wilson transforms Automorphism group of order 64 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, c*a*b*c*a*b*a*c*b*a*c*b ] Orientable map of genus 3 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 64 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*c*b*c*b ] Orientable map of genus 3 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 64 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^8 ] Orientable map of genus 4 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 64 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b ] ......................... Rotary maps with 17 edges ......................... Orientable map of genus 0 and type {2,17}_34 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 68 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^17 ] ......................... Rotary maps with 18 edges ......................... Orientable map of genus 0 and type {2,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 72 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^18 ] Non-orientable map of genus 1 and type {2,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 72 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_6 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 72 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (c*b*a*b)^3 ] Non-orientable map of genus 7 and type {4,9}_9 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 72 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^9 ] Orientable map of genus 4 and type {6,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 72 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^6, (a*b*c*b*a*b)^2 ] ......................... Rotary maps with 19 edges ......................... Orientable map of genus 0 and type {2,19}_38 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 76 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^19 ] ......................... Rotary maps with 20 edges ......................... Orientable map of genus 0 and type {2,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 80 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^20 ] Non-orientable map of genus 1 and type {2,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 80 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 4 and type {4,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 80 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^10 ] Chiral map of genus 1 and type {4,4}_10 isomorphic to its dual Automorphism group of order 40 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X^-2*Y^2*X ] ......................... Rotary maps with 21 edges ......................... Orientable map of genus 0 and type {2,21}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 84 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^21 ] Non-orientable map of genus 13 and type {6,14}_21 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 84 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 1 and type {3,6}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 42 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X*Y^-2*X^-1*Y^2*X^-1*Y ] ......................... Rotary maps with 22 edges ......................... Orientable map of genus 0 and type {2,22}_22 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 88 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^22 ] Non-orientable map of genus 1 and type {2,44}_44 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 88 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 23 edges ......................... Orientable map of genus 0 and type {2,23}_46 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 92 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^23 ] ......................... Rotary maps with 24 edges ......................... Orientable map of genus 0 and type {2,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^24 ] Non-orientable map of genus 1 and type {2,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 2 and type {3,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, b*c*a*b*c*b*c*b*a*b*c*b*c*b*a*c ] Orientable map of genus 3 and type {4,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^6 ] Orientable map of genus 5 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^12 ] Non-orientable map of genus 10 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*a*b*c*a*b*a*c*b*c*b*c*b*c ] Non-orientable map of genus 10 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^12 ] Orientable map of genus 6 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 6 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*a*b*a*b*a*c*b*c*b*c ] Orientable map of genus 6 and type {6,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^8 ] Orientable map of genus 8 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 96 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c ] ......................... Rotary maps with 25 edges ......................... Orientable map of genus 0 and type {2,25}_50 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 100 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^25 ] Orientable map of genus 6 and type {5,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 100 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, c*a*b*c*b*a*c*b*c*b ] ......................... Rotary maps with 26 edges ......................... Orientable map of genus 0 and type {2,26}_26 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 104 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^26 ] Non-orientable map of genus 1 and type {2,52}_52 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 104 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_26 isomorphic to its dual Automorphism group of order 52 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X^-2*Y^-2*X^2*Y^2*X ] ......................... Rotary maps with 27 edges ......................... Orientable map of genus 0 and type {2,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 108 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^27 ] Orientable map of genus 1 and type {3,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 108 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b ] Orientable map of genus 7 and type {6,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 108 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^9 ] Chiral map of genus 7 and type {6,9}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 54 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y*X^-3*Y^-1*X*Y ] ......................... Rotary maps with 28 edges ......................... Orientable map of genus 0 and type {2,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 112 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^28 ] Non-orientable map of genus 1 and type {2,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 112 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 6 and type {4,14}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 112 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^14 ] Chiral map of genus 7 and type {7,7}_4 isomorphic to its mirror-dual Automorphism group of order 56 with defining relations: [ (X*Y)^2, X^-7, Y*X^-3*Y^2*X^-1 ] ......................... Rotary maps with 29 edges ......................... Orientable map of genus 0 and type {2,29}_58 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 116 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^29 ] ......................... Rotary maps with 30 edges ......................... Orientable map of genus 0 and type {2,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^30 ] Non-orientable map of genus 1 and type {2,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 0 and type {3,5}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^5 ] Non-orientable map of genus 6 and type {3,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 5 and type {4,5}_6 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, a*b*c*b*a*b*a*c*b*a*b*c*b ] Non-orientable map of genus 13 and type {4,15}_15 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^15 ] Orientable map of genus 4 and type {5,5}_6 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, (c*b*a*b)^3 ] Non-orientable map of genus 10 and type {5,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*c*b*a*c*b*a*c ] Non-orientable map of genus 12 and type {6,6}_6 invariant under all six Wilson transforms Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, a*b*c*b*c*b*a*b*c*b*c*b*c ] Non-orientable map of genus 16 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*b*c*a*b*a*b*a*c*b*c*b*c*b, b*c*a*b*c*a*b*a*c*b*c*b*a*b*c ] Orientable map of genus 8 and type {6,10}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^10 ] Chiral map of genus 11 and type {12,12}_10 isomorphic to its dual Automorphism group of order 60 with defining relations: [ (X*Y)^2, X*Y^-1*X^2*Y^-2 ] ......................... Rotary maps with 31 edges ......................... Orientable map of genus 0 and type {2,31}_62 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 124 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^31 ] ......................... Rotary maps with 32 edges ......................... Orientable map of genus 0 and type {2,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^32 ] Non-orientable map of genus 1 and type {2,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (a*b*c*b)^4 ] Orientable map of genus 5 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^8 ] Orientable map of genus 7 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 7 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^16 ] Orientable map of genus 8 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 9 and type {8,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2 ] Orientable map of genus 9 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*a*b*a*b*a*c*b*a*c*b*c ] Orientable map of genus 9 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, c*a*b*c*b*a*b*a*b*c*b*a*c*b ] Orientable map of genus 11 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c ] ......................... Rotary maps with 33 edges ......................... Orientable map of genus 0 and type {2,33}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 132 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^33 ] Non-orientable map of genus 21 and type {6,22}_33 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 132 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b ] ......................... Rotary maps with 34 edges ......................... Orientable map of genus 0 and type {2,34}_34 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 136 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^34 ] Non-orientable map of genus 1 and type {2,68}_68 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 136 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_34 isomorphic to its dual Automorphism group of order 68 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y^-2*X^2*Y*X^-1*Y ] ......................... Rotary maps with 35 edges ......................... Orientable map of genus 0 and type {2,35}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 140 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^35 ] Non-orientable map of genus 25 and type {10,14}_35 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 140 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b ] ......................... Rotary maps with 36 edges ......................... Orientable map of genus 0 and type {2,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^36 ] Non-orientable map of genus 1 and type {2,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {3,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, b*c*a*b*c*b*c*a*b*c*a^2*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 1 and type {4,4}_6 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 6 and type {4,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^9 ] Non-orientable map of genus 16 and type {4,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^18 ] Orientable map of genus 8 and type {4,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^18 ] Orientable map of genus 10 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^12 ] Orientable map of genus 10 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^6 ] Chiral map of genus 10 and type {8,8}_6 isomorphic to its dual Automorphism group of order 72 with defining relations: [ (X*Y)^2, X^8, X*Y^-1*X^3*Y*X^-1*Y^-1 ] ......................... Rotary maps with 37 edges ......................... Orientable map of genus 0 and type {2,37}_74 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 148 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^37 ] ......................... Rotary maps with 38 edges ......................... Orientable map of genus 0 and type {2,38}_38 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 152 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^38 ] Non-orientable map of genus 1 and type {2,76}_76 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 152 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 39 edges ......................... Orientable map of genus 0 and type {2,39}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 156 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^39 ] Non-orientable map of genus 25 and type {6,26}_39 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 156 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 78 with defining relations: [ (X*Y)^2, X^3, Y^6, X^-1*Y^2*X^-1*Y*X^-1*Y^3*X^-1*Y^2 ] ......................... Rotary maps with 40 edges ......................... Orientable map of genus 0 and type {2,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 160 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^40 ] Non-orientable map of genus 1 and type {2,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 160 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 6 and type {4,5}_5 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 160 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, b*c*a*b*c*a*b*a*c*b*a*c*b*a*c ] Orientable map of genus 9 and type {4,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 160 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^20 ] Orientable map of genus 10 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 160 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 12 and type {8,10}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 160 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^10 ] Orientable map of genus 14 and type {8,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 160 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b ] Chiral map of genus 1 and type {4,4}_20 isomorphic to its dual Automorphism group of order 80 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y^-2*X^-2*Y^2*X^2*Y ] Chiral map of genus 11 and type {8,8}_10 isomorphic to its dual Automorphism group of order 80 with defining relations: [ (X*Y)^2, X^8, Y^-1*X^4*Y^-3, X*Y^-2*X^2*Y^-1*X*Y^-1 ] Chiral map of genus 11 and type {8,8}_20 isomorphic to its dual Automorphism group of order 80 with defining relations: [ (X*Y)^2, X^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1 ] ......................... Rotary maps with 41 edges ......................... Orientable map of genus 0 and type {2,41}_82 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 164 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^41 ] ......................... Rotary maps with 42 edges ......................... Orientable map of genus 0 and type {2,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 168 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^42 ] Non-orientable map of genus 1 and type {2,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 168 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 19 and type {4,21}_21 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 168 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^21 ] Orientable map of genus 12 and type {6,14}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 168 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^14 ] Chiral map of genus 8 and type {6,6}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 84 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y*X*Y^-1*X^-3*Y^-1*X^2*Y ] ......................... Rotary maps with 43 edges ......................... Orientable map of genus 0 and type {2,43}_86 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 172 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^43 ] ......................... Rotary maps with 44 edges ......................... Orientable map of genus 0 and type {2,44}_44 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 176 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^44 ] Non-orientable map of genus 1 and type {2,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 176 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 10 and type {4,22}_44 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 176 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^22 ] ......................... Rotary maps with 45 edges ......................... Orientable map of genus 0 and type {2,45}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 180 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^45 ] Orientable map of genus 13 and type {6,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 180 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^15 ] Non-orientable map of genus 33 and type {10,18}_45 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 180 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] ......................... Rotary maps with 46 edges ......................... Orientable map of genus 0 and type {2,46}_46 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 184 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^46 ] Non-orientable map of genus 1 and type {2,92}_92 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 184 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 47 edges ......................... Orientable map of genus 0 and type {2,47}_94 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 188 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^47 ] ......................... Rotary maps with 48 edges ......................... Orientable map of genus 0 and type {2,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^48 ] Non-orientable map of genus 1 and type {2,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {3,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 10 and type {4,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 5 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b ] Orientable map of genus 9 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 9 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^12 ] Orientable map of genus 11 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 11 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^24 ] Non-orientable map of genus 22 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 22 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^24 ] Orientable map of genus 12 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 9 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*b*a*b*a*c*b*a*b*c*b ] Orientable map of genus 11 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b ] Orientable map of genus 14 and type {6,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^16 ] Orientable map of genus 15 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*a*c*b*c*b*c*b ] Orientable map of genus 15 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^12 ] Orientable map of genus 15 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^12 ] Non-orientable map of genus 34 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*c*a*b*c*a*b*a*c*b*c*b*c*b*c ] Non-orientable map of genus 34 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 18 and type {12,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 192 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c ] ......................... Rotary maps with 49 edges ......................... Orientable map of genus 0 and type {2,49}_98 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 196 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^49 ] Orientable map of genus 15 and type {7,14}_14 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 196 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (b*a)^7 ] ......................... Rotary maps with 50 edges ......................... Orientable map of genus 0 and type {2,50}_50 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 200 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^50 ] Non-orientable map of genus 1 and type {2,100}_100 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 200 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (c*b*a*b)^5 ] Orientable map of genus 16 and type {10,10}_10 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (b*c)^10 ] Chiral map of genus 1 and type {4,4}_50 isomorphic to its dual Automorphism group of order 100 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^-1 ] Chiral map of genus 21 and type {20,20}_10 isomorphic to its dual Automorphism group of order 100 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^6*Y^-2*X*Y^-1 ] ......................... Rotary maps with 51 edges ......................... Orientable map of genus 0 and type {2,51}_102 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 204 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^51 ] Non-orientable map of genus 33 and type {6,34}_51 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 204 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] ......................... Rotary maps with 52 edges ......................... Orientable map of genus 0 and type {2,52}_52 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 208 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^52 ] Non-orientable map of genus 1 and type {2,104}_104 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 208 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 12 and type {4,26}_52 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 208 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^26 ] Chiral map of genus 1 and type {4,4}_26 isomorphic to its dual Automorphism group of order 104 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^-1*X ] ......................... Rotary maps with 53 edges ......................... Orientable map of genus 0 and type {2,53}_106 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 212 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^53 ] ......................... Rotary maps with 54 edges ......................... Orientable map of genus 0 and type {2,54}_54 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^54 ] Non-orientable map of genus 1 and type {2,108}_108 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 11 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, a*b*c*b*a*b*a*c*b*a*b*c*b ] Non-orientable map of genus 25 and type {4,27}_27 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^27 ] Orientable map of genus 10 and type {6,6}_6 invariant under all six Wilson transforms Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b ] Orientable map of genus 10 and type {6,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 29 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 29 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 16 and type {6,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^18 ] Chiral map of genus 16 and type {6,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 108 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^-2*Y^-4 ] ......................... Rotary maps with 55 edges ......................... Orientable map of genus 0 and type {2,55}_110 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 220 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^55 ] Non-orientable map of genus 41 and type {10,22}_55 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 220 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c ] Chiral map of genus 12 and type {5,10}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 110 with defining relations: [ (X*Y)^2, X^5, Y^-1*X*Y^-1*X^-2*Y^-4 ] Chiral map of genus 12 and type {5,10}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 110 with defining relations: [ (X*Y)^2, X^5, Y*X^-1*Y*X^2*Y^-1*X*Y ] ......................... Rotary maps with 56 edges ......................... Orientable map of genus 0 and type {2,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 224 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^56 ] Non-orientable map of genus 1 and type {2,112}_112 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 224 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 13 and type {4,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^28 ] Orientable map of genus 14 and type {4,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 18 and type {8,14}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^14 ] Orientable map of genus 20 and type {8,28}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 17 and type {7,14}_4 not isomorphic to its dual or mirror-dual Automorphism group of order 112 with defining relations: [ (X*Y)^2, X^-7, X^-1*Y*X^-2*Y^3 ] Chiral map of genus 21 and type {14,14}_4 isomorphic to its mirror-dual Automorphism group of order 112 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^3*Y^-1*X^8*Y^-2 ] ......................... Rotary maps with 57 edges ......................... Orientable map of genus 0 and type {2,57}_114 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 228 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^57 ] Non-orientable map of genus 37 and type {6,38}_57 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 228 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 114 with defining relations: [ (X*Y)^2, X^3, Y^6, X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X^-1*Y ] ......................... Rotary maps with 58 edges ......................... Orientable map of genus 0 and type {2,58}_58 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 232 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^58 ] Non-orientable map of genus 1 and type {2,116}_116 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 232 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_58 isomorphic to its dual Automorphism group of order 116 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y*X^-1*Y*X^2*Y^2*X^2*Y^2*X^-1 ] ......................... Rotary maps with 59 edges ......................... Orientable map of genus 0 and type {2,59}_118 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 236 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^59 ] ......................... Rotary maps with 60 edges ......................... Orientable map of genus 0 and type {2,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^60 ] Non-orientable map of genus 1 and type {2,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 5 and type {3,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 4 and type {4,5}_6 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 12 and type {4,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, a*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 6 and type {4,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b*a*b)^3, (b*c)^6 ] Orientable map of genus 12 and type {4,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^15 ] Non-orientable map of genus 28 and type {4,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^30 ] Orientable map of genus 14 and type {4,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^30 ] Orientable map of genus 9 and type {5,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b*c*b)^2 ] Non-orientable map of genus 22 and type {6,6}_6 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, a*b*c*b*c*b*a*b*c*b*c*b*c ] Non-orientable map of genus 30 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*a*b*c*a*b*a*c*b*c*b*a*b*c ] Non-orientable map of genus 30 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, a*b*c*b*c*b*a*b*a*c*b*a*c*b*c*b*c ] Non-orientable map of genus 30 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 17 and type {6,15}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*c ] Orientable map of genus 18 and type {6,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^20 ] Orientable map of genus 20 and type {10,12}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^12 ] Orientable map of genus 23 and type {12,20}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 11 and type {4,12}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 120 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y*X*Y^-2*X^-2*Y^-1*X*Y^2 ] Chiral map of genus 21 and type {12,12}_10 isomorphic to its dual Automorphism group of order 120 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^12 ] ......................... Rotary maps with 61 edges ......................... Orientable map of genus 0 and type {2,61}_122 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 244 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^61 ] ......................... Rotary maps with 62 edges ......................... Orientable map of genus 0 and type {2,62}_62 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 248 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^62 ] Non-orientable map of genus 1 and type {2,124}_124 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 248 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 63 edges ......................... Orientable map of genus 0 and type {2,63}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 252 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^63 ] Orientable map of genus 19 and type {6,21}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 252 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^21 ] Non-orientable map of genus 49 and type {14,18}_63 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 252 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 1 and type {3,6}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 126 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-2*X^-1*Y*X^-1*Y^3*X*Y^-1 ] Chiral map of genus 22 and type {9,18}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 126 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, X^-9, Y^2*X^-3*Y^4, Y^2*X^-1*Y*X^-1*Y^3*X^-1 ] ......................... Rotary maps with 64 edges ......................... Orientable map of genus 0 and type {2,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^64 ] Non-orientable map of genus 1 and type {2,128}_128 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 9 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8 ] Orientable map of genus 9 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 13 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 13 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^16 ] Orientable map of genus 15 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 15 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^32 ] Orientable map of genus 16 and type {4,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 17 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*b*c*b*a*c*b, (a*b)^8, (a*b*c*b)^4 ] Orientable map of genus 17 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^8 ] Orientable map of genus 17 and type {8,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (b*c)^8, b*a*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*a ] Orientable map of genus 21 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, a*b*a*b*c*b*a*b*a*b*c*b*c*b*c*b ] Orientable map of genus 21 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^16 ] Orientable map of genus 21 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 21 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^8 ] Orientable map of genus 21 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 21 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 23 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 256 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 25 and type {16,16}_8 isomorphic to its dual Automorphism group of order 128 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, Y^-2*X^3*Y*X^-1*Y^-1 ] ......................... Rotary maps with 65 edges ......................... Orientable map of genus 0 and type {2,65}_130 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 260 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^65 ] Non-orientable map of genus 49 and type {10,26}_65 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 260 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b ] ......................... Rotary maps with 66 edges ......................... Orientable map of genus 0 and type {2,66}_66 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 264 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^66 ] Non-orientable map of genus 1 and type {2,132}_132 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 264 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 31 and type {4,33}_33 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 264 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^33 ] Orientable map of genus 20 and type {6,22}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 264 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^22 ] ......................... Rotary maps with 67 edges ......................... Orientable map of genus 0 and type {2,67}_134 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 268 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^67 ] ......................... Rotary maps with 68 edges ......................... Orientable map of genus 0 and type {2,68}_68 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 272 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^68 ] Non-orientable map of genus 1 and type {2,136}_136 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 272 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 16 and type {4,34}_68 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 272 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^34 ] Chiral map of genus 1 and type {4,4}_34 isomorphic to its dual Automorphism group of order 136 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X^-2*Y^-2*X^-2*Y^2*X^2*Y^2*X ] Chiral map of genus 18 and type {8,8}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 136 with defining relations: [ (X*Y)^2, X^8, Y^-1*X^4*Y*X^-1*Y^-1 ] ......................... Rotary maps with 69 edges ......................... Orientable map of genus 0 and type {2,69}_138 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 276 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^69 ] Non-orientable map of genus 45 and type {6,46}_69 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 276 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] ......................... Rotary maps with 70 edges ......................... Orientable map of genus 0 and type {2,70}_70 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 280 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^70 ] Non-orientable map of genus 1 and type {2,140}_140 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 280 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 24 and type {10,14}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^14 ] Chiral map of genus 31 and type {28,28}_10 isomorphic to its dual Automorphism group of order 140 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^2*Y^-2*X^9*Y^-1 ] ......................... Rotary maps with 71 edges ......................... Orientable map of genus 0 and type {2,71}_142 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 284 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^71 ] ......................... Rotary maps with 72 edges ......................... Orientable map of genus 0 and type {2,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^72 ] Non-orientable map of genus 1 and type {2,144}_144 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 7 and type {3,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 1 and type {4,4}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (a*b*c*b)^6 ] Orientable map of genus 15 and type {4,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^18 ] Orientable map of genus 17 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^36 ] Non-orientable map of genus 34 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 34 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^36 ] Orientable map of genus 18 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 13 and type {6,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (b*c)^6, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b ] Orientable map of genus 16 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^8 ] Orientable map of genus 19 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c, c*b*a*b*c*b*c*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 22 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (b*c)^24 ] Orientable map of genus 22 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 19 and type {8,8}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, c*a*b*c*a*b*c*a*b*a*b*c*b*c*b*a*b*a*c*b ] Orientable map of genus 20 and type {8,9}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (c*b)^9 ] Orientable map of genus 24 and type {8,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 24 and type {8,18}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^18 ] Orientable map of genus 26 and type {8,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 25 and type {12,12}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^12 ] Orientable map of genus 28 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 28 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*a*b*a*b*a*b*a*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 10 and type {4,8}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 144 with defining relations: [ (X*Y)^2, X^4, Y^8, Y*X*Y^-1*X^-1*Y*X^-1*Y*X^-1*Y^2 ] Chiral map of genus 19 and type {8,8}_6 isomorphic to its dual Automorphism group of order 144 with defining relations: [ (X*Y)^2, X^8, Y^-2*X^3*Y^-1*X*Y^-1 ] ......................... Rotary maps with 73 edges ......................... Orientable map of genus 0 and type {2,73}_146 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 292 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^73 ] ......................... Rotary maps with 74 edges ......................... Orientable map of genus 0 and type {2,74}_74 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 296 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^74 ] Non-orientable map of genus 1 and type {2,148}_148 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 296 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_74 isomorphic to its dual Automorphism group of order 148 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^-1*X*Y^-1 ] ......................... Rotary maps with 75 edges ......................... Orientable map of genus 0 and type {2,75}_150 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 300 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^75 ] Orientable map of genus 1 and type {3,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 300 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 49 and type {6,50}_75 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 300 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 26 and type {10,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 300 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (c*b)^15 ] ......................... Rotary maps with 76 edges ......................... Orientable map of genus 0 and type {2,76}_76 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 304 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^76 ] Non-orientable map of genus 1 and type {2,152}_152 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 304 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 18 and type {4,38}_76 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 304 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^38 ] ......................... Rotary maps with 77 edges ......................... Orientable map of genus 0 and type {2,77}_154 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 308 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^77 ] Non-orientable map of genus 61 and type {14,22}_77 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 308 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] ......................... Rotary maps with 78 edges ......................... Orientable map of genus 0 and type {2,78}_78 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 312 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^78 ] Non-orientable map of genus 1 and type {2,156}_156 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 312 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 37 and type {4,39}_39 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 312 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^39 ] Orientable map of genus 24 and type {6,26}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 312 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^26 ] Chiral map of genus 14 and type {6,6}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 156 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^-3*Y*X^-2*Y^-1*X ] Chiral map of genus 27 and type {12,12}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 156 with defining relations: [ (X*Y)^2, (Y^-1*X)^3, X^-1*Y*X^4*Y^-1*X^2*Y^-1 ] Chiral map of genus 27 and type {12,12}_26 isomorphic to its dual Automorphism group of order 156 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^2 ] ......................... Rotary maps with 79 edges ......................... Orientable map of genus 0 and type {2,79}_158 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 316 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^79 ] ......................... Rotary maps with 80 edges ......................... Orientable map of genus 0 and type {2,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^80 ] Non-orientable map of genus 1 and type {2,160}_160 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 5 and type {4,5}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, (a*b*c*b)^4 ] Non-orientable map of genus 26 and type {4,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, b*c*a*b*c*b*a*b*c*a*b*c*b*a*c*b*a*b*c, (b*c)^10 ] Orientable map of genus 17 and type {4,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^20 ] Orientable map of genus 19 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 19 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^40 ] Orientable map of genus 20 and type {4,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 9 and type {5,5}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, c*a*b*a*b*c*b*a*b*a*c*b*c*b*a*b*c*b ] Non-orientable map of genus 30 and type {5,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b*c*b*c*b)^2, a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 46 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c, b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*a*c ] Orientable map of genus 27 and type {8,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^20 ] Orientable map of genus 27 and type {8,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^20 ] Orientable map of genus 28 and type {10,16}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^16 ] Orientable map of genus 32 and type {16,20}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_20 isomorphic to its dual Automorphism group of order 160 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^-1 ] Chiral map of genus 11 and type {4,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 160 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^8, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^2 ] Chiral map of genus 11 and type {4,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 160 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^8, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2 ] Chiral map of genus 21 and type {8,8}_20 isomorphic to its dual Automorphism group of order 160 with defining relations: [ (X*Y)^2, X^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1 ] Chiral map of genus 21 and type {8,8}_20 isomorphic to its dual Automorphism group of order 160 with defining relations: [ (X*Y)^2, X^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 31 and type {16,16}_10 isomorphic to its dual Automorphism group of order 160 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X*Y^-3*X^8*Y^-1*X^3 ] Chiral map of genus 31 and type {16,16}_20 isomorphic to its dual Automorphism group of order 160 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-2*X^2*Y^-1*X*Y^-1 ] ......................... Rotary maps with 81 edges ......................... Orientable map of genus 0 and type {2,81}_162 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 324 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^81 ] Orientable map of genus 1 and type {3,6}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 324 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 29 and type {6,6}_9 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 324 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*a ] Orientable map of genus 19 and type {6,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 324 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^9 ] Orientable map of genus 19 and type {6,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 324 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 25 and type {6,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 324 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^27 ] Orientable map of genus 28 and type {9,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 324 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (b*a)^9 ] Chiral map of genus 25 and type {6,27}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 162 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^3*X^-2*Y*X^2*Y^5 ] Chiral map of genus 28 and type {9,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 162 with defining relations: [ (X*Y)^2, X^-9, Y*X^-4*Y*X^-1*Y^2 ] ......................... Rotary maps with 82 edges ......................... Orientable map of genus 0 and type {2,82}_82 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 328 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^82 ] Non-orientable map of genus 1 and type {2,164}_164 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 328 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_82 isomorphic to its dual Automorphism group of order 164 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X ] ......................... Rotary maps with 83 edges ......................... Orientable map of genus 0 and type {2,83}_166 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 332 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^83 ] ......................... Rotary maps with 84 edges ......................... Orientable map of genus 0 and type {2,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^84 ] Non-orientable map of genus 1 and type {2,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 3 and type {3,7}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^7, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 9 and type {3,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c, c*b*c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b ] Non-orientable map of genus 16 and type {4,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, (b*c*b*a*b*c)^3 ] Orientable map of genus 10 and type {4,7}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b*a*b)^3, (c*b)^7 ] Orientable map of genus 18 and type {4,21}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^21 ] Non-orientable map of genus 40 and type {4,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^42 ] Orientable map of genus 20 and type {4,42}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^42 ] Non-orientable map of genus 30 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 34 and type {6,7}_7 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, (c*b)^7 ] Orientable map of genus 25 and type {6,21}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 26 and type {6,28}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^28 ] Non-orientable map of genus 44 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (c*b*a*b)^3, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 30 and type {12,14}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^14 ] Orientable map of genus 33 and type {12,28}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 336 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c ] Chiral map of genus 1 and type {3,6}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 168 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X*Y^-1*X*Y ] Chiral map of genus 22 and type {6,12}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 168 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^-3*Y*X^-1*Y^-1 ] Chiral map of genus 22 and type {6,12}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 168 with defining relations: [ (X*Y)^2, X^6, Y^-1*X^2*Y^-1*X^-2*Y^-1*X^2*Y^-1, Y*X^2*Y^-1*X^2*Y^4, X*Y^-3*X^2*Y*X^-1*Y^-2 ] Chiral map of genus 29 and type {12,12}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 168 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^12 ] Chiral map of genus 35 and type {21,21}_4 isomorphic to its mirror-dual Automorphism group of order 168 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^3*Y^-8*X^8*Y^-2 ] ......................... Rotary maps with 85 edges ......................... Orientable map of genus 0 and type {2,85}_170 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 340 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^85 ] Non-orientable map of genus 65 and type {10,34}_85 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 340 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b ] ......................... Rotary maps with 86 edges ......................... Orientable map of genus 0 and type {2,86}_86 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 344 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^86 ] Non-orientable map of genus 1 and type {2,172}_172 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 344 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 87 edges ......................... Orientable map of genus 0 and type {2,87}_174 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 348 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^87 ] Non-orientable map of genus 57 and type {6,58}_87 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 348 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] ......................... Rotary maps with 88 edges ......................... Orientable map of genus 0 and type {2,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 352 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^88 ] Non-orientable map of genus 1 and type {2,176}_176 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 352 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 21 and type {4,44}_44 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 352 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^44 ] Orientable map of genus 22 and type {4,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 352 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 30 and type {8,22}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 352 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^22 ] Orientable map of genus 32 and type {8,44}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 352 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 89 edges ......................... Orientable map of genus 0 and type {2,89}_178 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 356 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^89 ] ......................... Rotary maps with 90 edges ......................... Orientable map of genus 0 and type {2,90}_90 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^90 ] Non-orientable map of genus 1 and type {2,180}_180 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 14 and type {3,10}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b, (b*c)^10 ] Non-orientable map of genus 43 and type {4,45}_45 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^45 ] Non-orientable map of genus 50 and type {6,15}_15 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c ] Non-orientable map of genus 53 and type {6,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 28 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*a*b*c*b*c*b*c*b*c*a^2*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 28 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^30 ] Orientable map of genus 32 and type {10,18}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^18 ] Chiral map of genus 1 and type {4,4}_30 isomorphic to its dual Automorphism group of order 180 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y*X^-1*Y ] Chiral map of genus 41 and type {36,36}_10 isomorphic to its dual Automorphism group of order 180 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-1*Y^3*X^-10*Y^2*X^-2 ] ......................... Rotary maps with 91 edges ......................... Orientable map of genus 0 and type {2,91}_182 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 364 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^91 ] Non-orientable map of genus 73 and type {14,26}_91 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 364 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c ] ......................... Rotary maps with 92 edges ......................... Orientable map of genus 0 and type {2,92}_92 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 368 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^92 ] Non-orientable map of genus 1 and type {2,184}_184 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 368 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 22 and type {4,46}_92 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 368 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^46 ] ......................... Rotary maps with 93 edges ......................... Orientable map of genus 0 and type {2,93}_186 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 372 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^93 ] Non-orientable map of genus 61 and type {6,62}_93 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 372 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 186 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y*X^-1*Y^-1*X*Y^3*X*Y^-1*X*Y ] ......................... Rotary maps with 94 edges ......................... Orientable map of genus 0 and type {2,94}_94 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 376 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^94 ] Non-orientable map of genus 1 and type {2,188}_188 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 376 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] ......................... Rotary maps with 95 edges ......................... Orientable map of genus 0 and type {2,95}_190 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 380 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^95 ] Non-orientable map of genus 73 and type {10,38}_95 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 380 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] ......................... Rotary maps with 96 edges ......................... Orientable map of genus 0 and type {2,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^96 ] Non-orientable map of genus 1 and type {2,192}_192 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 5 and type {3,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 9 and type {4,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (a*b*c*b)^4, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 9 and type {4,6}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, b*c*a*b*c*a*b*c*a*b*a*b*c*b*a*c*b*c*b*a ] Orientable map of genus 17 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^12 ] Non-orientable map of genus 34 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b*c*b)^4 ] Non-orientable map of genus 34 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^12 ] Orientable map of genus 17 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^12 ] Orientable map of genus 17 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b ] Orientable map of genus 21 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^24 ] Orientable map of genus 21 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 21 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^24 ] Orientable map of genus 23 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 23 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^48 ] Non-orientable map of genus 46 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 46 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^48 ] Orientable map of genus 24 and type {4,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 17 and type {6,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^6, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 17 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (c*b*a*b)^3, (b*c)^6, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b ] Orientable map of genus 17 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, b*a*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 21 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b ] Orientable map of genus 21 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, c*a*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 21 and type {6,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, (b*c)^8 ] Orientable map of genus 30 and type {6,32}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^32 ] Orientable map of genus 29 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^12 ] Orientable map of genus 29 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 29 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^12 ] Orientable map of genus 29 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, (b*c)^12 ] Non-orientable map of genus 58 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b ] Non-orientable map of genus 58 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 29 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^12 ] Orientable map of genus 29 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*c*b ] Orientable map of genus 33 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 33 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^24 ] Orientable map of genus 33 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 33 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*a*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 33 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*a*b*c*b*c*b*c*b*c*a*b*c*a^2*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 33 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 35 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 70 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*a*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 35 and type {12,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b, (a*b)^12 ] Orientable map of genus 35 and type {12,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^16 ] Orientable map of genus 38 and type {12,32}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 39 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 39 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 384 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 17 and type {6,6}_8 isomorphic to its dual Automorphism group of order 192 with defining relations: [ (X*Y)^2, X^6, Y^6, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-1*Y^-3*X^3*Y^3*X^-2 ] ......................... Rotary maps with 97 edges ......................... Orientable map of genus 0 and type {2,97}_194 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 388 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^97 ] ......................... Rotary maps with 98 edges ......................... Orientable map of genus 0 and type {2,98}_98 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 392 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^98 ] Non-orientable map of genus 1 and type {2,196}_196 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 392 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_14 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (c*b*a*b)^7 ] Orientable map of genus 36 and type {14,14}_14 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (b*c)^14 ] ......................... Rotary maps with 99 edges ......................... Orientable map of genus 0 and type {2,99}_198 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 396 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^99 ] Orientable map of genus 31 and type {6,33}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 396 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^33 ] Non-orientable map of genus 81 and type {18,22}_99 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 396 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] .......................... Rotary maps with 100 edges .......................... Orientable map of genus 0 and type {2,100}_100 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 400 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^100 ] Non-orientable map of genus 1 and type {2,200}_200 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 400 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 24 and type {4,50}_100 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^50 ] Orientable map of genus 36 and type {10,20}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (b*c)^20 ] Orientable map of genus 36 and type {10,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^10 ] Chiral map of genus 1 and type {4,4}_50 isomorphic to its dual Automorphism group of order 200 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^-1*X*Y^-1*X ] Chiral map of genus 21 and type {4,20}_10 not isomorphic to its dual or mirror-dual Automorphism group of order 200 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^-1*X^-1*Y*X^-1*Y*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^-2*X^-1*Y^2*X*Y^-1*X^-2*Y^-5 ] Chiral map of genus 26 and type {8,8}_10 isomorphic to its mirror-dual Automorphism group of order 200 with defining relations: [ (X*Y)^2, X^8, (X*Y^-2*X)^2, (X*Y^-1)^4, X*Y^-1*X^4*Y*X^-2*Y^-1 ] Chiral map of genus 41 and type {20,20}_10 isomorphic to its dual Automorphism group of order 200 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X^2*Y*X^-1*Y, X*Y^-3*X*Y^-1*X^7*Y^-1*X*Y^-2*X*Y^-1*X ] .......................... Rotary maps with 101 edges .......................... Orientable map of genus 0 and type {2,101}_202 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 404 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^101 ] .......................... Rotary maps with 102 edges .......................... Orientable map of genus 0 and type {2,102}_102 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 408 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^102 ] Non-orientable map of genus 1 and type {2,204}_204 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 408 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 49 and type {4,51}_51 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^51 ] Orientable map of genus 32 and type {6,34}_102 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^34 ] Chiral map of genus 35 and type {12,12}_34 isomorphic to its dual Automorphism group of order 204 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-2 ] .......................... Rotary maps with 103 edges .......................... Orientable map of genus 0 and type {2,103}_206 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 412 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^103 ] .......................... Rotary maps with 104 edges .......................... Orientable map of genus 0 and type {2,104}_104 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 416 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^104 ] Non-orientable map of genus 1 and type {2,208}_208 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 416 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 25 and type {4,52}_52 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 416 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^52 ] Orientable map of genus 26 and type {4,104}_104 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 416 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 36 and type {8,26}_104 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 416 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^26 ] Orientable map of genus 38 and type {8,52}_104 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 416 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_52 isomorphic to its dual Automorphism group of order 208 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X^-2*Y^-2*X^-2*Y^2*X^2*Y^2*X^2*Y^-2 ] Chiral map of genus 27 and type {8,8}_26 isomorphic to its dual Automorphism group of order 208 with defining relations: [ (X*Y)^2, X^8, Y^-1*X^4*Y^-3, X*Y^-2*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 27 and type {8,8}_52 isomorphic to its dual Automorphism group of order 208 with defining relations: [ (X*Y)^2, X^8, Y^-1*X^4*Y^-3, X*Y^-1*X*Y^-2*X^2*Y^-1*X*Y^-1*X*Y^-1 ] .......................... Rotary maps with 105 edges .......................... Orientable map of genus 0 and type {2,105}_210 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 420 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^105 ] Non-orientable map of genus 69 and type {6,70}_105 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 420 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 81 and type {10,42}_105 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 420 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 85 and type {14,30}_105 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 420 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 29 and type {6,15}_70 not isomorphic to its dual or mirror-dual Automorphism group of order 210 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^-1*Y*X^-2*Y*X^2*Y*X^-1*Y^-2 ] Chiral map of genus 43 and type {15,30}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 210 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, X^2*Y^-2*X^8*Y^-1*X*Y^-1 ] .......................... Rotary maps with 106 edges .......................... Orientable map of genus 0 and type {2,106}_106 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 424 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^106 ] Non-orientable map of genus 1 and type {2,212}_212 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 424 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_106 isomorphic to its dual Automorphism group of order 212 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X*Y^-1*X ] .......................... Rotary maps with 107 edges .......................... Orientable map of genus 0 and type {2,107}_214 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 428 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^107 ] .......................... Rotary maps with 108 edges .......................... Orientable map of genus 0 and type {2,108}_108 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^108 ] Non-orientable map of genus 1 and type {2,216}_216 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {3,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 10 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 10 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (a*b*c*b*c*b*a*b*c*b)^2 ] Orientable map of genus 24 and type {4,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^27 ] Non-orientable map of genus 52 and type {4,54}_54 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^54 ] Orientable map of genus 26 and type {4,54}_108 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^54 ] Orientable map of genus 25 and type {6,9}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (c*b)^9, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b ] Orientable map of genus 28 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 28 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, (b*c)^12 ] Orientable map of genus 28 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^12 ] Orientable map of genus 28 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 28 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*a*b)^2, (a*b*c*b*c*b*c*b)^2 ] Orientable map of genus 34 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^36 ] Orientable map of genus 34 and type {9,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 40 and type {12,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^18 ] Orientable map of genus 40 and type {12,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 432 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, (b*c)^18 ] Chiral map of genus 25 and type {6,9}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 216 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-9, X*Y^-1*X^2*Y^-1*X^-3*Y^-1*X^2*Y^2 ] Chiral map of genus 34 and type {6,36}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 216 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^-6*X^3*Y*X^-1*Y^-5 ] Chiral map of genus 28 and type {8,8}_6 isomorphic to its dual Automorphism group of order 216 with defining relations: [ (X*Y)^2, X^8, Y*X*Y^-1*X^2*Y*X^-1*Y, Y^2*X^4*Y^-2*X*Y ] Chiral map of genus 34 and type {9,12}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 216 with defining relations: [ (X*Y)^2, (X*Y^-1*X)^2, X^-9, Y*X^-1*Y^2*X^2*Y^2*X^-1*Y, Y^4*X^-2*Y^-3*X*Y ] Chiral map of genus 40 and type {12,18}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 216 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y^-3*X^3*Y*X^-1*Y^-2 ] Chiral map of genus 43 and type {12,36}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 216 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, X^12 ] Chiral map of genus 46 and type {24,24}_6 isomorphic to its dual Automorphism group of order 216 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y*X^5*Y^3*X^-1, Y^-1*X^6*Y^-1*X*Y^-1*X^2 ] .......................... Rotary maps with 109 edges .......................... Orientable map of genus 0 and type {2,109}_218 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 436 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^109 ] .......................... Rotary maps with 110 edges .......................... Orientable map of genus 0 and type {2,110}_110 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 440 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^110 ] Non-orientable map of genus 1 and type {2,220}_220 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 440 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 40 and type {10,22}_110 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^22 ] Chiral map of genus 34 and type {10,10}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 220 with defining relations: [ (X*Y)^2, X^10, Y^-1*X^5*Y^-1*X*Y^-2 ] Chiral map of genus 34 and type {10,10}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 220 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, X^10, X*Y^-1*X^4*Y^-2*X*Y^-1 ] Chiral map of genus 51 and type {44,44}_10 isomorphic to its dual Automorphism group of order 220 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X*Y^-3*X*Y^-1*X*Y^-1*X^9*Y^-1*X^3*Y^-1 ] .......................... Rotary maps with 111 edges .......................... Orientable map of genus 0 and type {2,111}_222 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 444 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^111 ] Non-orientable map of genus 73 and type {6,74}_111 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 444 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_74 not isomorphic to its dual or mirror-dual Automorphism group of order 222 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X^-1*Y^2*X^-1*Y*X^-1*Y ] .......................... Rotary maps with 112 edges .......................... Orientable map of genus 0 and type {2,112}_112 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^112 ] Non-orientable map of genus 1 and type {2,224}_224 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 25 and type {4,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^28 ] Orientable map of genus 27 and type {4,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 27 and type {4,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^56 ] Orientable map of genus 28 and type {4,112}_112 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 39 and type {8,28}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^28 ] Orientable map of genus 39 and type {8,28}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^28 ] Orientable map of genus 42 and type {14,16}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^16 ] Orientable map of genus 46 and type {16,28}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 448 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 41 and type {14,14}_4 isomorphic to its mirror-dual Automorphism group of order 224 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y^3*X^-1, X^-14 ] Chiral map of genus 49 and type {28,28}_4 isomorphic to its mirror-dual Automorphism group of order 224 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y^3*X^-1, X^-10*Y*X^-1*Y^2 ] Chiral map of genus 49 and type {28,28}_4 isomorphic to its mirror-dual Automorphism group of order 224 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^-2*Y^12*X^-1*Y*X^-9*Y^2*X^-1 ] .......................... Rotary maps with 113 edges .......................... Orientable map of genus 0 and type {2,113}_226 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 452 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^113 ] .......................... Rotary maps with 114 edges .......................... Orientable map of genus 0 and type {2,114}_114 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 456 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^114 ] Non-orientable map of genus 1 and type {2,228}_228 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 456 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 55 and type {4,57}_57 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 456 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^57 ] Orientable map of genus 36 and type {6,38}_114 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 456 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^38 ] Chiral map of genus 20 and type {6,6}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 228 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y*X^-1*Y*X*Y^-1*X^-1*Y*X^-3*Y^-1*X^2*Y*X^-2 ] .......................... Rotary maps with 115 edges .......................... Orientable map of genus 0 and type {2,115}_230 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 460 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^115 ] Non-orientable map of genus 89 and type {10,46}_115 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 460 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 116 edges .......................... Orientable map of genus 0 and type {2,116}_116 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 464 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^116 ] Non-orientable map of genus 1 and type {2,232}_232 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 464 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 28 and type {4,58}_116 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 464 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^58 ] Chiral map of genus 1 and type {4,4}_58 isomorphic to its dual Automorphism group of order 232 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X ] .......................... Rotary maps with 117 edges .......................... Orientable map of genus 0 and type {2,117}_234 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 468 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^117 ] Orientable map of genus 37 and type {6,39}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 468 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^39 ] Non-orientable map of genus 97 and type {18,26}_117 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 468 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 1 and type {3,6}_78 not isomorphic to its dual or mirror-dual Automorphism group of order 234 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X^-1*Y*X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X*Y^-2*X*Y^-1 ] Chiral map of genus 40 and type {9,18}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 234 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, X^-9, Y^2*X^-3*Y^4, Y*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^2 ] .......................... Rotary maps with 118 edges .......................... Orientable map of genus 0 and type {2,118}_118 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 472 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^118 ] Non-orientable map of genus 1 and type {2,236}_236 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 472 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 119 edges .......................... Orientable map of genus 0 and type {2,119}_238 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 476 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^119 ] Non-orientable map of genus 97 and type {14,34}_119 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 476 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b ] .......................... Rotary maps with 120 edges .......................... Orientable map of genus 0 and type {2,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^120 ] Non-orientable map of genus 1 and type {2,240}_240 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 15 and type {3,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b, c*a*b*c*a*b*c*b*c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 11 and type {4,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*a*b*c*b*a*b*c*a*b*a*b*c*b*c*b*a*b*c*b*a ] Non-orientable map of genus 38 and type {4,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, a*b*c*b*a*b*a*c*b*a*b*c*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Non-orientable map of genus 38 and type {4,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*b*c*a*b*c*a*b*a*c*b*c*b*c*b*a*b*c ] Non-orientable map of genus 46 and type {4,15}_15 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (c*b)^15 ] Orientable map of genus 27 and type {4,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^30 ] Orientable map of genus 29 and type {4,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^60 ] Non-orientable map of genus 58 and type {4,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 58 and type {4,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^60 ] Orientable map of genus 30 and type {4,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 17 and type {5,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*c*b ] Orientable map of genus 27 and type {5,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, c*a*b*c*b*c*b*a*c*b*c*b*c*b, b*c*a*b*c*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c ] Orientable map of genus 21 and type {6,6}_6 invariant under all six Wilson transforms Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (a*b*c*b*c*b*a*b)^2 ] Non-orientable map of genus 52 and type {6,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 29 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 62 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 62 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*a*b)^2, a*b*a*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 35 and type {6,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*a ] Non-orientable map of genus 70 and type {6,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*b*a*b*c*b*a*b*c*b*c*b*a*c*b, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b ] Non-orientable map of genus 70 and type {6,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b ] Orientable map of genus 35 and type {6,20}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 38 and type {6,40}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^40 ] Orientable map of genus 38 and type {8,15}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (c*b)^15 ] Orientable map of genus 42 and type {8,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c*b ] Orientable map of genus 42 and type {8,30}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^30 ] Orientable map of genus 44 and type {8,60}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 39 and type {10,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*c*b*c*b*c*b, b*c*a*b*a*b*a*b*a*c*b*c*b*a*b*c ] Non-orientable map of genus 78 and type {10,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*c*b*a*c*b*a*c, (a*b)^10 ] Non-orientable map of genus 78 and type {10,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, a*b*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b, (a*b)^10, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b ] Orientable map of genus 44 and type {10,24}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^24 ] Orientable map of genus 43 and type {12,15}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 45 and type {12,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^20 ] Orientable map of genus 47 and type {12,30}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*c ] Orientable map of genus 48 and type {12,40}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 50 and type {20,24}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 52 and type {24,30}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 53 and type {24,40}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, c*a*b*c*a*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] Chiral map of genus 21 and type {4,12}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^12 ] Chiral map of genus 41 and type {8,24}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X^-1*Y^2*X^2*Y*X^-1*Y^-2 ] Chiral map of genus 41 and type {8,24}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^2*X*Y^-1*X^2*Y^-2*X*Y ] Chiral map of genus 41 and type {12,12}_20 isomorphic to its dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X^5*Y^-1*X^2*Y ] Chiral map of genus 41 and type {12,12}_20 isomorphic to its dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-2*X ] Chiral map of genus 45 and type {15,15}_4 isomorphic to its mirror-dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y^2*X^-2, X^-1*Y^2*X^-9*Y*X^-1*Y ] Chiral map of genus 51 and type {24,24}_10 isomorphic to its dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^-1*X^6*Y^-1*X*Y^-1*X^9*Y^-1*X^4 ] Chiral map of genus 51 and type {24,24}_20 isomorphic to its dual Automorphism group of order 240 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-1*X^6*Y^-1*X*Y^-1*X*Y^-1 ] .......................... Rotary maps with 121 edges .......................... Orientable map of genus 0 and type {2,121}_242 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 484 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^121 ] Orientable map of genus 45 and type {11,22}_22 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 484 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (b*a)^11 ] .......................... Rotary maps with 122 edges .......................... Orientable map of genus 0 and type {2,122}_122 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 488 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^122 ] Non-orientable map of genus 1 and type {2,244}_244 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 488 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_122 isomorphic to its dual Automorphism group of order 244 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y ] .......................... Rotary maps with 123 edges .......................... Orientable map of genus 0 and type {2,123}_246 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 492 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^123 ] Non-orientable map of genus 81 and type {6,82}_123 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 492 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 124 edges .......................... Orientable map of genus 0 and type {2,124}_124 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 496 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^124 ] Non-orientable map of genus 1 and type {2,248}_248 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 496 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 30 and type {4,62}_124 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 496 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^62 ] .......................... Rotary maps with 125 edges .......................... Orientable map of genus 0 and type {2,125}_250 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 500 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^125 ] Orientable map of genus 26 and type {5,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c ] Orientable map of genus 46 and type {10,25}_50 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (c*b)^25 ] Chiral map of genus 46 and type {10,25}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 250 with defining relations: [ (X*Y)^2, Y^2*X^-3*Y^-1*X*Y^2 ] Chiral map of genus 46 and type {10,25}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 250 with defining relations: [ (X*Y)^2, X*Y^-2*X^-2*Y^-3*X ] .......................... Rotary maps with 126 edges .......................... Orientable map of genus 0 and type {2,126}_126 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^126 ] Non-orientable map of genus 1 and type {2,252}_252 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 8 and type {3,7}_9 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^7, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 61 and type {4,63}_63 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^63 ] Non-orientable map of genus 77 and type {6,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 40 and type {6,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 40 and type {6,42}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^42 ] Non-orientable map of genus 56 and type {7,7}_9 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, (c*b)^7, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b ] Non-orientable map of genus 72 and type {9,9}_9 plus image(s) under Wilson transforms [ D ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*b*a*b*a*b*a*b*c*b*c*b*a*c*b, (b*a)^9, (c*b)^9 ] Orientable map of genus 48 and type {14,18}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^18 ] Chiral map of genus 22 and type {6,6}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 252 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, X^2*Y^-1*X^2*Y^-1*X^3*Y^-1*X*Y*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 22 and type {6,6}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 252 with defining relations: [ (X*Y)^2, X^6, Y^6, Y*X*Y^-1*X^-2*Y^3*X^-1*Y ] Chiral map of genus 50 and type {18,18}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 252 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, Y*X^-12*Y^5 ] .......................... Rotary maps with 127 edges .......................... Orientable map of genus 0 and type {2,127}_254 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 508 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^127 ] .......................... Rotary maps with 128 edges .......................... Orientable map of genus 0 and type {2,128}_128 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^128 ] Non-orientable map of genus 1 and type {2,256}_256 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_16 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (a*b*c*b)^8 ] Orientable map of genus 17 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (b*c)^8, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 17 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 17 and type {4,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c*b*a*c*b ] Orientable map of genus 25 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 25 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 25 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^16 ] Orientable map of genus 29 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 29 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^32 ] Orientable map of genus 31 and type {4,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 31 and type {4,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^64 ] Orientable map of genus 32 and type {4,128}_128 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 33 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8 ] Orientable map of genus 33 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^8, b*c*b*a*b*c*b*a*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 33 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*b*c*b*a*c*b, (a*b)^8, (b*c)^8 ] Orientable map of genus 33 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, (b*c)^8 ] Orientable map of genus 33 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (b*c)^8 ] Orientable map of genus 33 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*a ] Orientable map of genus 33 and type {8,8}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 33 and type {8,8}_16 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, c*a*b*c*a*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*b*c*a*b*c*b*c*b*a*c*b*c ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^16 ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*c*b*c, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 41 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^16 ] Orientable map of genus 45 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 45 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^32 ] Orientable map of genus 45 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 45 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 47 and type {8,64}_64 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {16,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, b*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*c*b*a, a*b*c*b*c*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*a*b*a*b ] Orientable map of genus 49 and type {16,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, a*b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b ] Orientable map of genus 49 and type {16,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, c*b*c*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b, (a*b)^16 ] Orientable map of genus 53 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 53 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 25 and type {4,16}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 256 with defining relations: [ (X*Y)^2, X^4, X*Y^-3*X^-1*Y*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 41 and type {8,16}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 256 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, Y^-2*X*Y^-1*X^2*Y^2*X^-1*Y^-1, Y^2*X^-1*Y*X^2*Y^-2*X*Y ] Chiral map of genus 45 and type {8,32}_32 not isomorphic to its dual or mirror-dual Automorphism group of order 256 with defining relations: [ (X*Y)^2, X^8, Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-1, Y^-4*X^3*Y*X^-1*Y^-3 ] Chiral map of genus 53 and type {16,32}_32 not isomorphic to its dual or mirror-dual Automorphism group of order 256 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-1)^4, (X*Y^-3)^2, Y^-1*X^6*Y*X^-1*Y^-1*X*Y^-1, Y^-2*X^-1*Y*X^3*Y^-5 ] .......................... Rotary maps with 129 edges .......................... Orientable map of genus 0 and type {2,129}_258 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 516 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^129 ] Non-orientable map of genus 85 and type {6,86}_129 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 516 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_86 not isomorphic to its dual or mirror-dual Automorphism group of order 258 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X*Y^-1*X*Y^3*X^-1*Y^2*X^-1*Y ] .......................... Rotary maps with 130 edges .......................... Orientable map of genus 0 and type {2,130}_130 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 520 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^130 ] Non-orientable map of genus 1 and type {2,260}_260 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 520 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 48 and type {10,26}_130 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 520 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^26 ] Chiral map of genus 1 and type {4,4}_130 isomorphic to its dual Automorphism group of order 260 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y*X^-1*Y*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^-1 ] Chiral map of genus 1 and type {4,4}_130 isomorphic to its dual Automorphism group of order 260 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 53 and type {20,20}_26 isomorphic to its dual Automorphism group of order 260 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-2 ] Chiral map of genus 61 and type {52,52}_10 isomorphic to its dual Automorphism group of order 260 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-2*Y^2*X^-1*Y*X^-3*Y*X^-9*Y*X^-1*Y^3*X^-1*Y ] .......................... Rotary maps with 131 edges .......................... Orientable map of genus 0 and type {2,131}_262 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 524 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^131 ] .......................... Rotary maps with 132 edges .......................... Orientable map of genus 0 and type {2,132}_132 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^132 ] Non-orientable map of genus 1 and type {2,264}_264 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 30 and type {4,33}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^33 ] Non-orientable map of genus 64 and type {4,66}_66 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^66 ] Orientable map of genus 32 and type {4,66}_132 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^66 ] Orientable map of genus 41 and type {6,33}_44 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 42 and type {6,44}_132 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^44 ] Orientable map of genus 50 and type {12,22}_132 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^22 ] Orientable map of genus 53 and type {12,44}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 528 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 133 edges .......................... Orientable map of genus 0 and type {2,133}_266 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 532 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^133 ] Non-orientable map of genus 109 and type {14,38}_133 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 532 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] .......................... Rotary maps with 134 edges .......................... Orientable map of genus 0 and type {2,134}_134 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 536 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^134 ] Non-orientable map of genus 1 and type {2,268}_268 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 536 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 135 edges .......................... Orientable map of genus 0 and type {2,135}_270 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 540 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^135 ] Orientable map of genus 37 and type {6,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 540 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^15 ] Orientable map of genus 43 and type {6,45}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 540 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^45 ] Non-orientable map of genus 105 and type {10,54}_135 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 540 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 113 and type {18,30}_45 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 540 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c ] Chiral map of genus 43 and type {6,45}_90 not isomorphic to its dual or mirror-dual Automorphism group of order 270 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^7*X*Y^-1*X*Y*X^-1*Y^-4*X*Y^2 ] Chiral map of genus 61 and type {30,45}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 270 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, X^-1*Y*X^-1*Y*X^-8*Y^3 ] .......................... Rotary maps with 136 edges .......................... Orientable map of genus 0 and type {2,136}_136 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 544 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^136 ] Non-orientable map of genus 1 and type {2,272}_272 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 544 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 33 and type {4,68}_68 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 544 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^68 ] Orientable map of genus 34 and type {4,136}_136 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 544 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 48 and type {8,34}_136 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 544 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^34 ] Orientable map of genus 50 and type {8,68}_136 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 544 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_68 isomorphic to its dual Automorphism group of order 272 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^-1*X*Y^-1 ] Chiral map of genus 35 and type {8,8}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 272 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1 ] Chiral map of genus 35 and type {8,8}_34 isomorphic to its dual Automorphism group of order 272 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^-2*X^-1*Y*X*Y^-1*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 35 and type {8,8}_68 isomorphic to its dual Automorphism group of order 272 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-2 ] Chiral map of genus 52 and type {16,16}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 272 with defining relations: [ (X*Y)^2, X*Y^-2*X^2*Y^-3 ] Chiral map of genus 52 and type {16,16}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 272 with defining relations: [ (X*Y)^2, Y^-3*X^2*Y^-1*X*Y^-1 ] .......................... Rotary maps with 137 edges .......................... Orientable map of genus 0 and type {2,137}_274 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 548 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^137 ] .......................... Rotary maps with 138 edges .......................... Orientable map of genus 0 and type {2,138}_138 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 552 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^138 ] Non-orientable map of genus 1 and type {2,276}_276 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 552 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 67 and type {4,69}_69 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 552 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^69 ] Orientable map of genus 44 and type {6,46}_138 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 552 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^46 ] .......................... Rotary maps with 139 edges .......................... Orientable map of genus 0 and type {2,139}_278 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 556 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^139 ] .......................... Rotary maps with 140 edges .......................... Orientable map of genus 0 and type {2,140}_140 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 560 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^140 ] Non-orientable map of genus 1 and type {2,280}_280 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 560 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 34 and type {4,70}_140 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 560 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^70 ] Orientable map of genus 52 and type {10,28}_140 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 560 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^28 ] Orientable map of genus 54 and type {14,20}_140 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 560 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^20 ] Orientable map of genus 59 and type {20,28}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 560 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c ] Chiral map of genus 31 and type {4,28}_70 not isomorphic to its dual or mirror-dual Automorphism group of order 280 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^5*X*Y^-2*X^2*Y^-1*X*Y^6 ] Chiral map of genus 61 and type {28,28}_10 isomorphic to its dual Automorphism group of order 280 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-1*Y^4*X^-1*Y*X^-3*Y*X^-9*Y*X^-1*Y^3*X^-1*Y^2 ] Chiral map of genus 63 and type {35,35}_4 isomorphic to its mirror-dual Automorphism group of order 280 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-1*Y, X^-22*Y^2*X^-10*Y ] .......................... Rotary maps with 141 edges .......................... Orientable map of genus 0 and type {2,141}_282 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 564 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^141 ] Non-orientable map of genus 93 and type {6,94}_141 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 564 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 142 edges .......................... Orientable map of genus 0 and type {2,142}_142 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 568 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^142 ] Non-orientable map of genus 1 and type {2,284}_284 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 568 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 143 edges .......................... Orientable map of genus 0 and type {2,143}_286 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 572 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^143 ] Non-orientable map of genus 121 and type {22,26}_143 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 572 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] .......................... Rotary maps with 144 edges .......................... Orientable map of genus 0 and type {2,144}_144 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^144 ] Non-orientable map of genus 1 and type {2,288}_288 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {3,6}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 13 and type {3,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, (b*c)^12 ] Orientable map of genus 1 and type {4,4}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 19 and type {4,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, (a*b*c*b)^6 ] Orientable map of genus 19 and type {4,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*c*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*c*b*c ] Non-orientable map of genus 58 and type {4,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^18 ] Orientable map of genus 29 and type {4,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^18 ] Orientable map of genus 33 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^36 ] Orientable map of genus 33 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^36 ] Orientable map of genus 35 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 35 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^72 ] Non-orientable map of genus 70 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 70 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^72 ] Orientable map of genus 36 and type {4,144}_144 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 25 and type {6,6}_6 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (b*a*b*a*b*c)^3, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 25 and type {6,6}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*c*b, b*c*a*b*a*b*c*a*b*a*b*a*b*c*b*a*b*c*b*a*b*a ] Orientable map of genus 37 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (b*c)^12 ] Orientable map of genus 37 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 37 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*a*c*b*c*b*c*b, b*c*a*b*a*b*c*a*b*a*b*a*b*c*b*a*b*c*b*a*b*a ] Orientable map of genus 37 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*a*b*c*b*c*a*b*c*b*a*b*c*b*c*b*c*b*a*b*c ] Orientable map of genus 40 and type {6,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^16 ] Orientable map of genus 46 and type {6,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (b*c)^48 ] Orientable map of genus 46 and type {6,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 37 and type {8,8}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, a*b*c*b*a*b*c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Orientable map of genus 37 and type {8,8}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, (a*b*c*b)^6 ] Orientable map of genus 39 and type {8,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^9 ] Orientable map of genus 47 and type {8,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, (b*c)^18 ] Orientable map of genus 47 and type {8,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^18 ] Orientable map of genus 51 and type {8,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 51 and type {8,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^36 ] Orientable map of genus 51 and type {8,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^36 ] Non-orientable map of genus 106 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 106 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {12,12}_12 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, (a*b)^12, (b*c)^12 ] Orientable map of genus 49 and type {12,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*c*b*c*b*c*b, c*a*b*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (a*b)^12 ] Orientable map of genus 49 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*a*c*b*a*c, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b ] Orientable map of genus 52 and type {12,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, c*b*c*a*b*c*b*c*b*c*a*b*a*b*a*b*c*b*a*c*b*a*c*b ] Orientable map of genus 55 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, (a*b)^12, c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 55 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, (b*c)^24 ] Orientable map of genus 55 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^12 ] Orientable map of genus 55 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2 ] Orientable map of genus 58 and type {12,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 58 and type {12,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, a*b*c*a*b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 56 and type {16,18}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^18 ] Orientable map of genus 60 and type {16,36}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 576 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 19 and type {4,8}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 288 with defining relations: [ (X*Y)^2, X^4, Y^8, Y^-3*X^-1*Y*X^2*Y^4*X ] Chiral map of genus 37 and type {8,8}_12 isomorphic to its dual Automorphism group of order 288 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, Y*X^-3*Y*X^2*Y^4*X^-1, Y*X*Y^-1*X^-4*Y^-1*X^3*Y ] Chiral map of genus 55 and type {16,16}_6 isomorphic to its dual Automorphism group of order 288 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X^5*Y*X^-1*Y^2, X^16 ] Chiral map of genus 55 and type {16,16}_12 isomorphic to its dual Automorphism group of order 288 with defining relations: [ (X*Y)^2, Y^-2*X^3*Y^-1*X*Y^-1 ] .......................... Rotary maps with 145 edges .......................... Orientable map of genus 0 and type {2,145}_290 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 580 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^145 ] Non-orientable map of genus 113 and type {10,58}_145 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 580 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 146 edges .......................... Orientable map of genus 0 and type {2,146}_146 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 584 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^146 ] Non-orientable map of genus 1 and type {2,292}_292 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 584 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_146 isomorphic to its dual Automorphism group of order 292 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X*Y^-1 ] .......................... Rotary maps with 147 edges .......................... Orientable map of genus 0 and type {2,147}_294 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 588 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^147 ] Orientable map of genus 1 and type {3,6}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 588 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 97 and type {6,98}_147 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 588 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 57 and type {14,21}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 588 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (c*b)^21 ] Chiral map of genus 1 and type {3,6}_98 not isomorphic to its dual or mirror-dual Automorphism group of order 294 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X^-1*Y*X^-1*Y^2*X^-1*Y^-3*X*Y^-1*X*Y^3*X*Y^-2*X*Y^-1*X*Y^-2 ] Chiral map of genus 43 and type {6,21}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 294 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^3*X*Y^-1*X^3*Y*X^-2*Y^2 ] Chiral map of genus 64 and type {21,42}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 294 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, X^12*Y^-1*X*Y^-2*X*Y^-3*X ] .......................... Rotary maps with 148 edges .......................... Orientable map of genus 0 and type {2,148}_148 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 592 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^148 ] Non-orientable map of genus 1 and type {2,296}_296 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 592 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 36 and type {4,74}_148 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 592 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^74 ] Chiral map of genus 1 and type {4,4}_74 isomorphic to its dual Automorphism group of order 296 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X ] .......................... Rotary maps with 149 edges .......................... Orientable map of genus 0 and type {2,149}_298 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 596 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^149 ] .......................... Rotary maps with 150 edges .......................... Orientable map of genus 0 and type {2,150}_150 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^150 ] Non-orientable map of genus 1 and type {2,300}_300 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 73 and type {4,75}_75 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^75 ] Orientable map of genus 16 and type {5,5}_6 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*a*b*c*b*a*b*c*b*a*b*a*c*b*c*b*a*b*c*b*a*b ] Non-orientable map of genus 62 and type {5,10}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, b*c*a*b*a*b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*c ] Orientable map of genus 26 and type {6,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^6, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 48 and type {6,50}_150 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^50 ] Non-orientable map of genus 97 and type {10,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^10, c*b*c*a*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*a*c*b ] Orientable map of genus 56 and type {10,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^10, c*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*c*b*c*b ] Orientable map of genus 56 and type {10,30}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 600 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^30 ] Chiral map of genus 51 and type {12,12}_10 isomorphic to its dual Automorphism group of order 300 with defining relations: [ (X*Y)^2, (Y^-1*X)^3, Y^-2*X^4*Y*X^-1*Y^-2 ] Chiral map of genus 51 and type {12,12}_50 isomorphic to its dual Automorphism group of order 300 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, X^-2*Y^2*X*Y^-1*X^-2*Y^-1*X*Y^2*X^-1*Y ] Chiral map of genus 71 and type {60,60}_10 isomorphic to its dual Automorphism group of order 300 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-1*Y^6*X^-1*Y*X^-3*Y*X^-9*Y*X^-1*Y^3*X^-1*Y*X^-1 ] .......................... Rotary maps with 151 edges .......................... Orientable map of genus 0 and type {2,151}_302 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 604 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^151 ] .......................... Rotary maps with 152 edges .......................... Orientable map of genus 0 and type {2,152}_152 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 608 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^152 ] Non-orientable map of genus 1 and type {2,304}_304 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 608 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 37 and type {4,76}_76 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 608 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^76 ] Orientable map of genus 38 and type {4,152}_152 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 608 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 54 and type {8,38}_152 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 608 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^38 ] Orientable map of genus 56 and type {8,76}_152 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 608 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 153 edges .......................... Orientable map of genus 0 and type {2,153}_306 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 612 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^153 ] Orientable map of genus 49 and type {6,51}_102 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 612 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^51 ] Non-orientable map of genus 129 and type {18,34}_153 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 612 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 154 edges .......................... Orientable map of genus 0 and type {2,154}_154 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 616 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^154 ] Non-orientable map of genus 1 and type {2,308}_308 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 616 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 60 and type {14,22}_154 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 616 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^22 ] .......................... Rotary maps with 155 edges .......................... Orientable map of genus 0 and type {2,155}_310 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 620 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^155 ] Non-orientable map of genus 121 and type {10,62}_155 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 620 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 32 and type {5,10}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 310 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y^2*X*Y^-2*X^-1*Y^4*X^-1 ] Chiral map of genus 32 and type {5,10}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 310 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, Y^-1*X^-1*Y^2*X^2*Y*X^-1*Y^-2 ] .......................... Rotary maps with 156 edges .......................... Orientable map of genus 0 and type {2,156}_156 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^156 ] Non-orientable map of genus 1 and type {2,312}_312 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 36 and type {4,39}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^39 ] Non-orientable map of genus 76 and type {4,78}_78 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^78 ] Orientable map of genus 38 and type {4,78}_156 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^78 ] Orientable map of genus 49 and type {6,39}_52 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 50 and type {6,52}_156 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^52 ] Orientable map of genus 60 and type {12,26}_156 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^26 ] Orientable map of genus 63 and type {12,52}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 624 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {3,6}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 312 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X^-1*Y^2*X^-1*Y^2*X^-1*Y ] Chiral map of genus 27 and type {4,12}_78 not isomorphic to its dual or mirror-dual Automorphism group of order 312 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^12, Y^-1*X*Y^-1*X*Y^-2*X^-2*Y^-1*X*Y^2*X^-1*Y^-1 ] Chiral map of genus 40 and type {6,12}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 312 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^12, Y^-1*X^-1*Y*X*Y^-1*X^-2*Y*X^-2*Y^-1*X^2*Y^-1 ] Chiral map of genus 40 and type {6,12}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 312 with defining relations: [ (X*Y)^2, X^6, Y^-1*X^2*Y^-1*X^-2*Y^-1*X^2*Y^-1, Y*X^2*Y^-1*X^2*Y^4, Y^-1*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^-2 ] Chiral map of genus 53 and type {12,12}_26 isomorphic to its dual Automorphism group of order 312 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, X*Y^-1*X*Y^-2*X^2*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 53 and type {12,12}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 312 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, X^12, Y^-1*X^2*Y^-1*X^3*Y^-1*X*Y^-1*X^2 ] Chiral map of genus 53 and type {12,12}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 312 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^3*Y*X^-2*Y^-1, Y^3*X^3*Y^-1*X*Y^2, X^12 ] .......................... Rotary maps with 157 edges .......................... Orientable map of genus 0 and type {2,157}_314 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 628 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^157 ] .......................... Rotary maps with 158 edges .......................... Orientable map of genus 0 and type {2,158}_158 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 632 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^158 ] Non-orientable map of genus 1 and type {2,316}_316 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 632 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 159 edges .......................... Orientable map of genus 0 and type {2,159}_318 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 636 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^159 ] Non-orientable map of genus 105 and type {6,106}_159 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 636 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 160 edges .......................... Orientable map of genus 0 and type {2,160}_160 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^160 ] Non-orientable map of genus 1 and type {2,320}_320 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 9 and type {4,5}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, a*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*a*c*b*c ] Orientable map of genus 25 and type {4,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, (b*c)^10 ] Orientable map of genus 25 and type {4,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*c*b*a*b*c*b*a*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 66 and type {4,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 66 and type {4,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (b*c)^20 ] Orientable map of genus 33 and type {4,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^20 ] Orientable map of genus 37 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^40 ] Orientable map of genus 39 and type {4,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 39 and type {4,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^80 ] Orientable map of genus 40 and type {4,160}_160 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 29 and type {5,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 29 and type {5,8}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2 ] Orientable map of genus 45 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b ] Non-orientable map of genus 90 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (b*c)^10 ] Non-orientable map of genus 90 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, (b*c)^10 ] Orientable map of genus 45 and type {8,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c, (a*b*c*b)^4 ] Orientable map of genus 53 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^20 ] Non-orientable map of genus 106 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 106 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 53 and type {8,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^20 ] Orientable map of genus 57 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 57 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^40 ] Orientable map of genus 57 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 57 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 59 and type {8,80}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 60 and type {10,32}_160 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^32 ] Orientable map of genus 63 and type {16,20}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^20 ] Orientable map of genus 63 and type {16,20}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, (b*c)^20 ] Orientable map of genus 67 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 67 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 68 and type {20,32}_160 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 640 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_40 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y ] Chiral map of genus 21 and type {4,8}_10 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^4, Y^8, (Y^-1*X)^5, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2 ] Chiral map of genus 21 and type {4,8}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, Y^-1*X*Y^-2*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 21 and type {4,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, Y^-2*X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 31 and type {4,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y*X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y^-2*X*Y^2 ] Chiral map of genus 31 and type {4,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^16 ] Chiral map of genus 41 and type {8,8}_10 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, Y^8, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^-1*X*Y^-1*X^3*Y^-3*X ] Chiral map of genus 41 and type {8,8}_20 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-2*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 41 and type {8,8}_40 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-2*X^2*Y^-1 ] Chiral map of genus 41 and type {8,8}_40 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1 ] Chiral map of genus 41 and type {8,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y*X^-1*Y^-1 ] Chiral map of genus 41 and type {8,8}_40 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X*Y^-2*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 51 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-3*X^4*Y^-5, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 51 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-3*X^4*Y^-5, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1 ] Chiral map of genus 61 and type {16,16}_20 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, X^-1*Y^3*X^-9*Y^3 ] Chiral map of genus 61 and type {16,16}_20 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 61 and type {16,16}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, Y^-1*X^4*Y^-3, Y^-1*X^2*Y^-1*X^3*Y*X^-1*Y^-1*X^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 71 and type {32,32}_10 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^14*X^-11*Y*X^-3*Y^3 ] Chiral map of genus 71 and type {32,32}_20 isomorphic to its dual Automorphism group of order 320 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, X^-1*Y^3*X^-7*Y^2*X^-1*Y*X^-1 ] .......................... Rotary maps with 161 edges .......................... Orientable map of genus 0 and type {2,161}_322 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 644 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^161 ] Non-orientable map of genus 133 and type {14,46}_161 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 644 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 162 edges .......................... Orientable map of genus 0 and type {2,162}_162 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^162 ] Non-orientable map of genus 1 and type {2,324}_324 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 10 and type {3,9}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^9, b*c*a*b*c*a*b*c*b*c*a*b*c*b*a*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 1 and type {4,4}_18 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (c*b*a*b)^9 ] Non-orientable map of genus 47 and type {4,9}_9 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (c*b)^9 ] Non-orientable map of genus 79 and type {4,81}_81 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^81 ] Orientable map of genus 28 and type {6,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b ] Orientable map of genus 28 and type {6,6}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^6, c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 28 and type {6,6}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b ] Non-orientable map of genus 83 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b*c*b*c*b*c*b)^2 ] Orientable map of genus 46 and type {6,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^18 ] Orientable map of genus 46 and type {6,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, (b*c)^18 ] Orientable map of genus 46 and type {6,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b*c*b*c*b*a*b)^2 ] Non-orientable map of genus 101 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 101 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b ] Orientable map of genus 52 and type {6,54}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^54 ] Orientable map of genus 46 and type {9,9}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^9, c*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*c*b, b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b*a ] Orientable map of genus 64 and type {18,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 648 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, a*b*a*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*a*b*a*b*c*b*c*b, (a*b)^18 ] Chiral map of genus 46 and type {6,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 324 with defining relations: [ (X*Y)^2, X^6, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^-1*Y*X*Y^-1*X^2*Y^-4 ] Chiral map of genus 52 and type {6,54}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 324 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^9*X*Y^-1*X^2*Y^-3*X*Y^5 ] Chiral map of genus 64 and type {18,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 324 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, X*Y^-2*X*Y^-2*X^12 ] .......................... Rotary maps with 163 edges .......................... Orientable map of genus 0 and type {2,163}_326 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 652 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^163 ] .......................... Rotary maps with 164 edges .......................... Orientable map of genus 0 and type {2,164}_164 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 656 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^164 ] Non-orientable map of genus 1 and type {2,328}_328 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 656 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 40 and type {4,82}_164 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 656 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^82 ] Chiral map of genus 1 and type {4,4}_82 isomorphic to its dual Automorphism group of order 328 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 42 and type {8,8}_82 not isomorphic to its dual or mirror-dual Automorphism group of order 328 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, X^2*Y^-4*X^4*Y^-1*X ] .......................... Rotary maps with 165 edges .......................... Orientable map of genus 0 and type {2,165}_330 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 660 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^165 ] Non-orientable map of genus 35 and type {5,5}_5 invariant under all six Wilson transforms Automorphism group of order 660 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, b*c*a*b*c*a*b*a*c*b*a*c*b*a*c ] Non-orientable map of genus 46 and type {5,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 660 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*a*c*b*c, (c*b*a*b)^5 ] Non-orientable map of genus 109 and type {6,110}_165 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 660 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 129 and type {10,66}_165 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 660 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 141 and type {22,30}_165 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 660 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 56 and type {10,15}_66 not isomorphic to its dual or mirror-dual Automorphism group of order 330 with defining relations: [ (X*Y)^2, X^-5*Y^-1*X*Y^2 ] Chiral map of genus 56 and type {10,15}_66 not isomorphic to its dual or mirror-dual Automorphism group of order 330 with defining relations: [ (X*Y)^2, Y^-3*X^-2*Y^-1*X*Y^-1*X ] Chiral map of genus 67 and type {15,30}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 330 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y^4, X^-2*Y*X^3*Y^-1*X*Y^2, X^-3*Y*X^-9*Y*X^-1 ] Chiral map of genus 67 and type {15,30}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 330 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X*Y^-2*X^2*Y*X^-1*Y^2, X^-5*Y*X^-4*Y*X^-4 ] .......................... Rotary maps with 166 edges .......................... Orientable map of genus 0 and type {2,166}_166 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 664 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^166 ] Non-orientable map of genus 1 and type {2,332}_332 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 664 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 167 edges .......................... Orientable map of genus 0 and type {2,167}_334 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 668 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^167 ] .......................... Rotary maps with 168 edges .......................... Orientable map of genus 0 and type {2,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^168 ] Non-orientable map of genus 1 and type {2,336}_336 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 8 and type {3,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 8 and type {3,8}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, b*c*b*c*a*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 30 and type {4,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, b*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c*b*c ] Orientable map of genus 15 and type {4,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (b*c*b*a*b*c)^3 ] Non-orientable map of genus 30 and type {4,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 19 and type {4,7}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^7, b*c*a*b*c*b*a*b*c*a*b*a*b*c*b*c*b*a*b*c*b*a ] Non-orientable map of genus 44 and type {4,8}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, a*b*c*b*a*b*a*c*b*a*b*c*b, (b*c)^8, b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 22 and type {4,8}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, (a*b*c*b*c*b*a*b*c*b)^2, c*b*c*b*a*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 39 and type {4,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^42 ] Orientable map of genus 41 and type {4,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^84 ] Non-orientable map of genus 82 and type {4,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 82 and type {4,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^84 ] Orientable map of genus 42 and type {4,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 29 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (a*b*c*b)^4, c*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*a*b*c*b ] Non-orientable map of genus 58 and type {6,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, c*a*b*a*b*c*b*c*b*a*b*a*c*b*a*b*c*b*c*b*a*b ] Orientable map of genus 33 and type {6,7}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (c*b)^7, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 33 and type {6,7}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (c*b)^7, (a*b*c*b*c*b*a*b)^2 ] Non-orientable map of genus 72 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c, c*b*c*b*c*b*a*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 72 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c, c*b*c*a*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 72 and type {6,8}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c ] Non-orientable map of genus 90 and type {6,14}_14 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 51 and type {6,28}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 54 and type {6,56}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^56 ] Orientable map of genus 43 and type {8,8}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (c*b*a*b)^3, (a*b)^8, (b*c)^8, (a*b*c*b*c*b*a*b*a*b)^2 ] Orientable map of genus 56 and type {8,21}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (c*b)^21 ] Orientable map of genus 60 and type {8,42}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 60 and type {8,42}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^42 ] Orientable map of genus 62 and type {8,84}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 63 and type {12,21}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*c*a*b*c*b*c*a*b*a*b*a*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 65 and type {12,28}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^28 ] Orientable map of genus 67 and type {12,42}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 68 and type {12,56}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 66 and type {14,24}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^24 ] Orientable map of genus 72 and type {24,28}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 74 and type {24,42}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 75 and type {24,56}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 672 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 15 and type {3,12}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, X^3, (X*Y^-5)^2, Y*X^-1*Y^2*X*Y^-2*X*Y^-1*X*Y^-2*X*Y^3*X^-1*Y ] Chiral map of genus 29 and type {6,6}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y^-1*X^-3*Y^-1*X^2*Y*X^-2*Y^-1*X ] Chiral map of genus 43 and type {6,12}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, X^6, (X*Y^-1*X)^2, Y^-4*X^3*Y^-2, Y*X*Y^-1*X*Y^-3*X*Y^-1*X*Y^2*X^-1*Y^-2*X*Y^-1*X*Y ] Chiral map of genus 50 and type {6,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y*X*Y^-1*X^-1*Y*X^-3*Y^-1*X*Y^4 ] Chiral map of genus 50 and type {6,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, X^6, X*Y^-3*X^2*Y*X^-1*Y^-2, Y^-2*X^2*Y^-1*X^2*Y^-5 ] Chiral map of genus 57 and type {12,12}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^12 ] Chiral map of genus 64 and type {12,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, X^2*Y^-1*X^3*Y*X^-1*Y^-2 ] Chiral map of genus 64 and type {12,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, X*Y^-2*X^3*Y*X^-1*Y^-1*X, X^-1*Y^3*X^2*Y^2*X^-1*Y ] Chiral map of genus 65 and type {14,21}_12 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y^4, Y^-1*X^-5*Y*X^-3*Y^-1 ] Chiral map of genus 73 and type {21,42}_4 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y*X^-1*Y^2, X*Y^-1*X*Y^-4*X*Y^-1*X^8*Y^-4 ] Chiral map of genus 71 and type {24,24}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, Y^-2*X*Y^-1*X*Y^-1*X*Y^-2*X^8*Y^-2*X*Y^-2*X^2 ] Chiral map of genus 71 and type {24,24}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, Y^-1*X^6*Y^-5 ] Chiral map of genus 77 and type {42,42}_4 isomorphic to its mirror-dual Automorphism group of order 336 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^-2*Y^25*X^-1*Y*X^-11*Y*X^-1 ] .......................... Rotary maps with 169 edges .......................... Orientable map of genus 0 and type {2,169}_338 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 676 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^169 ] Orientable map of genus 66 and type {13,26}_26 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 676 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (b*a)^13 ] .......................... Rotary maps with 170 edges .......................... Orientable map of genus 0 and type {2,170}_170 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 680 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^170 ] Non-orientable map of genus 1 and type {2,340}_340 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 680 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 64 and type {10,34}_170 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 680 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^34 ] Chiral map of genus 1 and type {4,4}_170 isomorphic to its dual Automorphism group of order 340 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y^2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^2*X^2*Y^2*X^2*Y^2*X^-2 ] Chiral map of genus 1 and type {4,4}_170 isomorphic to its dual Automorphism group of order 340 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^-1*X*Y^-1*X ] Chiral map of genus 69 and type {20,20}_34 isomorphic to its dual Automorphism group of order 340 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-1*X*Y^-1*X^2*Y^-2*X*Y^-1 ] Chiral map of genus 81 and type {68,68}_10 isomorphic to its dual Automorphism group of order 340 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-1*Y*X^-8*Y*X^-2*Y*X^-11*Y*X^-3*Y^5 ] .......................... Rotary maps with 171 edges .......................... Orientable map of genus 0 and type {2,171}_342 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 684 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^171 ] Orientable map of genus 55 and type {6,57}_114 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 684 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^57 ] Non-orientable map of genus 145 and type {18,38}_171 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 684 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 1 and type {3,6}_114 not isomorphic to its dual or mirror-dual Automorphism group of order 342 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-1*X*Y^3*X*Y^-2*X*Y^-2*X*Y^-1 ] Chiral map of genus 58 and type {9,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 342 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, X^-9, Y^2*X^-3*Y^4, X^-1*Y*X*Y^-2*X*Y^-2*X^-1*Y*X^-1*Y^2*X^-1*Y^-2 ] Chiral map of genus 58 and type {9,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 342 with defining relations: [ (X*Y)^2, X^-9, X^-1*Y*X^-3*Y^3*X^-1 ] Chiral map of genus 58 and type {9,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 342 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, X^-9, X^-2*Y*X^-2*Y^2*X^-1*Y ] Chiral map of genus 58 and type {9,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 342 with defining relations: [ (X*Y)^2, X^-9, Y^3*X^-2*Y*X^-1*Y^2 ] .......................... Rotary maps with 172 edges .......................... Orientable map of genus 0 and type {2,172}_172 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 688 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^172 ] Non-orientable map of genus 1 and type {2,344}_344 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 688 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 42 and type {4,86}_172 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 688 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^86 ] .......................... Rotary maps with 173 edges .......................... Orientable map of genus 0 and type {2,173}_346 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 692 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^173 ] .......................... Rotary maps with 174 edges .......................... Orientable map of genus 0 and type {2,174}_174 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 696 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^174 ] Non-orientable map of genus 1 and type {2,348}_348 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 696 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 85 and type {4,87}_87 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 696 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^87 ] Orientable map of genus 56 and type {6,58}_174 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 696 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^58 ] Chiral map of genus 59 and type {12,12}_58 isomorphic to its dual Automorphism group of order 348 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, X^-2*Y^2*X^-1*Y*X^-2*Y^-1*X*Y^-1*X*Y^2 ] .......................... Rotary maps with 175 edges .......................... Orientable map of genus 0 and type {2,175}_350 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 700 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^175 ] Orientable map of genus 66 and type {10,35}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 700 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (c*b)^35 ] Non-orientable map of genus 145 and type {14,50}_175 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 700 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 176 edges .......................... Orientable map of genus 0 and type {2,176}_176 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^176 ] Non-orientable map of genus 1 and type {2,352}_352 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 41 and type {4,44}_44 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^44 ] Orientable map of genus 43 and type {4,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 43 and type {4,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^88 ] Orientable map of genus 44 and type {4,176}_176 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 63 and type {8,44}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^44 ] Orientable map of genus 63 and type {8,44}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^44 ] Orientable map of genus 70 and type {16,22}_176 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^22 ] Orientable map of genus 74 and type {16,44}_176 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 704 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 177 edges .......................... Orientable map of genus 0 and type {2,177}_354 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 708 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^177 ] Non-orientable map of genus 117 and type {6,118}_177 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 708 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 178 edges .......................... Orientable map of genus 0 and type {2,178}_178 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 712 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^178 ] Non-orientable map of genus 1 and type {2,356}_356 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 712 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_178 isomorphic to its dual Automorphism group of order 356 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^-2*X^2*Y^-1 ] .......................... Rotary maps with 179 edges .......................... Orientable map of genus 0 and type {2,179}_358 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 716 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^179 ] .......................... Rotary maps with 180 edges .......................... Orientable map of genus 0 and type {2,180}_180 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^180 ] Non-orientable map of genus 1 and type {2,360}_360 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 17 and type {3,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 13 and type {3,10}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^10, c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 10 and type {4,5}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, (c*b*a*b)^5 ] Non-orientable map of genus 32 and type {4,6}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 56 and type {4,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, (b*c*b*a*b*c)^3, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 37 and type {4,20}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (a*b*c*b)^6, b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 42 and type {4,45}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^45 ] Non-orientable map of genus 88 and type {4,90}_90 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^90 ] Orientable map of genus 44 and type {4,90}_180 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^90 ] Orientable map of genus 19 and type {5,5}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, (a*b*c*b)^4 ] Non-orientable map of genus 50 and type {5,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*a*b*a*b*c*b*a*b*c*a*b*a*b*c*b*c*b*a*c ] Non-orientable map of genus 65 and type {5,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^8, (b*c*b*a*b*c)^3, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b ] Non-orientable map of genus 62 and type {6,6}_6 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*b*a*c*b ] Non-orientable map of genus 86 and type {6,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, (a*b*c*b*c*b*c*b*a*b)^2 ] Non-orientable map of genus 86 and type {6,10}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^10, b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 86 and type {6,10}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^10, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*c*b*c ] Non-orientable map of genus 92 and type {6,12}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*a, b*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*b*a*c ] Orientable map of genus 49 and type {6,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {6,15}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (c*b)^15 ] Orientable map of genus 52 and type {6,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^20 ] Non-orientable map of genus 110 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a ] Orientable map of genus 58 and type {6,60}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^60 ] Orientable map of genus 58 and type {6,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 101 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (c*b*a*b)^3, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 68 and type {10,36}_180 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^36 ] Orientable map of genus 64 and type {12,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^15 ] Orientable map of genus 70 and type {12,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^30 ] Orientable map of genus 70 and type {12,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, (b*c)^30 ] Orientable map of genus 70 and type {12,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b, (a*b)^12 ] Non-orientable map of genus 144 and type {18,20}_45 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, a*b*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 72 and type {18,20}_180 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^20 ] Orientable map of genus 77 and type {20,36}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 720 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*b*c*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {4,4}_30 isomorphic to its dual Automorphism group of order 360 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X*Y^-1*X ] Chiral map of genus 41 and type {4,36}_90 not isomorphic to its dual or mirror-dual Automorphism group of order 360 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^-10*X*Y*X^-1*Y^-1*X*Y^2*X^-1*Y^-4 ] Chiral map of genus 61 and type {12,12}_30 isomorphic to its dual Automorphism group of order 360 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X^12, X^2*Y^-2*X^3*Y*X^-1*Y^-3 ] Chiral map of genus 61 and type {12,12}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 360 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, X^12 ] Chiral map of genus 81 and type {36,36}_10 isomorphic to its dual Automorphism group of order 360 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-2*Y^9*X^-2*Y*X^-3*Y^2*X^-8*Y*X^-3*Y^5 ] Chiral map of genus 82 and type {40,40}_6 isomorphic to its dual Automorphism group of order 360 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y*X^5*Y^3*X^-1, X^-2*Y^2*X^-13*Y*X^-2 ] .......................... Rotary maps with 181 edges .......................... Orientable map of genus 0 and type {2,181}_362 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 724 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^181 ] .......................... Rotary maps with 182 edges .......................... Orientable map of genus 0 and type {2,182}_182 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 728 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^182 ] Non-orientable map of genus 1 and type {2,364}_364 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 728 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 72 and type {14,26}_182 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 728 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^26 ] Chiral map of genus 79 and type {28,28}_26 isomorphic to its dual Automorphism group of order 364 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, X*Y^-1*X^6*Y^-1*X*Y^-2*X*Y^-1 ] .......................... Rotary maps with 183 edges .......................... Orientable map of genus 0 and type {2,183}_366 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 732 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^183 ] Non-orientable map of genus 121 and type {6,122}_183 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 732 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_122 not isomorphic to its dual or mirror-dual Automorphism group of order 366 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-1*X*Y^-2*X*Y^-3*X^-1*Y*X^-1*Y^3*X*Y^-2*X*Y^-1*X*Y^-2 ] .......................... Rotary maps with 184 edges .......................... Orientable map of genus 0 and type {2,184}_184 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 736 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^184 ] Non-orientable map of genus 1 and type {2,368}_368 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 736 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 45 and type {4,92}_92 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 736 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^92 ] Orientable map of genus 46 and type {4,184}_184 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 736 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 66 and type {8,46}_184 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 736 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^46 ] Orientable map of genus 68 and type {8,92}_184 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 736 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 185 edges .......................... Orientable map of genus 0 and type {2,185}_370 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 740 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^185 ] Non-orientable map of genus 145 and type {10,74}_185 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 740 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 186 edges .......................... Orientable map of genus 0 and type {2,186}_186 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 744 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^186 ] Non-orientable map of genus 1 and type {2,372}_372 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 744 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 91 and type {4,93}_93 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 744 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^93 ] Orientable map of genus 60 and type {6,62}_186 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 744 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^62 ] Chiral map of genus 32 and type {6,6}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 372 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y*X^-2*Y*X^-2*Y*X^3*Y*X^-1*Y*X^-2*Y*X^-2 ] .......................... Rotary maps with 187 edges .......................... Orientable map of genus 0 and type {2,187}_374 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 748 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^187 ] Non-orientable map of genus 161 and type {22,34}_187 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 748 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 188 edges .......................... Orientable map of genus 0 and type {2,188}_188 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 752 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^188 ] Non-orientable map of genus 1 and type {2,376}_376 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 752 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 46 and type {4,94}_188 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 752 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^94 ] .......................... Rotary maps with 189 edges .......................... Orientable map of genus 0 and type {2,189}_378 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 756 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^189 ] Orientable map of genus 55 and type {6,21}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 756 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^21 ] Orientable map of genus 61 and type {6,63}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 756 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^63 ] Non-orientable map of genus 157 and type {14,54}_189 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 756 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 161 and type {18,42}_63 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 756 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 1 and type {3,6}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^-3*X*Y^-1*X*Y^3*X*Y^-2*X^-1*Y^2*X^-1*Y ] Chiral map of genus 43 and type {6,9}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-9, X*Y^-1*X^-1*Y*X^2*Y^-1*X^2*Y*X^-2*Y^-1*X^2*Y^-1 ] Chiral map of genus 43 and type {6,9}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-9, X^2*Y^-1*X^2*Y^-1*X^2*Y*X^-2*Y^-1*X^2*Y^-1 ] Chiral map of genus 43 and type {6,9}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-9, Y^2*X*Y^-1*X^2*Y^-1*X^3*Y*X^-2*Y*X^-2 ] Chiral map of genus 61 and type {6,63}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^-11*X^2*Y^-1*X*Y^4*X^-1*Y^-5 ] Chiral map of genus 64 and type {9,18}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, X^-9, Y^2*X^-3*Y^4, Y^2*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-1*X*Y ] Chiral map of genus 85 and type {27,54}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, Y^-1*X*Y^-1*X*Y^-3*X*Y^-2*X^11*Y^-1*X*Y^-4 ] Chiral map of genus 88 and type {42,63}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 378 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, Y^-1*X^3*Y^-2*X*Y^-2*X^8*Y^-1*X^2*Y^-1 ] .......................... Rotary maps with 190 edges .......................... Orientable map of genus 0 and type {2,190}_190 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 760 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^190 ] Non-orientable map of genus 1 and type {2,380}_380 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 760 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 72 and type {10,38}_190 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 760 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^38 ] Chiral map of genus 91 and type {76,76}_10 isomorphic to its dual Automorphism group of order 380 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X*Y^-1*X^11*Y^-1*X*Y^-3*X^3*Y^-1*X^10*Y^-2*X^2*Y^-1*X ] .......................... Rotary maps with 191 edges .......................... Orientable map of genus 0 and type {2,191}_382 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 764 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^191 ] .......................... Rotary maps with 192 edges .......................... Orientable map of genus 0 and type {2,192}_192 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^192 ] Non-orientable map of genus 1 and type {2,384}_384 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {3,6}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 21 and type {3,16}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, b*c*a*b*c*b*c*b*c*a*b*c*a^2*b*a*c*b*c*b*c*b*a*c*b*c, b*c*a*b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 17 and type {4,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, (a*b*c*b*c*b)^4 ] Orientable map of genus 17 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (a*b*c*b)^4, (a*b*c*b*c*b)^4 ] Orientable map of genus 17 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*a*b*c*b*a*b*c*b ] Orientable map of genus 33 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c*b, (b*c)^12 ] Orientable map of genus 33 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b*a*b*c, (b*c)^12 ] Orientable map of genus 33 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*c*b*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b, c*b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*a*b*c*b*a*b*c*b ] Orientable map of genus 33 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*b*c*b*c, (b*c)^12 ] Orientable map of genus 33 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 33 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 41 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*b*c*b*c, b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 41 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^24 ] Orientable map of genus 41 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c*b, c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 41 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^24 ] Non-orientable map of genus 82 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*b*c*b*a*b*c*b*a*b*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 82 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b*c*b*c*b)^4 ] Non-orientable map of genus 82 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b*a*b*c, c*b*c*a*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 82 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^24 ] Orientable map of genus 45 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 45 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^48 ] Orientable map of genus 45 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 45 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^48 ] Orientable map of genus 47 and type {4,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 47 and type {4,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^96 ] Non-orientable map of genus 94 and type {4,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 94 and type {4,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^96 ] Orientable map of genus 48 and type {4,192}_192 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 33 and type {6,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 33 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*a*b*c*a*b*a*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 33 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 33 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (c*b*a*b)^3, (b*c)^6, a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c, (c*b*a*b*a*b*c*b)^3 ] Orientable map of genus 41 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (b*c)^8, (a*b*c*b*a*b)^4 ] Orientable map of genus 41 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^8, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 41 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, (b*c)^8 ] Orientable map of genus 41 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*c, a*b*a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 41 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, b*c*a*b*c*b*c*b*c*a*b*c*a^2*b*a*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 41 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 82 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b)^4, (b*c)^8, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*a*b*a*c*b*c, b*c*b*a*b*a*b*c*a*b*c*b*a*b*c*b*c*b*a*b*a ] Non-orientable map of genus 82 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, (b*c)^8, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*a*b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b*a ] Orientable map of genus 41 and type {6,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b ] Orientable map of genus 53 and type {6,16}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c, b*c*a*b*c*b*c*b*c*a*b*c*a^2*b*a*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 53 and type {6,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, (b*c)^16 ] Orientable map of genus 53 and type {6,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 62 and type {6,64}_192 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^64 ] Orientable map of genus 57 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*a, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, a*b*c*a*b*a*b*a*b*a*c*b*a*b*c*b*c*b ] Orientable map of genus 57 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*a*c*b ] Orientable map of genus 57 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 114 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4 ] Non-orientable map of genus 114 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*a*c ] Non-orientable map of genus 114 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^12 ] Non-orientable map of genus 114 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*a*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b*c, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*a, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*c*b ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*c*b*c, (b*c)^12 ] Orientable map of genus 57 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^24 ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^24 ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*a, c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, c*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^24 ] Orientable map of genus 65 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, (b*c)^24 ] Non-orientable map of genus 130 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*a*c ] Non-orientable map of genus 130 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b ] Non-orientable map of genus 130 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 130 and type {8,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*a*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b*c, c*b*c*a*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^48 ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 69 and type {8,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 71 and type {8,96}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 142 and type {8,96}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 69 and type {12,16}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, c*a*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b, a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*b*a*c*b*a*c*b ] Orientable map of genus 69 and type {12,16}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*c*b*a*b*c)^3, a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*b*a*c*b*a*c*b ] Orientable map of genus 69 and type {12,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b, (a*b)^12 ] Orientable map of genus 69 and type {12,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^12, (b*c)^16 ] Orientable map of genus 69 and type {12,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, c*b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 69 and type {12,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 75 and type {12,32}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 75 and type {12,32}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^32 ] Orientable map of genus 78 and type {12,64}_192 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*a*c, c*b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, (b*c)^24 ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c, (a*b)^16 ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^24 ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (b*c)^24 ] Orientable map of genus 77 and type {16,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, (b*c)^24 ] Orientable map of genus 83 and type {24,32}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c ] Orientable map of genus 83 and type {24,32}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 768 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 17 and type {4,6}_12 not isomorphic to its dual or mirror-dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, X^4, Y^6, Y^-1*X^-1*Y*X^-1*Y*X^2*Y*X^-1*Y^-1*X*Y^-1, (X*Y^-2)^4 ] Chiral map of genus 33 and type {6,6}_8 isomorphic to its dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, X^6, Y^6, Y*X*Y^-1*X^2*Y*X^-1*Y, (X*Y^-1*X)^4 ] Chiral map of genus 33 and type {6,6}_8 isomorphic to its dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, X^6, Y^6, Y^-1*X^2*Y^-1*X^-2*Y^3*X ] Chiral map of genus 41 and type {6,8}_12 not isomorphic to its dual or mirror-dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, X^6, Y^8, (X*Y^-1)^4, X*Y^-3*X^-2*Y*X^-1*Y^-1*X^2*Y^-1, Y^3*X*Y^-1*X^-2*Y^-1*X^2*Y*X^-1 ] Chiral map of genus 49 and type {6,12}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, X^6, Y^-2*X^-1*Y*X^2*Y^-1*X*Y^-2, Y^2*X^2*Y^-1*X^-1*Y*X^-1*Y^-1*X^2*Y ] Chiral map of genus 49 and type {6,12}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, X^6, Y^-2*X^-1*Y*X^2*Y^-1*X*Y^-2, Y^-2*X^2*Y^-1*X^-1*Y*X^-1*Y^-1*X^2*Y^-1 ] Chiral map of genus 65 and type {12,12}_8 isomorphic to its dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, X^12, Y^-1*X^6*Y^-5, X*Y^-1*X*Y^-1*X^3*Y^-3*X*Y^-1 ] Chiral map of genus 65 and type {12,12}_8 isomorphic to its dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, X^12, Y^-1*X^6*Y^-5, X^2*Y^-2*X^3*Y^-1*X*Y^3 ] Chiral map of genus 65 and type {12,12}_8 isomorphic to its dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, Y^-1*X*Y^-1*X^3*Y*X^-1*Y^-2, Y*X^-1*Y*X^3*Y^-1*X*Y^2 ] Chiral map of genus 81 and type {16,48}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-1)^4, (X*Y^-3)^2, Y^-1*X^6*Y*X^-1*Y^-1*X*Y^-1, Y^-5*X^2*Y^-1*X^-2*Y^-6 ] Chiral map of genus 89 and type {48,48}_8 isomorphic to its dual Automorphism group of order 384 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y, Y^-1*X^6*Y^-1*X^2*Y^-2 ] .......................... Rotary maps with 193 edges .......................... Orientable map of genus 0 and type {2,193}_386 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 772 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^193 ] .......................... Rotary maps with 194 edges .......................... Orientable map of genus 0 and type {2,194}_194 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 776 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^194 ] Non-orientable map of genus 1 and type {2,388}_388 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 776 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_194 isomorphic to its dual Automorphism group of order 388 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X ] .......................... Rotary maps with 195 edges .......................... Orientable map of genus 0 and type {2,195}_390 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 780 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^195 ] Non-orientable map of genus 129 and type {6,130}_195 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 780 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 153 and type {10,78}_195 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 780 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 169 and type {26,30}_195 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 780 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] Chiral map of genus 53 and type {6,15}_130 not isomorphic to its dual or mirror-dual Automorphism group of order 390 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X*Y^-1*X^2*Y^-1*X^3*Y*X^-2*Y^2 ] Chiral map of genus 79 and type {15,30}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 390 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^2, X^-15 ] .......................... Rotary maps with 196 edges .......................... Orientable map of genus 0 and type {2,196}_196 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 784 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^196 ] Non-orientable map of genus 1 and type {2,392}_392 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 784 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_14 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 784 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 48 and type {4,98}_196 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 784 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^98 ] Orientable map of genus 50 and type {8,8}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 784 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*a*b)^2, (a*b*c*b)^4, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*c*b ] Orientable map of genus 78 and type {14,28}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 784 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^14, (b*c)^28 ] Orientable map of genus 78 and type {14,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 784 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^14 ] Chiral map of genus 91 and type {49,49}_4 isomorphic to its mirror-dual Automorphism group of order 392 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^3*Y^-33*X^12*Y^-1 ] .......................... Rotary maps with 197 edges .......................... Orientable map of genus 0 and type {2,197}_394 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 788 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^197 ] .......................... Rotary maps with 198 edges .......................... Orientable map of genus 0 and type {2,198}_198 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 792 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^198 ] Non-orientable map of genus 1 and type {2,396}_396 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 792 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 97 and type {4,99}_99 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 792 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^99 ] Non-orientable map of genus 125 and type {6,44}_44 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 792 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 64 and type {6,66}_66 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 792 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 64 and type {6,66}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 792 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^66 ] Orientable map of genus 80 and type {18,22}_198 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 792 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^22 ] .......................... Rotary maps with 199 edges .......................... Orientable map of genus 0 and type {2,199}_398 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 796 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^199 ] .......................... Rotary maps with 200 edges .......................... Orientable map of genus 0 and type {2,200}_200 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^200 ] Non-orientable map of genus 1 and type {2,400}_400 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_20 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (a*b*c*b)^10 ] Non-orientable map of genus 86 and type {4,25}_25 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (c*b)^25 ] Orientable map of genus 49 and type {4,100}_100 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^100 ] Orientable map of genus 50 and type {4,200}_200 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 51 and type {8,8}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 51 and type {8,8}_20 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, a*b*a*c*b*c*a*b*a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 72 and type {8,50}_200 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^50 ] Orientable map of genus 74 and type {8,100}_200 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 76 and type {10,40}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (b*c)^40 ] Orientable map of genus 76 and type {10,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, (a*b)^10 ] Orientable map of genus 81 and type {20,20}_20 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^20 ] Orientable map of genus 86 and type {20,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, b*a*b*c*b*c*b*c*a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a ] Orientable map of genus 86 and type {20,40}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 800 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_100 isomorphic to its dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^-2*X^2*Y^-1 ] Chiral map of genus 41 and type {4,20}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^20 ] Chiral map of genus 51 and type {8,8}_4 isomorphic to its dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, (X*Y^-1)^4, X^-2*Y^-4*X^4*Y^2 ] Chiral map of genus 51 and type {8,8}_10 isomorphic to its mirror-dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, X^-2*Y^-4*X^4*Y^-2 ] Chiral map of genus 51 and type {8,8}_50 isomorphic to its dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X*Y^-1*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 51 and type {8,8}_100 isomorphic to its dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X^-1*Y*X^-1*Y*X^-1*Y*X^-2*Y^-1*X*Y^2*X^-1*Y*X^-1*Y ] Chiral map of genus 71 and type {8,40}_10 not isomorphic to its dual or mirror-dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1, X^-1*Y^2*X*Y^-2*X^2*Y^-6 ] Chiral map of genus 71 and type {8,40}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y*X^2*Y^-2*X^2*Y^2*X^-1*Y*X^-1, Y^6*X^2*Y*X^-1*Y^-2*X*Y ] Chiral map of genus 81 and type {20,20}_20 isomorphic to its dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X*Y^-1*X^2*Y^-1*X*Y^2*X^-1, X^3*Y^-3*X*Y^-1*X^6*Y^-1*X*Y^-1*X*Y^-2 ] Chiral map of genus 91 and type {40,40}_10 isomorphic to its dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^-1*X^13*Y^-1*X*Y^-3*X^3*Y^-1*X^9*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 91 and type {40,40}_20 isomorphic to its dual Automorphism group of order 400 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, Y^-2*X*Y^-3*X*Y^-1*X^5*Y^-1*X*Y^-1*X*Y^-2*X ] .......................... Rotary maps with 201 edges .......................... Orientable map of genus 0 and type {2,201}_402 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 804 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^201 ] Non-orientable map of genus 133 and type {6,134}_201 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 804 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_134 not isomorphic to its dual or mirror-dual Automorphism group of order 402 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^3*X*Y^-2*X*Y^-1*X*Y^-2*X*Y ] .......................... Rotary maps with 202 edges .......................... Orientable map of genus 0 and type {2,202}_202 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 808 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^202 ] Non-orientable map of genus 1 and type {2,404}_404 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 808 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_202 isomorphic to its dual Automorphism group of order 404 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1 ] .......................... Rotary maps with 203 edges .......................... Orientable map of genus 0 and type {2,203}_406 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 812 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^203 ] Non-orientable map of genus 169 and type {14,58}_203 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 812 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 59 and type {7,14}_58 not isomorphic to its dual or mirror-dual Automorphism group of order 406 with defining relations: [ (X*Y)^2, X^7, Y*X*Y^-2*X^2*Y*X^-1*Y^2, Y*X*Y^-1*X^-3*Y^4*X^-1 ] Chiral map of genus 59 and type {7,14}_58 not isomorphic to its dual or mirror-dual Automorphism group of order 406 with defining relations: [ (X*Y)^2, X^7, Y*X*Y^-1*X^2*Y*X^-1*Y ] Chiral map of genus 59 and type {7,14}_58 not isomorphic to its dual or mirror-dual Automorphism group of order 406 with defining relations: [ (X*Y)^2, X^7, Y*X*Y^-1*X^-3*Y*X^-3*Y ] .......................... Rotary maps with 204 edges .......................... Orientable map of genus 0 and type {2,204}_204 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^204 ] Non-orientable map of genus 1 and type {2,408}_408 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 48 and type {4,51}_102 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^51 ] Non-orientable map of genus 100 and type {4,102}_102 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^102 ] Orientable map of genus 50 and type {4,102}_204 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^102 ] Orientable map of genus 65 and type {6,51}_68 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b ] Orientable map of genus 66 and type {6,68}_204 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^68 ] Orientable map of genus 80 and type {12,34}_204 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^34 ] Orientable map of genus 83 and type {12,68}_102 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 816 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 35 and type {4,12}_102 not isomorphic to its dual or mirror-dual Automorphism group of order 408 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^12, Y*X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 69 and type {12,12}_34 isomorphic to its dual Automorphism group of order 408 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, Y^-2*X^-1*Y*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 86 and type {24,24}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 408 with defining relations: [ (X*Y)^2, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, Y^-1*X^6*Y^-2*X^3 ] .......................... Rotary maps with 205 edges .......................... Orientable map of genus 0 and type {2,205}_410 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 820 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^205 ] Non-orientable map of genus 161 and type {10,82}_205 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 820 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 42 and type {5,10}_82 not isomorphic to its dual or mirror-dual Automorphism group of order 410 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y^-1*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y^-2*X^2 ] Chiral map of genus 42 and type {5,10}_82 not isomorphic to its dual or mirror-dual Automorphism group of order 410 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, X^-1*Y*X^-1*Y*X^-2*Y*X^-1*Y^-3 ] .......................... Rotary maps with 206 edges .......................... Orientable map of genus 0 and type {2,206}_206 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 824 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^206 ] Non-orientable map of genus 1 and type {2,412}_412 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 824 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 207 edges .......................... Orientable map of genus 0 and type {2,207}_414 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 828 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^207 ] Orientable map of genus 67 and type {6,69}_138 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 828 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^69 ] Non-orientable map of genus 177 and type {18,46}_207 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 828 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] .......................... Rotary maps with 208 edges .......................... Orientable map of genus 0 and type {2,208}_208 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^208 ] Non-orientable map of genus 1 and type {2,416}_416 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {4,52}_52 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^52 ] Orientable map of genus 51 and type {4,104}_104 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 51 and type {4,104}_104 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^104 ] Orientable map of genus 52 and type {4,208}_208 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 75 and type {8,52}_104 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^52 ] Orientable map of genus 75 and type {8,52}_104 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^52 ] Orientable map of genus 84 and type {16,26}_208 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^26 ] Orientable map of genus 88 and type {16,52}_208 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 832 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_52 isomorphic to its dual Automorphism group of order 416 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 27 and type {4,8}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 416 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, X^-1*Y^2*X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 27 and type {4,8}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 416 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, X^-1*Y^2*X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y^-1*X*Y*X^-1*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 53 and type {8,8}_52 isomorphic to its dual Automorphism group of order 416 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X^-1*Y*X*Y^-1*X^-1*Y*X^-1*Y*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y^2 ] Chiral map of genus 53 and type {8,8}_52 isomorphic to its dual Automorphism group of order 416 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X^-1*Y*X*Y^-1*X^-1*Y*X^-1*Y*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 79 and type {16,16}_26 isomorphic to its dual Automorphism group of order 416 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, Y^-3*X*Y^-1*X^8*Y^-2*X ] Chiral map of genus 79 and type {16,16}_52 isomorphic to its dual Automorphism group of order 416 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-2*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y^-1 ] .......................... Rotary maps with 209 edges .......................... Orientable map of genus 0 and type {2,209}_418 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 836 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^209 ] Non-orientable map of genus 181 and type {22,38}_209 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 836 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] .......................... Rotary maps with 210 edges .......................... Orientable map of genus 0 and type {2,210}_210 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^210 ] Non-orientable map of genus 1 and type {2,420}_420 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 103 and type {4,105}_105 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^105 ] Non-orientable map of genus 130 and type {6,35}_35 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a, b*c*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*c ] Orientable map of genus 68 and type {6,70}_210 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^70 ] Non-orientable map of genus 150 and type {10,21}_35 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^10, b*c*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*a*c, b*c*a*b*c*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*c*b*a ] Orientable map of genus 80 and type {10,42}_210 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^42 ] Orientable map of genus 84 and type {14,30}_210 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^30 ] Orientable map of genus 94 and type {30,42}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 840 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Chiral map of genus 64 and type {6,30}_70 not isomorphic to its dual or mirror-dual Automorphism group of order 420 with defining relations: [ (X*Y)^2, X^6, X*Y^-3*X^2*Y*X^-1*Y^-2, Y^3*X*Y^-2*X*Y^3*X^-2*Y^2 ] Chiral map of genus 64 and type {6,30}_70 not isomorphic to its dual or mirror-dual Automorphism group of order 420 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X*Y^-1*X^-1*Y*X^2*Y^-1*X^2*Y*X^-2*Y^-1*X^2*Y^-1, Y^5*X*Y^-1*X^3*Y*X^-2*Y^3 ] Chiral map of genus 92 and type {30,30}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 420 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^5*Y^-1*X*Y^-1*X^3*Y^-2*X^10*Y^-1*X*Y^-2*X*Y^-1*X ] Chiral map of genus 101 and type {84,84}_10 isomorphic to its dual Automorphism group of order 420 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^-1*X^15*Y^-1*X*Y^-3*X^3*Y^-1*X^9*Y^-1*X^2*Y^-1*X*Y^-1*X^2 ] .......................... Rotary maps with 211 edges .......................... Orientable map of genus 0 and type {2,211}_422 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 844 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^211 ] .......................... Rotary maps with 212 edges .......................... Orientable map of genus 0 and type {2,212}_212 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 848 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^212 ] Non-orientable map of genus 1 and type {2,424}_424 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 848 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 52 and type {4,106}_212 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 848 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^106 ] Chiral map of genus 1 and type {4,4}_106 isomorphic to its dual Automorphism group of order 424 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^-1 ] .......................... Rotary maps with 213 edges .......................... Orientable map of genus 0 and type {2,213}_426 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 852 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^213 ] Non-orientable map of genus 141 and type {6,142}_213 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 852 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 214 edges .......................... Orientable map of genus 0 and type {2,214}_214 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 856 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^214 ] Non-orientable map of genus 1 and type {2,428}_428 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 856 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 215 edges .......................... Orientable map of genus 0 and type {2,215}_430 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 860 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^215 ] Non-orientable map of genus 169 and type {10,86}_215 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 860 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 216 edges .......................... Orientable map of genus 0 and type {2,216}_216 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^216 ] Non-orientable map of genus 1 and type {2,432}_432 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 19 and type {3,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*c*b*a*c*b, a*b*c*a*b*c*a*b*c*a*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 37 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (a*b*c*b)^6, (b*c)^12 ] Orientable map of genus 37 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, b*c*a*b*c*a*b*c*b*c*b*a*b*c*b*c*b*a*b*c*b*c, (a*b*c*b)^6 ] Orientable map of genus 51 and type {4,54}_54 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^54 ] Orientable map of genus 53 and type {4,108}_108 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^108 ] Non-orientable map of genus 106 and type {4,108}_108 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 106 and type {4,108}_108 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^108 ] Orientable map of genus 54 and type {4,216}_216 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 37 and type {6,6}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, c*a*b*c*b*c*b*a*b*c*b*a*b*c*b*c*b*a*c*b*c*b ] Orientable map of genus 37 and type {6,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^6, c*a*b*c*a*b*c*b*a*b*c*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 46 and type {6,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b ] Orientable map of genus 46 and type {6,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, (a*b*c*b*a*b*c*b*a*b)^2 ] Orientable map of genus 55 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c, c*a*b*c*a*b*c*b*a*b*c*b*c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b*a*c*b*a*c*b ] Orientable map of genus 61 and type {6,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (b*c)^18 ] Orientable map of genus 64 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^24 ] Orientable map of genus 64 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (b*c)^24 ] Orientable map of genus 64 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 64 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^24 ] Orientable map of genus 64 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (a*b*c*b*a*b*c*b*a*b)^2, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 70 and type {6,72}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (b*c)^72 ] Orientable map of genus 64 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 64 and type {8,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, b*c*a*b*a*b*c*a*b*c*b*a*b*c*b*a*b*c*b*c*b*a ] Orientable map of genus 74 and type {8,27}_108 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (c*b)^27 ] Orientable map of genus 78 and type {8,54}_108 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 78 and type {8,54}_216 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^54 ] Orientable map of genus 80 and type {8,108}_216 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 67 and type {9,12}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, b*c*a*b*c*b*c*a*b*c*b*a*b*c*b*c*b*c*b*a*b*c ] Orientable map of genus 76 and type {9,24}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 73 and type {12,12}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, (a*b)^12, (b*c)^12 ] Orientable map of genus 73 and type {12,12}_12 invariant under all six Wilson transforms Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, (b*c)^12 ] Orientable map of genus 73 and type {12,12}_12 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*b*c*b*a*c*b, (a*b)^12, (a*b*c*b)^6 ] Orientable map of genus 73 and type {12,12}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*a*b*a*b*a*b*a*b*c*b*c*b*c*b, b*a*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*a, (a*b*c*b)^6 ] Non-orientable map of genus 146 and type {12,12}_12 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*b*c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b*c*b ] Orientable map of genus 79 and type {12,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (b*c)^18 ] Orientable map of genus 79 and type {12,18}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 82 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 82 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, (a*b)^12, b*c*b*c*a*b*c*b*c*b*c*b*c*a^2*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 82 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, c*b*c*a*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 82 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*a*b*a, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b ] Orientable map of genus 82 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*c*b)^2, c*b*c*a*b*a*b*a*b*a*c*b*c*b*a*b*a*b ] Orientable map of genus 85 and type {12,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^36 ] Orientable map of genus 88 and type {12,72}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 88 and type {18,24}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, c*a*b*c*a*b*c*a*b*a*b*a*b*a*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 88 and type {18,24}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^24 ] Orientable map of genus 88 and type {18,24}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, (a*b*c*b*a*b*a*b*a*b*a*b)^2, (a*b)^18 ] Orientable map of genus 94 and type {24,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 94 and type {24,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 864 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 10 and type {3,8}_12 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^3, Y^8, Y*X^-1*Y^3*X^-1*Y^2*X^2*Y^-3*X*Y^-2*X*Y ] Chiral map of genus 28 and type {4,8}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^4, Y^8, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^2*X^-1*Y*X*Y^-1*X*Y^4*X^-1 ] Chiral map of genus 46 and type {4,24}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^4, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^2*X^-1*Y*X*Y^-1*X^-1*Y^2*X^-1*Y^2, Y^2*X*Y^-5*X^2*Y^-2*X*Y^3 ] Chiral map of genus 46 and type {6,8}_12 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^6, Y^8, Y^-1*X^2*Y^-1*X^-2*Y^4*X, (Y*X^-1*Y)^3 ] Chiral map of genus 61 and type {6,18}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^-1*Y*X^-2*Y*X^3*Y^-1*X*Y*X^-1*Y^-1 ] Chiral map of genus 70 and type {6,72}_72 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^12*X^2*Y*X^-2*Y^11 ] Chiral map of genus 55 and type {8,8}_6 isomorphic to its dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^8, Y^8, Y*X*Y^-1*X^2*Y*X^-1*Y, X^-1*Y^-4*X^-2*Y^-1*X*Y^3 ] Chiral map of genus 64 and type {8,12}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^8, (X*Y^-3)^2, Y^-1*X*Y^-1*X^3*Y^-2*X^2 ] Chiral map of genus 64 and type {8,12}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^8, (X*Y^-3)^2, Y^-1*X^3*Y^-1*X^-4*Y^-1*X*Y^-1, Y^2*X*Y^-1*X^3*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 64 and type {8,12}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^8, (X*Y^-3)^2, Y^-1*X*Y^-1*X^3*Y*X^-1*Y^-1*X ] Chiral map of genus 73 and type {8,24}_6 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1)^4, Y^3*X^3*Y^-1*X*Y^2 ] Chiral map of genus 67 and type {9,12}_72 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, (X*Y^-1*X)^2, X^-9, (X*Y^-5)^2, Y^-2*X*Y^-2*X^-2*Y^-1*X*Y^-2*X*Y^-1 ] Chiral map of genus 76 and type {9,24}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, (X*Y^-1*X)^2, X^-9, X*Y^-3*X^-2*Y^5 ] Chiral map of genus 79 and type {12,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, X^12, Y*X*Y^-1*X^5*Y*X^-2*Y^3 ] Chiral map of genus 79 and type {12,18}_72 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, (X*Y^-2)^2, X^12, (X*Y^-1*X^4)^2, Y^-1*X^2*Y^-1*X^-3*Y*X^-1*Y*X^-2*Y^-1 ] Chiral map of genus 82 and type {12,24}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y*X^-1*Y^2*X^2*Y^3*X^-1 ] Chiral map of genus 85 and type {12,36}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^12, X^-1*Y^6*X^-2*Y^4*X^-1*Y^-2 ] Chiral map of genus 88 and type {12,72}_72 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^12, X*Y^-6*X^2*Y^-1*X*Y^5 ] Chiral map of genus 88 and type {18,24}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, (X*Y^-1*X)^2, Y^2*X*Y^-2*X^-2*Y^-1*X*Y^-2*X*Y, Y^-5*X^-2*Y^-3*X*Y^-2 ] Chiral map of genus 88 and type {18,24}_72 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y^-2*X^4*Y*X^-1*Y^-1*X, Y^-2*X^2*Y^-1*X^2*Y^-5 ] Chiral map of genus 91 and type {24,24}_6 isomorphic to its dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X^5*Y*X^-1*Y^2, X^-1*Y^4*X^-5*Y*X^-2*Y*X^-6*Y*X^-1*Y*X^-1 ] Chiral map of genus 94 and type {24,36}_72 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y^-3*X^3*Y*X^-1*Y^-2 ] Chiral map of genus 97 and type {24,72}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, Y^3*X^-1*Y^3*X^-1*Y^2*X^-9*Y*X^-2*Y*X^-1 ] Chiral map of genus 97 and type {24,72}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 432 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^2*Y^-1*X^4*Y^-5 ] .......................... Rotary maps with 217 edges .......................... Orientable map of genus 0 and type {2,217}_434 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 868 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^217 ] Non-orientable map of genus 181 and type {14,62}_217 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 868 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 218 edges .......................... Orientable map of genus 0 and type {2,218}_218 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 872 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^218 ] Non-orientable map of genus 1 and type {2,436}_436 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 872 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_218 isomorphic to its dual Automorphism group of order 436 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X*Y^-1*X*Y^-1 ] .......................... Rotary maps with 219 edges .......................... Orientable map of genus 0 and type {2,219}_438 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 876 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^219 ] Non-orientable map of genus 145 and type {6,146}_219 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 876 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_146 not isomorphic to its dual or mirror-dual Automorphism group of order 438 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X*Y^-1*X*Y^3*X^-1*Y^2*X^-1*Y^2*X^-1*Y ] .......................... Rotary maps with 220 edges .......................... Orientable map of genus 0 and type {2,220}_220 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 880 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^220 ] Non-orientable map of genus 1 and type {2,440}_440 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 880 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 54 and type {4,110}_220 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 880 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^110 ] Orientable map of genus 84 and type {10,44}_220 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 880 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^44 ] Orientable map of genus 90 and type {20,22}_220 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 880 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^22 ] Orientable map of genus 95 and type {20,44}_110 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 880 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 51 and type {4,44}_110 not isomorphic to its dual or mirror-dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^11*X*Y^-1*X*Y*X^-1*Y^-5*X*Y^4 ] Chiral map of genus 78 and type {10,20}_44 not isomorphic to its dual or mirror-dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, X^10, (X*Y^-2*X^2)^2, (X*Y^-1*X*Y^-1*X)^2, Y^-1*X*Y^-2*X^2*Y^-3*X ] Chiral map of genus 78 and type {10,20}_44 not isomorphic to its dual or mirror-dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, X^10, Y^-2*X^4*Y^-1*X^2*Y^-1 ] Chiral map of genus 78 and type {10,20}_44 not isomorphic to its dual or mirror-dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, X^10, Y^-1*X*Y^-1*X^3*Y^-4 ] Chiral map of genus 78 and type {10,20}_44 not isomorphic to its dual or mirror-dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, X^10, X*Y^-2*X^3*Y^-1*X^2*Y^-1, X*Y^-1*X*Y^-1*X^2*Y^-4 ] Chiral map of genus 89 and type {20,20}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, Y*X^5*Y^3*X^-1, Y*X*Y^-1*X^3*Y*X^-1*Y*X^-1, Y^3*X^-2*Y^2*X^-11*Y*X^-1 ] Chiral map of genus 89 and type {20,20}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^-1*Y*X^-4*Y^2*X^-10*Y*X^-1 ] Chiral map of genus 101 and type {44,44}_10 isomorphic to its dual Automorphism group of order 440 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X^2*Y*X^-1*Y, X^2*Y^-13*X^3*Y^-5*X^11*Y^-1*X*Y^-1*X^3*Y^-1*X*Y^-1*X ] .......................... Rotary maps with 221 edges .......................... Orientable map of genus 0 and type {2,221}_442 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 884 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^221 ] Non-orientable map of genus 193 and type {26,34}_221 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 884 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] .......................... Rotary maps with 222 edges .......................... Orientable map of genus 0 and type {2,222}_222 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 888 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^222 ] Non-orientable map of genus 1 and type {2,444}_444 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 888 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 109 and type {4,111}_111 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 888 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^111 ] Orientable map of genus 72 and type {6,74}_222 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 888 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^74 ] Chiral map of genus 38 and type {6,6}_74 not isomorphic to its dual or mirror-dual Automorphism group of order 444 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y^-1*X^-2*Y*X^2*Y^-1*X^2*Y^-1*X^-3*Y^-1*X^2*Y*X^-1*Y^-2*X^2 ] Chiral map of genus 75 and type {12,12}_74 not isomorphic to its dual or mirror-dual Automorphism group of order 444 with defining relations: [ (X*Y)^2, (Y^-1*X)^3, X^12, Y^-2*X^5*Y^-1*X^3*Y^-1 ] Chiral map of genus 75 and type {12,12}_74 isomorphic to its dual Automorphism group of order 444 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, Y^-2*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y^-1*X ] .......................... Rotary maps with 223 edges .......................... Orientable map of genus 0 and type {2,223}_446 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 892 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^223 ] .......................... Rotary maps with 224 edges .......................... Orientable map of genus 0 and type {2,224}_224 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^224 ] Non-orientable map of genus 1 and type {2,448}_448 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 50 and type {4,7}_7 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^7, (a*b*c*b)^4, b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c ] Orientable map of genus 49 and type {4,28}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^28 ] Orientable map of genus 53 and type {4,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^56 ] Orientable map of genus 55 and type {4,112}_112 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 55 and type {4,112}_112 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^112 ] Orientable map of genus 56 and type {4,224}_224 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 77 and type {8,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^28 ] Orientable map of genus 77 and type {8,28}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^28 ] Orientable map of genus 81 and type {8,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {8,56}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^56 ] Orientable map of genus 81 and type {8,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {8,56}_56 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 83 and type {8,112}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 90 and type {14,32}_224 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^32 ] Orientable map of genus 91 and type {16,28}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^28 ] Orientable map of genus 91 and type {16,28}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, (b*c)^28 ] Orientable map of genus 95 and type {16,56}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 95 and type {16,56}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 98 and type {28,32}_224 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 896 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 89 and type {14,28}_4 not isomorphic to its dual or mirror-dual Automorphism group of order 448 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^6*Y*X^-2*Y^2, X^14 ] Chiral map of genus 97 and type {28,28}_4 isomorphic to its mirror-dual Automorphism group of order 448 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y*X^-1*Y^2, X^-4*Y^9*X^-2*Y*X^-9*Y*X^-1*Y ] Chiral map of genus 105 and type {56,56}_4 isomorphic to its mirror-dual Automorphism group of order 448 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y*X^-1*Y^2, X^-4*Y^9*X^-2*Y*X^-8*Y*X^-3 ] Chiral map of genus 105 and type {56,56}_4 isomorphic to its mirror-dual Automorphism group of order 448 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-1*Y, X*Y^-1*X^38*Y^-2*X^14 ] .......................... Rotary maps with 225 edges .......................... Orientable map of genus 0 and type {2,225}_450 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 900 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^225 ] Orientable map of genus 1 and type {3,6}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 900 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 73 and type {6,75}_150 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 900 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^75 ] Orientable map of genus 66 and type {9,10}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 900 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b, (b*c)^10 ] Orientable map of genus 86 and type {10,45}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 900 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (c*b)^45 ] Orientable map of genus 91 and type {15,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 900 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (b*a)^15 ] Non-orientable map of genus 193 and type {18,50}_225 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 900 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] .......................... Rotary maps with 226 edges .......................... Orientable map of genus 0 and type {2,226}_226 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 904 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^226 ] Non-orientable map of genus 1 and type {2,452}_452 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 904 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_226 isomorphic to its dual Automorphism group of order 452 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^2*X^2*Y^2*X^2*Y^2*X^-2*Y^-2 ] .......................... Rotary maps with 227 edges .......................... Orientable map of genus 0 and type {2,227}_454 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 908 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^227 ] .......................... Rotary maps with 228 edges .......................... Orientable map of genus 0 and type {2,228}_228 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^228 ] Non-orientable map of genus 1 and type {2,456}_456 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 54 and type {4,57}_114 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^57 ] Non-orientable map of genus 112 and type {4,114}_114 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^114 ] Orientable map of genus 56 and type {4,114}_228 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^114 ] Orientable map of genus 73 and type {6,57}_76 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 74 and type {6,76}_228 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^76 ] Orientable map of genus 90 and type {12,38}_228 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^38 ] Orientable map of genus 93 and type {12,76}_114 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 912 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {3,6}_76 not isomorphic to its dual or mirror-dual Automorphism group of order 456 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^3*X^-1*Y*X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X*Y^-2*X*Y^-1*X*Y^-2*X*Y ] Chiral map of genus 58 and type {6,12}_76 not isomorphic to its dual or mirror-dual Automorphism group of order 456 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^12, Y^-1*X^2*Y^-1*X^-2*Y*X^3*Y*X^-2*Y*X^-1*Y^-1 ] Chiral map of genus 58 and type {6,12}_76 not isomorphic to its dual or mirror-dual Automorphism group of order 456 with defining relations: [ (X*Y)^2, X^6, Y^-1*X^2*Y^-1*X^-2*Y^-1*X^2*Y^-1, Y*X^2*Y^-1*X^2*Y^4, X^-1*Y*X*Y^-2*X*Y^-2*X*Y^-1*X*Y^-3*X*Y^-1 ] Chiral map of genus 77 and type {12,12}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 456 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, X^12, X*Y^-1*X^2*Y^-1*X^-3*Y*X^-2*Y^-1*X^2*Y^2 ] .......................... Rotary maps with 229 edges .......................... Orientable map of genus 0 and type {2,229}_458 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 916 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^229 ] .......................... Rotary maps with 230 edges .......................... Orientable map of genus 0 and type {2,230}_230 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 920 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^230 ] Non-orientable map of genus 1 and type {2,460}_460 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 920 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 88 and type {10,46}_230 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 920 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^46 ] Chiral map of genus 111 and type {92,92}_10 isomorphic to its dual Automorphism group of order 460 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^-1*X*Y^-25*X^10*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-2 ] .......................... Rotary maps with 231 edges .......................... Orientable map of genus 0 and type {2,231}_462 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 924 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^231 ] Non-orientable map of genus 153 and type {6,154}_231 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 924 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 193 and type {14,66}_231 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 924 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 201 and type {22,42}_231 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 924 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 71 and type {6,33}_154 not isomorphic to its dual or mirror-dual Automorphism group of order 462 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X*Y^-1*X^-1*Y*X^2*Y^-1*X^2*Y*X^-2*Y^-1*X^2*Y^-1, X*Y^-6*X^2*Y^-1*X*Y*X^-1*Y^-1*X*Y^2 ] Chiral map of genus 106 and type {33,66}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 462 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, Y^4*X^-3*Y*X^-2*Y*X^-1*Y*X^-1*Y*X^-10*Y^4*X^-1*Y^2*X^-1 ] .......................... Rotary maps with 232 edges .......................... Orientable map of genus 0 and type {2,232}_232 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 928 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^232 ] Non-orientable map of genus 1 and type {2,464}_464 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 928 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 57 and type {4,116}_116 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 928 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^116 ] Orientable map of genus 58 and type {4,232}_232 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 928 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 84 and type {8,58}_232 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 928 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^58 ] Orientable map of genus 86 and type {8,116}_232 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 928 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_116 isomorphic to its dual Automorphism group of order 464 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^-1 ] Chiral map of genus 59 and type {8,8}_58 isomorphic to its dual Automorphism group of order 464 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X*Y^-1*X*Y^-1*X^-1*Y*X^2*Y^-2*X^-2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 59 and type {8,8}_116 isomorphic to its dual Automorphism group of order 464 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X*Y^-1*X*Y^-1*X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2 ] .......................... Rotary maps with 233 edges .......................... Orientable map of genus 0 and type {2,233}_466 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 932 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^233 ] .......................... Rotary maps with 234 edges .......................... Orientable map of genus 0 and type {2,234}_234 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 936 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^234 ] Non-orientable map of genus 1 and type {2,468}_468 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 936 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 115 and type {4,117}_117 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 936 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^117 ] Non-orientable map of genus 149 and type {6,52}_52 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 936 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 76 and type {6,78}_78 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 936 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 76 and type {6,78}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 936 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^78 ] Orientable map of genus 96 and type {18,26}_234 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 936 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^26 ] Chiral map of genus 1 and type {4,4}_78 isomorphic to its dual Automorphism group of order 468 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^-2*X^2*Y^2*X ] Chiral map of genus 40 and type {6,6}_78 not isomorphic to its dual or mirror-dual Automorphism group of order 468 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^3*Y^3*X^-2, X^-1*Y^-3*X*Y^-1*X*Y^3*X^-1*Y, Y*X*Y^-1*X*Y^-1*X^-2*Y^-1*X^2*Y*X^-2*Y ] Chiral map of genus 40 and type {6,6}_78 not isomorphic to its dual or mirror-dual Automorphism group of order 468 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, X^2*Y^2*X^2*Y^-1*X*Y^-1*X^-3*Y^-1*X^2*Y*X^-2*Y^-1*X^2*Y^-1 ] Chiral map of genus 92 and type {18,18}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 468 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^3*Y*X^-2*Y*X^-1, X*Y^-3*X^11*Y^-3 ] Chiral map of genus 105 and type {36,36}_26 isomorphic to its dual Automorphism group of order 468 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, Y^-4*X^6*Y^-1*X*Y^-2*X*Y^-1*X*Y^-1 ] Chiral map of genus 105 and type {36,36}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 468 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^3*Y*X^-2*Y^-1, Y^3*X^3*Y^-1*X*Y^2, X*Y^-1*X*Y^-1*X^13*Y^-1 ] .......................... Rotary maps with 235 edges .......................... Orientable map of genus 0 and type {2,235}_470 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 940 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^235 ] Non-orientable map of genus 185 and type {10,94}_235 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 940 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 236 edges .......................... Orientable map of genus 0 and type {2,236}_236 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 944 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^236 ] Non-orientable map of genus 1 and type {2,472}_472 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 944 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 58 and type {4,118}_236 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 944 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^118 ] .......................... Rotary maps with 237 edges .......................... Orientable map of genus 0 and type {2,237}_474 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 948 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^237 ] Non-orientable map of genus 157 and type {6,158}_237 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 948 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_158 not isomorphic to its dual or mirror-dual Automorphism group of order 474 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-3*X*Y^-1*X*Y^3*X*Y^-2*X*Y^-1*X*Y^-2*X*Y^-1 ] .......................... Rotary maps with 238 edges .......................... Orientable map of genus 0 and type {2,238}_238 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 952 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^238 ] Non-orientable map of genus 1 and type {2,476}_476 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 952 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 96 and type {14,34}_238 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 952 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^34 ] Chiral map of genus 103 and type {28,28}_34 isomorphic to its dual Automorphism group of order 476 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-1*X^6*Y^-2*X*Y^-1*X*Y^-1 ] .......................... Rotary maps with 239 edges .......................... Orientable map of genus 0 and type {2,239}_478 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 956 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^239 ] .......................... Rotary maps with 240 edges .......................... Orientable map of genus 0 and type {2,240}_240 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^240 ] Non-orientable map of genus 1 and type {2,480}_480 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 21 and type {4,6}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 37 and type {4,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*a*b*c*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 41 and type {4,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, c*b*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b, a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c ] Orientable map of genus 45 and type {4,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, (c*b)^15 ] Non-orientable map of genus 98 and type {4,20}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*a*b*c*b)^2, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 98 and type {4,20}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, a*b*c*b*a*b*a*c*b*a*b*c*b, a*b*c*a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 106 and type {4,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^30 ] Non-orientable map of genus 106 and type {4,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (b*c)^30 ] Orientable map of genus 53 and type {4,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^30 ] Orientable map of genus 57 and type {4,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^60 ] Orientable map of genus 57 and type {4,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^60 ] Orientable map of genus 59 and type {4,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 59 and type {4,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^120 ] Non-orientable map of genus 118 and type {4,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 118 and type {4,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^120 ] Orientable map of genus 60 and type {4,240}_240 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 50 and type {5,5}_6 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, a*b*c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b ] Orientable map of genus 41 and type {6,6}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (a*b*c*b*a*b*c*b*a*b)^2, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c*b ] Orientable map of genus 51 and type {6,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*c*b*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*a*b ] Orientable map of genus 51 and type {6,8}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b*a*c*b ] Orientable map of genus 57 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, (b*c)^10, c*b*c*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c*b ] Orientable map of genus 61 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*a*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 65 and type {6,15}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, a*b*c*a*b*c*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 69 and type {6,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 69 and type {6,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b, c*a*b*c*a*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 69 and type {6,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, (b*c)^20 ] Non-orientable map of genus 142 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, c*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 142 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*a*b)^2, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b*c ] Non-orientable map of genus 142 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, (a*b*c*b*a*b*c*b*a*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 142 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, a*b*a*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c, b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b*a ] Orientable map of genus 73 and type {6,30}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, a*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 150 and type {6,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 150 and type {6,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*b*a*b*c*b*a*b*c*b*c*b*a*c*b ] Orientable map of genus 75 and type {6,40}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, c*b*c*b*c*a*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 78 and type {6,80}_240 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^80 ] Orientable map of genus 67 and type {8,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*a*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*a*c*b, (b*c)^10, c*b*c*b*a*b*c*a*b*a*b*a*c*b*c*b*a*b*c*b*a*b ] Non-orientable map of genus 134 and type {8,10}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*a*b*c*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 134 and type {8,10}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*a*b*c*a*b*a*c*b*c*b*c*b*a*b*c ] Orientable map of genus 71 and type {8,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*b*a*b*c*b*a*b*a*c*b*c*b*a*b*c*b*a*b ] Non-orientable map of genus 150 and type {8,15}_15 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, (c*b)^15 ] Orientable map of genus 75 and type {8,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^15 ] Non-orientable map of genus 150 and type {8,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (c*b)^15 ] Orientable map of genus 83 and type {8,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, (b*c)^30 ] Non-orientable map of genus 166 and type {8,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, c*b*c*b*c*b*c*a*b*c*b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 83 and type {8,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^30 ] Orientable map of genus 87 and type {8,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 87 and type {8,60}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^60 ] Orientable map of genus 87 and type {8,60}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^60 ] Non-orientable map of genus 178 and type {8,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 178 and type {8,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 154 and type {10,12}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*b*a*c, (a*b)^10 ] Orientable map of genus 77 and type {10,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*c*b*c*b*c*b, (a*b)^10, (a*b*c*b*a*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*c*b*a*c*b*a*c*b ] Orientable map of genus 77 and type {10,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^10, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b ] Non-orientable map of genus 174 and type {10,24}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^10, b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c, b*c*a*b*c*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*c*b*a ] Non-orientable map of genus 174 and type {10,24}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, a*b*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b, (a*b)^10 ] Orientable map of genus 92 and type {10,48}_240 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^48 ] Orientable map of genus 81 and type {12,12}_12 invariant under all six Wilson transforms Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*b*a*c*b*c*b*a*b*a*b, b*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*c ] Orientable map of genus 89 and type {12,20}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, (a*b)^12, a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 89 and type {12,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^12, (b*c)^20 ] Orientable map of genus 89 and type {12,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c, (a*b)^12 ] Orientable map of genus 93 and type {12,30}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 190 and type {12,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*a*b*a, a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*c*b ] Non-orientable map of genus 190 and type {12,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*a*b*a ] Orientable map of genus 95 and type {12,40}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 95 and type {12,40}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 95 and type {12,40}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^40 ] Orientable map of genus 98 and type {12,80}_240 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 98 and type {16,30}_240 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^30 ] Orientable map of genus 102 and type {16,60}_240 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 198 and type {20,24}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 198 and type {20,24}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*c*b*a*c*b*a*c ] Orientable map of genus 99 and type {20,24}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c, (a*b)^20 ] Orientable map of genus 99 and type {20,24}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^24 ] Orientable map of genus 104 and type {20,48}_240 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {24,40}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] Orientable map of genus 105 and type {24,40}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 108 and type {30,48}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 112 and type {48,60}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 960 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*a*b*a*b*a*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b ] Chiral map of genus 41 and type {4,12}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^4, Y^-1*X^-1*Y*X^-1*Y*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^3*X^-1*Y*X^-1*Y*X^-1*Y^-1*X*Y^2 ] Chiral map of genus 41 and type {4,12}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^12, Y^-1*X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 51 and type {4,24}_120 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^24 ] Chiral map of genus 51 and type {4,24}_120 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^-1*X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y*X^-1*Y^-1*X*Y^-1, Y^-2*X^-1*Y^2*X*Y^-2*X^-1*Y^2*X^-1*Y^-2*X*Y*X^-1*Y^-1 ] Chiral map of genus 65 and type {6,15}_10 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^6, Y*X*Y^-2*X^3*Y^2, X*Y^-1*X^-2*Y*X^3*Y*X^-2*Y^-1 ] Chiral map of genus 71 and type {8,12}_120 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1, Y^12 ] Chiral map of genus 71 and type {8,12}_120 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^12 ] Chiral map of genus 81 and type {8,24}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^-2*X^-1*Y*X*Y^-2*X*Y*X^-1*Y^-6 ] Chiral map of genus 81 and type {8,24}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1, Y^-2*X^-1*Y*X*Y^-2*X*Y*X^-1*Y^-6 ] Chiral map of genus 81 and type {12,12}_20 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, X^12, Y^-2*X^5*Y^-1*X*Y^-1*X^2 ] Chiral map of genus 81 and type {12,12}_20 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^2*X^-1*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 91 and type {12,24}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y*X*Y^-3*X*Y^4, X^12, Y^-2*X^5*Y^-3*X*Y^-1, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-2*X ] Chiral map of genus 91 and type {12,24}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y*X*Y^-3*X*Y^4, X^12, Y^-2*X^5*Y^-3*X*Y^-1, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-2*X^2*Y^-1 ] Chiral map of genus 97 and type {15,30}_4 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^6*Y*X^-1*Y*X^-1*Y, X^-15 ] Chiral map of genus 101 and type {16,48}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, X^-1*Y^3*X^-9*Y^3 ] Chiral map of genus 101 and type {16,48}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y*X^2*Y^-1*X^3*Y^2*X^-1*Y^2, X^2*Y^-2*X^3*Y*X^-1*Y^-3 ] Chiral map of genus 101 and type {24,24}_20 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-2*X ] Chiral map of genus 101 and type {24,24}_20 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, X^-1*Y^3*X^-1*Y*X^-9*Y^7*X^-1*Y ] Chiral map of genus 101 and type {24,24}_40 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^5*Y^-1*X^2*Y ] Chiral map of genus 101 and type {24,24}_40 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^3*Y^-1*X*Y^-2, X^7*Y^-1*X*Y*X^-1*Y ] Chiral map of genus 105 and type {30,30}_4 isomorphic to its mirror-dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y^2*X^-2, X^-2*Y^14*X^-11*Y^2*X^-1 ] Chiral map of genus 111 and type {48,48}_10 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^21*Y^-1*X*Y^-6*X^9*Y^-2*X*Y^-3*X*Y^-1*X*Y^-1 ] Chiral map of genus 111 and type {48,48}_20 isomorphic to its dual Automorphism group of order 480 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, X^-2*Y^2*X^-1*Y*X^-9*Y^9 ] .......................... Rotary maps with 241 edges .......................... Orientable map of genus 0 and type {2,241}_482 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 964 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^241 ] .......................... Rotary maps with 242 edges .......................... Orientable map of genus 0 and type {2,242}_242 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 968 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^242 ] Non-orientable map of genus 1 and type {2,484}_484 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 968 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_22 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 968 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (c*b*a*b)^11 ] Orientable map of genus 100 and type {22,22}_22 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 968 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b, (b*c)^22 ] .......................... Rotary maps with 243 edges .......................... Orientable map of genus 0 and type {2,243}_486 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^243 ] Orientable map of genus 1 and type {3,6}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 28 and type {3,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b, c*b*c*a*b*c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Non-orientable map of genus 83 and type {6,6}_9 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*a, b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*a*c*b*c, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b ] Orientable map of genus 55 and type {6,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (c*b)^9 ] Orientable map of genus 55 and type {6,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (c*b)^9, a*b*c*a*b*a*b*c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b ] Orientable map of genus 55 and type {6,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (c*b)^9, b*c*a*b*c*b*a*b*a*b*c*a*b*a*c*b*a*b*a*c*b*a ] Orientable map of genus 55 and type {6,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*a*c*b*c*b*c*b, b*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*b*c, a*b*c*a*b*a*b*c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b ] Orientable map of genus 73 and type {6,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 73 and type {6,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 73 and type {6,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^27 ] Orientable map of genus 79 and type {6,81}_162 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^81 ] Orientable map of genus 82 and type {9,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b, c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 82 and type {9,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^9, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, b*a*b*c*b*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b*c ] Orientable map of genus 82 and type {9,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^9, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 82 and type {9,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, c*a*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b, c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 82 and type {9,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^9, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, b*c*a*b*c*a*b*c*a*b*a*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 100 and type {18,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 972 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (c*b)^27 ] Chiral map of genus 28 and type {3,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, X^3, (Y^2*X^-1*Y^2)^3, Y*X*Y^-2*X^-1*Y^3*X^-1*Y^-4*X*Y^2 ] Chiral map of genus 55 and type {6,9}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-9, X*Y^-1*X^2*Y^-1*X^-2*Y*X^3*Y*X^-2*Y^-1*X^2*Y^2 ] Chiral map of genus 79 and type {6,81}_162 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^-14*X^2*Y^-1*X*Y^4*X^-1*Y^-8 ] Chiral map of genus 82 and type {9,18}_6 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, (X*Y^-1*X)^2, X^-9, (Y*X^-1*Y)^3, Y^2*X*Y^-5*X^-2*Y^5 ] Chiral map of genus 82 and type {9,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, (X*Y^-1*X)^2, X^-9, X^-1*Y*X*Y^-1*X^-2*Y^-2*X*Y^-2, Y^2*X*Y^-5*X^-2*Y^5 ] Chiral map of genus 82 and type {9,18}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, (X*Y^-1*X)^2, X^-9, Y*X^-1*Y^2*X^2*Y^2*X^-1*Y, X^-1*Y*X*Y^-5*X^-1*Y^6 ] Chiral map of genus 100 and type {18,27}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, Y*X^-4*Y^2*X^-2 ] Chiral map of genus 100 and type {18,27}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^-2*Y^3*X^-1 ] Chiral map of genus 100 and type {18,27}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, Y^2*X^-3*Y*X^-1*Y^2 ] Chiral map of genus 100 and type {18,27}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y^4*X^-3*Y^-1*X*Y^4 ] Chiral map of genus 109 and type {27,54}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 486 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-1*Y^2, Y*X*Y^-1*X^3*Y^2*X^-2, Y*X^-1*Y*X^-1*Y*X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-10*Y^4 ] .......................... Rotary maps with 244 edges .......................... Orientable map of genus 0 and type {2,244}_244 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 976 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^244 ] Non-orientable map of genus 1 and type {2,488}_488 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 976 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 60 and type {4,122}_244 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 976 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^122 ] Chiral map of genus 1 and type {4,4}_122 isomorphic to its dual Automorphism group of order 488 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X ] .......................... Rotary maps with 245 edges .......................... Orientable map of genus 0 and type {2,245}_490 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 980 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^245 ] Non-orientable map of genus 193 and type {10,98}_245 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 980 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 99 and type {14,35}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 980 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^14, (c*b)^35 ] .......................... Rotary maps with 246 edges .......................... Orientable map of genus 0 and type {2,246}_246 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 984 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^246 ] Non-orientable map of genus 1 and type {2,492}_492 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 984 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 121 and type {4,123}_123 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 984 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^123 ] Orientable map of genus 80 and type {6,82}_246 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 984 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^82 ] Chiral map of genus 83 and type {12,12}_82 isomorphic to its dual Automorphism group of order 492 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, X^2*Y^-2*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y^-1*X*Y^-1*X*Y^2 ] .......................... Rotary maps with 247 edges .......................... Orientable map of genus 0 and type {2,247}_494 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 988 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^247 ] Non-orientable map of genus 217 and type {26,38}_247 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 988 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] .......................... Rotary maps with 248 edges .......................... Orientable map of genus 0 and type {2,248}_248 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 992 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^248 ] Non-orientable map of genus 1 and type {2,496}_496 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 992 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 61 and type {4,124}_124 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 992 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^124 ] Orientable map of genus 62 and type {4,248}_248 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 992 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 90 and type {8,62}_248 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 992 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^62 ] Orientable map of genus 92 and type {8,124}_248 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 992 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 249 edges .......................... Orientable map of genus 0 and type {2,249}_498 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 996 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^249 ] Non-orientable map of genus 165 and type {6,166}_249 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 996 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 250 edges .......................... Orientable map of genus 0 and type {2,250}_250 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^250 ] Non-orientable map of genus 1 and type {2,500}_500 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 77 and type {4,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^10, a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 76 and type {10,10}_10 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, (a*b)^10, a*b*c*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b*c*b, (b*c)^10 ] Orientable map of genus 76 and type {10,10}_10 invariant under all six Wilson transforms Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^10, (b*c)^10 ] Non-orientable map of genus 177 and type {10,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^10, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 177 and type {10,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*c*b)^2, (a*b)^10, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c, c*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b*a*b ] Non-orientable map of genus 177 and type {10,20}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*c*b)^2, (a*b)^10, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b, c*b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*a*b ] Orientable map of genus 96 and type {10,50}_50 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1000 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (b*c)^50 ] Chiral map of genus 1 and type {4,4}_50 isomorphic to its dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^-2*X^2*Y^2*X^2*Y ] Chiral map of genus 1 and type {4,4}_250 isomorphic to its dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 96 and type {10,50}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, X^10, X*Y^-1*X^4*Y^-1*X*Y^-2, Y*X*Y^-3*X^3*Y^6 ] Chiral map of genus 96 and type {10,50}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, X^10, X*Y^-1*X^4*Y^-1*X*Y^-2, Y^-2*X^-1*Y*X*Y^-1*X^2*Y^-6 ] Chiral map of genus 101 and type {20,20}_10 isomorphic to its dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^-1*X*Y^-1*X^3*Y^-3*X, X^-2*Y^2*X^3*Y*X^-1*Y^-3 ] Chiral map of genus 101 and type {20,20}_50 isomorphic to its dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^-1*Y*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-2 ] Chiral map of genus 101 and type {20,20}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, X^6*Y^-2*X*Y^-1 ] Chiral map of genus 101 and type {20,20}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, Y^-1*X^5*Y^-1*X^2*Y^-1 ] Chiral map of genus 121 and type {100,100}_10 isomorphic to its dual Automorphism group of order 500 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^21*Y^-2*X*Y^-1*X*Y^-3*X^11*Y^-2*X*Y^-3*X*Y^-1*X*Y^-1 ] .......................... Rotary maps with 251 edges .......................... Orientable map of genus 0 and type {2,251}_502 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1004 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^251 ] .......................... Rotary maps with 252 edges .......................... Orientable map of genus 0 and type {2,252}_252 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^252 ] Non-orientable map of genus 1 and type {2,504}_504 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 7 and type {3,7}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^7, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 23 and type {3,8}_21 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c, b*c*a*b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 15 and type {3,9}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^9, a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 50 and type {3,14}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 55 and type {4,28}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (a*b*c*b)^6, c*a*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 60 and type {4,63}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^63 ] Non-orientable map of genus 124 and type {4,126}_126 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^126 ] Orientable map of genus 62 and type {4,126}_252 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^126 ] Non-orientable map of genus 98 and type {6,7}_9 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (c*b)^7, a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b*c ] Non-orientable map of genus 98 and type {6,7}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (c*b)^7, a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 114 and type {6,9}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (c*b)^9, b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*a*b*c ] Non-orientable map of genus 134 and type {6,14}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b, a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 146 and type {6,21}_21 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b*c*b*a*b)^2, a*b*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*c*b*c, b*c*b*c*a*b*c*b*a*b*a*b*c*b*c*b*c*b*a*b*a ] Orientable map of genus 73 and type {6,21}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (c*b)^21 ] Orientable map of genus 76 and type {6,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^28 ] Orientable map of genus 82 and type {6,84}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^84 ] Orientable map of genus 82 and type {6,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 55 and type {7,7}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, (c*b)^7, (b*c*b*a*b*c)^3, (a*b*c*b*a*b*c*b*a*b)^2 ] Orientable map of genus 63 and type {7,9}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (c*b*a*b)^3, (b*a)^7, (c*b)^9, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 63 and type {7,9}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, (a*b*c*b*c*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*c*b ] Non-orientable map of genus 146 and type {7,14}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, (b*c*b*a*b*c)^3, b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b*a ] Non-orientable map of genus 146 and type {7,14}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b ] Non-orientable map of genus 149 and type {8,12}_21 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b)^8, (a*b*c*b*c*b*c*b)^2, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*b*a*c*b*a ] Orientable map of genus 71 and type {9,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^9, (c*b)^9, b*c*a*b*a*b*a*b*a*b*a*c*b*a*c*b*c*b*a*c ] Non-orientable map of genus 162 and type {9,14}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*a*b)^2, (b*a)^9, a*b*a*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b*c ] Non-orientable map of genus 170 and type {9,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b, (b*a)^9 ] Orientable map of genus 94 and type {12,21}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^21 ] Orientable map of genus 100 and type {12,42}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^42 ] Orientable map of genus 100 and type {12,42}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, (b*c)^42 ] Orientable map of genus 100 and type {12,42}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Non-orientable map of genus 182 and type {14,14}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b*a ] Orientable map of genus 102 and type {14,36}_252 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^36 ] Non-orientable map of genus 198 and type {18,18}_18 plus image(s) under Wilson transforms [ D ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*b*a*b*a*b*a*b*c*b*c*b*a*c*b, b*a*b*c*b*a*b*a*b*a*c*b*a*c*b*a*c*b*a ] Non-orientable map of genus 208 and type {18,28}_63 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, a*b*c*a*b*a*b*a*b*a*b*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 104 and type {18,28}_252 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^28 ] Orientable map of genus 111 and type {28,36}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1008 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c ] Chiral map of genus 1 and type {3,6}_84 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-2*X^-1*Y*X^-1*Y^3*X*Y^-2*X*Y^-1*X*Y^-3*X*Y^-1 ] Chiral map of genus 22 and type {3,12}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, X^3, Y^12, (Y^2*X^-1*Y^2)^3, Y*X*Y^-2*X*Y^-2*X*Y^-1*X*Y^-3*X*Y^3 ] Chiral map of genus 64 and type {6,12}_84 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, X^6, Y^2*X^2*Y^-1*X^-1*Y*X^-1*Y^-1*X^2*Y, Y^-1*X^2*Y^-1*X^-3*Y^-1*X*Y^-3 ] Chiral map of genus 64 and type {6,12}_84 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, X^6, Y^-1*X^2*Y^-1*X^-2*Y^-1*X^2*Y^-1, Y*X^2*Y^-1*X^2*Y^4, Y^2*X*Y^-2*X*Y^-1*X^-2*Y^2*X^-1*Y^2*X^-1*Y ] Chiral map of genus 64 and type {6,12}_84 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^12, X^-1*Y*X^2*Y^-1*X^2*Y^-1*X^2*Y*X^-2*Y*X^-1*Y ] Chiral map of genus 64 and type {6,12}_84 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, X^6, X*Y^-3*X^2*Y*X^-1*Y^-2, Y^12 ] Chiral map of genus 85 and type {9,18}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, X^-9, Y^2*X^-3*Y^4, Y*X*Y^-1*X*Y^-3*X^-1*Y*X^2*Y^3*X^-1*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 85 and type {12,12}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^3*Y*X^-2*Y^-1, X^12, Y^-1*X^6*Y^-5 ] Chiral map of genus 85 and type {12,12}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, X^12, Y^-1*X*Y^-2*X*Y^-1*X^-2*Y^2*X^-1*Y^2*X^-1*Y^-2 ] Chiral map of genus 106 and type {18,36}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^-18 ] Chiral map of genus 106 and type {18,36}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y^2*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y^2*X^-1*Y*X^2*Y^-2*X*Y, X^2*Y^-1*X^2*Y^-1*X^8*Y^-1*X^2*Y^-1 ] Chiral map of genus 113 and type {36,36}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^4*Y^-5*X^2*Y^-4*X^11*Y^-1*X*Y^-2*X^2*Y^-1*X*Y^-1*X ] Chiral map of genus 118 and type {56,56}_6 isomorphic to its dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y*X^5*Y^3*X^-1, X^-7*Y*X^-1*Y^3*X^-1*Y*X^-8*Y*X^-2*Y*X^-2 ] Chiral map of genus 119 and type {63,63}_4 isomorphic to its mirror-dual Automorphism group of order 504 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^-2*Y^42*X^-1*Y*X^-12*Y^5 ] .......................... Rotary maps with 253 edges .......................... Orientable map of genus 0 and type {2,253}_506 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1012 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^253 ] Non-orientable map of genus 221 and type {22,46}_253 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1012 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 93 and type {11,22}_46 not isomorphic to its dual or mirror-dual Automorphism group of order 506 with defining relations: [ (X*Y)^2, X^-11, Y*X^-5*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 93 and type {11,22}_46 not isomorphic to its dual or mirror-dual Automorphism group of order 506 with defining relations: [ (X*Y)^2, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, X^-11, Y*X^-5*Y*X^-2*Y^2 ] Chiral map of genus 93 and type {11,22}_46 not isomorphic to its dual or mirror-dual Automorphism group of order 506 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^3*Y^-1*X*Y*X^-1, X^-11 ] Chiral map of genus 93 and type {11,22}_46 not isomorphic to its dual or mirror-dual Automorphism group of order 506 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-1*Y^2, X^-11 ] Chiral map of genus 93 and type {11,22}_46 not isomorphic to its dual or mirror-dual Automorphism group of order 506 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X^2*Y^2*X^-1*Y, X^-11 ] .......................... Rotary maps with 254 edges .......................... Orientable map of genus 0 and type {2,254}_254 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1016 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^254 ] Non-orientable map of genus 1 and type {2,508}_508 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1016 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 255 edges .......................... Orientable map of genus 0 and type {2,255}_510 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1020 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^255 ] Non-orientable map of genus 169 and type {6,170}_255 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1020 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 201 and type {10,102}_255 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1020 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 225 and type {30,34}_255 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1020 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] .......................... Rotary maps with 256 edges .......................... Orientable map of genus 0 and type {2,256}_256 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^256 ] Non-orientable map of genus 1 and type {2,512}_512 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_16 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 33 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (b*c)^8, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 33 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*b*c*a*b*c*b*a*b*c*a*b*a*c*b*c*b*a*c*b*a*b*c*b ] Orientable map of genus 33 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 33 and type {4,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 33 and type {4,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Orientable map of genus 33 and type {4,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, b*a*b*c*a*b*c*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c*b*a*c*b*c ] Orientable map of genus 33 and type {4,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, (a*b*c*b)^8 ] Orientable map of genus 33 and type {4,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*c*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*c*b*c*b ] Orientable map of genus 49 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*a*b*c*b*c*b*c*a*b*a*b*c*b*c*b*c*b*c*b*a ] Orientable map of genus 49 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*b*c*b*c, (b*c)^16 ] Orientable map of genus 49 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*a*b*c*b*c*b*c*a*b*a*b*c*b*c*b*c*b*c*b*a, c*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 49 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 49 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 49 and type {4,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*a*b*a*b*c*b*c*b*c*b*c*b*a, (b*c)^16 ] Orientable map of genus 57 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*b*c*b*c, b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 57 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*a*b*a*b*c*b*c*b*c*b*c*b*a, b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 57 and type {4,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^32 ] Orientable map of genus 61 and type {4,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 61 and type {4,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^64 ] Orientable map of genus 63 and type {4,128}_128 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 63 and type {4,128}_128 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^128 ] Orientable map of genus 64 and type {4,256}_256 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 65 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, b*c*a*b*c*a*b*a*b*a*b*a*b*c*b*c*b*a*b*a*b*a ] Orientable map of genus 65 and type {8,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, b*c*a*b*c*a*b*a*b*a*b*a*b*c*b*c*b*a*b*a*b*a ] Orientable map of genus 65 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (b*c)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b ] Orientable map of genus 65 and type {8,8}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*a, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 65 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b ] Orientable map of genus 65 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*c, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b ] Orientable map of genus 65 and type {8,8}_8 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*c, b*c*a*b*c*a*b*a*b*a*b*a*b*c*b*c*b*a*b*a*b*a ] Orientable map of genus 65 and type {8,8}_16 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*a*c*b*c*b*a*b*a*c*b*c ] Orientable map of genus 65 and type {8,8}_16 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, (a*b*c*b)^8 ] Orientable map of genus 65 and type {8,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b ] Orientable map of genus 65 and type {8,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*a*b*c*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b, b*c*a*b*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*c ] Orientable map of genus 65 and type {8,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*c*a*b*a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 65 and type {8,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*a, a*b*c*a*b*a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 65 and type {8,8}_16 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, b*c*a*b*c*a*b*a*b*a*b*a*b*c*b*c*b*a*b*a*b*a, c*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^16 ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, (b*c)^16 ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, b*c*a*b*c*a*b*c*b*a*b*a*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (b*c)^16 ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*a*b*c*a*b*a*b*a*c*b*a*c*b*c*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, a*b*c*b*a*b*a*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, b*c*a*b*c*b*c*b*c*a*b*a*b*a*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (b*c)^16 ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*a*b*c*a*b*a*b*a*c*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, c*b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b, c*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, b*c*a*b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^16 ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*a*b*a*b*a*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*a*b*c*b*c*b*c*a*b*a*b*c*b*c*b*c*b*c*b*a ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, c*b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*a*b*a*b*c*b*c*b*c*b*c*b*a, c*b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*c*b*c, (b*c)^16 ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, b*c*a*b*c*a*b*a*b*a*b*a*b*c*b*c*b*a*b*a*b*a, c*b*c*a*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {8,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (b*c)^16 ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*b^2*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^32 ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b, b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*c*b*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {8,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^32 ] Orientable map of genus 93 and type {8,64}_64 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 93 and type {8,64}_64 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^64 ] Orientable map of genus 93 and type {8,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 93 and type {8,64}_64 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 95 and type {8,128}_128 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 97 and type {16,16}_16 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*b*c*b*a*c*b, b*c*a*b*c*b*c*b*c*a*b*a*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*a ] Orientable map of genus 97 and type {16,16}_16 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, a*b*a*b*a*b*a*b*a*b*a*c*b*a*c*b*a*c*b*c, b*c*a*b*a*b*c*b*c*a*b*a*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 97 and type {16,16}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*a*c, a*b*c*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b*a*b ] Orientable map of genus 97 and type {16,16}_16 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*a*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 97 and type {16,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, c*b*c*b*a*b*c*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, (a*b)^16 ] Orientable map of genus 97 and type {16,16}_16 invariant under all six Wilson transforms Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*a*b*c*a*b*a*b*a*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 97 and type {16,16}_16 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*a*c, b*c*a*b*c*a*b*c*b*a*b*a*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^16, c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^16, c*b*c*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, (b*c)^32 ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, c*b*c*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*a*b*a*b, (a*b)^16 ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^32 ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^16 ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {16,32}_32 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, b*c*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 109 and type {16,64}_64 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 109 and type {16,64}_64 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1024 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 65 and type {8,8}_8 isomorphic to its dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1)^4, X^-2*Y*X^3*Y^-1*X*Y^2, Y^2*X^-1*Y*X^2*Y^-2*X*Y ] Chiral map of genus 65 and type {8,8}_8 isomorphic to its mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, Y^8, X^-2*Y*X^3*Y^-1*X*Y^2, Y*X*Y^-2*X^2*Y*X^-1*Y^2 ] Chiral map of genus 65 and type {8,8}_16 isomorphic to its dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, Y^8, X^-1*Y^-4*X^2*Y^4*X^-1, Y^-1*X^3*Y^-1*X^-2*Y^-1*X^3*Y^-1, Y*X^2*Y^-1*X^3*Y^2*X^-1*Y^2, Y^-1*X*Y^-2*X^3*Y*X^-1*Y^-2*X ] Chiral map of genus 81 and type {8,16}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, (X*Y^-3)^2, X^-2*Y*X^3*Y^-1*X*Y^2 ] Chiral map of genus 81 and type {8,16}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, X^-2*Y*X^3*Y^-1*X*Y^2, Y*X*Y^-3*X*Y^4 ] Chiral map of genus 81 and type {8,16}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, Y*X*Y^-2*X^2*Y*X^-1*Y^2, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y ] Chiral map of genus 81 and type {8,16}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, Y^2*X^-1*Y*X^2*Y^-2*X*Y ] Chiral map of genus 81 and type {8,16}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, Y^-1*X^-1*Y^2*X^2*Y^-1*X*Y^-2 ] Chiral map of genus 93 and type {8,64}_64 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^8, Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-1, Y^-8*X^2*Y^-2*X*Y*X^-1*Y^-5 ] Chiral map of genus 97 and type {16,16}_8 isomorphic to its dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, X^-2*Y*X^3*Y^-1*X*Y^2, Y^2*X^-1*Y*X^2*Y^-2*X*Y, X*Y^-1*X^5*Y*X^-1*Y^-2*X ] Chiral map of genus 97 and type {16,16}_8 isomorphic to its mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, (X*Y^-1)^4, X^-2*Y*X^3*Y^-1*X*Y^2, Y*X*Y^-2*X^2*Y*X^-1*Y^2 ] Chiral map of genus 97 and type {16,16}_16 isomorphic to its dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-2*X^-1*Y*X^3*Y*X^-1*Y*X^-1*Y^-1 ] Chiral map of genus 97 and type {16,16}_16 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, Y^-2*X*Y^-1*X^2*Y^2*X^-1*Y^-1, X^-1*Y*X^6*Y^-2*X*Y^3 ] Chiral map of genus 105 and type {16,32}_32 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y, Y*X^6*Y*X^-2*Y^2, X^2*Y^-1*X^10*Y^-3 ] Chiral map of genus 105 and type {16,32}_32 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y, Y*X^6*Y*X^-1*Y^2*X^-1, Y^-4*X^3*Y*X^-1*Y^-3 ] Chiral map of genus 105 and type {16,32}_32 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y, Y*X^6*Y*X^-1*Y^2*X^-1, Y^4*X^3*Y^-2*X*Y^2, X^16 ] Chiral map of genus 109 and type {16,64}_64 not isomorphic to its dual or mirror-dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-1)^4, (X*Y^-3)^2, Y^-1*X^6*Y*X^-1*Y^-1*X*Y^-1, Y^-8*X^-3*Y^2*X^-1*Y^-6 ] Chiral map of genus 113 and type {32,32}_16 isomorphic to its dual Automorphism group of order 512 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-1)^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X^4*Y*X^-2*Y^5 ] .......................... Rotary maps with 257 edges .......................... Orientable map of genus 0 and type {2,257}_514 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1028 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^257 ] .......................... Rotary maps with 258 edges .......................... Orientable map of genus 0 and type {2,258}_258 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1032 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^258 ] Non-orientable map of genus 1 and type {2,516}_516 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1032 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 127 and type {4,129}_129 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1032 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^129 ] Orientable map of genus 84 and type {6,86}_258 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1032 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^86 ] Chiral map of genus 44 and type {6,6}_86 not isomorphic to its dual or mirror-dual Automorphism group of order 516 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y*X^-1*Y*X^2*Y^-1*X^2*Y^-1*X^2*Y*X^-2*Y^-1*X^2*Y*X^-1*Y*X^-2 ] .......................... Rotary maps with 259 edges .......................... Orientable map of genus 0 and type {2,259}_518 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1036 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^259 ] Non-orientable map of genus 217 and type {14,74}_259 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1036 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 260 edges .......................... Orientable map of genus 0 and type {2,260}_260 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1040 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^260 ] Non-orientable map of genus 1 and type {2,520}_520 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1040 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 64 and type {4,130}_260 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1040 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^130 ] Orientable map of genus 100 and type {10,52}_260 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1040 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^52 ] Orientable map of genus 108 and type {20,26}_260 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1040 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^26 ] Orientable map of genus 113 and type {20,52}_130 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1040 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_130 isomorphic to its dual Automorphism group of order 520 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y*X^2*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^-1 ] Chiral map of genus 1 and type {4,4}_130 isomorphic to its dual Automorphism group of order 520 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^-2*X*Y^-1*X*Y^-1*X ] Chiral map of genus 53 and type {4,20}_130 not isomorphic to its dual or mirror-dual Automorphism group of order 520 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^-2*X^-1*Y^2*X*Y^-2*X^2*Y^-1*X*Y^2*X^-1*Y^-1 ] Chiral map of genus 61 and type {4,52}_130 not isomorphic to its dual or mirror-dual Automorphism group of order 520 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^13*X*Y^-1*X*Y*X^-1*Y^-5*X*Y^6 ] Chiral map of genus 105 and type {20,20}_26 isomorphic to its dual Automorphism group of order 520 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, X^-2*Y^2*X^-1*Y*X^-9*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 121 and type {52,52}_10 isomorphic to its dual Automorphism group of order 520 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X^2*Y*X^-1*Y, X^-22*Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-2*Y*X^-1*Y*X^-9*Y*X^-1*Y^3*X^-1*Y^2*X^-1 ] .......................... Rotary maps with 261 edges .......................... Orientable map of genus 0 and type {2,261}_522 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1044 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^261 ] Orientable map of genus 85 and type {6,87}_174 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1044 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^87 ] Non-orientable map of genus 225 and type {18,58}_261 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1044 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 262 edges .......................... Orientable map of genus 0 and type {2,262}_262 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1048 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^262 ] Non-orientable map of genus 1 and type {2,524}_524 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1048 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 263 edges .......................... Orientable map of genus 0 and type {2,263}_526 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1052 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^263 ] .......................... Rotary maps with 264 edges .......................... Orientable map of genus 0 and type {2,264}_264 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^264 ] Non-orientable map of genus 1 and type {2,528}_528 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 63 and type {4,66}_66 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^66 ] Non-orientable map of genus 130 and type {4,132}_132 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 130 and type {4,132}_132 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^132 ] Orientable map of genus 65 and type {4,132}_132 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^132 ] Orientable map of genus 66 and type {4,264}_264 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 83 and type {6,44}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 86 and type {6,88}_264 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^88 ] Orientable map of genus 92 and type {8,33}_132 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (c*b)^33 ] Orientable map of genus 96 and type {8,66}_132 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 96 and type {8,66}_264 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^66 ] Orientable map of genus 98 and type {8,132}_264 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 103 and type {12,33}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, b*c*a*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 105 and type {12,44}_132 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^44 ] Orientable map of genus 107 and type {12,66}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 108 and type {12,88}_264 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 110 and type {22,24}_264 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, (b*c)^24 ] Orientable map of genus 116 and type {24,44}_264 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 118 and type {24,66}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 119 and type {24,88}_132 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1056 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] .......................... Rotary maps with 265 edges .......................... Orientable map of genus 0 and type {2,265}_530 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1060 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^265 ] Non-orientable map of genus 209 and type {10,106}_265 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1060 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 266 edges .......................... Orientable map of genus 0 and type {2,266}_266 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1064 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^266 ] Non-orientable map of genus 1 and type {2,532}_532 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1064 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 108 and type {14,38}_266 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1064 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^38 ] .......................... Rotary maps with 267 edges .......................... Orientable map of genus 0 and type {2,267}_534 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1068 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^267 ] Non-orientable map of genus 177 and type {6,178}_267 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1068 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 268 edges .......................... Orientable map of genus 0 and type {2,268}_268 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1072 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^268 ] Non-orientable map of genus 1 and type {2,536}_536 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1072 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 66 and type {4,134}_268 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1072 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^134 ] .......................... Rotary maps with 269 edges .......................... Orientable map of genus 0 and type {2,269}_538 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1076 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^269 ] .......................... Rotary maps with 270 edges .......................... Orientable map of genus 0 and type {2,270}_270 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^270 ] Non-orientable map of genus 1 and type {2,540}_540 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 133 and type {4,135}_135 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^135 ] Non-orientable map of genus 155 and type {6,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (a*b*c*b*a*b*c*b*a*b)^2, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 82 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^30 ] Orientable map of genus 82 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, a*b*c*a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 82 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, (b*c)^30 ] Non-orientable map of genus 170 and type {6,45}_45 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a, b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 173 and type {6,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 173 and type {6,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (a*b*c*b*a*b*c*b*a*b)^2, c*b*c*a*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 88 and type {6,90}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^90 ] Non-orientable map of genus 158 and type {9,10}_45 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, (b*c)^10, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*c*b*c ] Orientable map of genus 104 and type {10,54}_270 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^54 ] Orientable map of genus 112 and type {18,30}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b, (a*b)^18 ] Orientable map of genus 112 and type {18,30}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1080 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^30 ] Chiral map of genus 46 and type {4,12}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 540 with defining relations: [ (X*Y)^2, X^4, Y*X*Y^-3*X*Y^4, Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^-1*X*Y, Y^2*X*Y^-1*X*Y^-1*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y*X^-1*Y*X^-1 ] Chiral map of genus 88 and type {6,90}_90 not isomorphic to its dual or mirror-dual Automorphism group of order 540 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^15*X^2*Y*X^-2*Y^14 ] Chiral map of genus 91 and type {12,12}_30 isomorphic to its dual Automorphism group of order 540 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, Y*X^-1*Y^-1*X*Y^-2*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y^2*X^-2 ] Chiral map of genus 91 and type {12,12}_30 isomorphic to its dual Automorphism group of order 540 with defining relations: [ (X*Y)^2, Y^-1*X^4*Y^-3, X^2*Y^-1*X^3*Y^2*X^-1*Y^-1, X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y^-1*X*Y^2 ] Chiral map of genus 112 and type {18,30}_90 not isomorphic to its dual or mirror-dual Automorphism group of order 540 with defining relations: [ (X*Y)^2, Y^-2*X^4*Y*X^-1*Y^-1*X, Y^2*X*Y^-3*X^2*Y^-3*X*Y^2 ] Chiral map of genus 124 and type {30,90}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 540 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y^3*X^3*Y^-1*X*Y^2, X^-1*Y*X^-1*Y*X^-1*Y^11*X^-12*Y*X^-1 ] Chiral map of genus 131 and type {108,108}_10 isomorphic to its dual Automorphism group of order 540 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^25*X^-2*Y^2*X^-1*Y^3*X^-1*Y^2*X^-9*Y*X^-1*Y^3*X^-1*Y^3 ] .......................... Rotary maps with 271 edges .......................... Orientable map of genus 0 and type {2,271}_542 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1084 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^271 ] .......................... Rotary maps with 272 edges .......................... Orientable map of genus 0 and type {2,272}_272 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^272 ] Non-orientable map of genus 1 and type {2,544}_544 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 65 and type {4,68}_68 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^68 ] Orientable map of genus 67 and type {4,136}_136 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 67 and type {4,136}_136 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^136 ] Orientable map of genus 68 and type {4,272}_272 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 99 and type {8,68}_136 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^68 ] Orientable map of genus 99 and type {8,68}_136 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^68 ] Orientable map of genus 112 and type {16,34}_272 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^34 ] Orientable map of genus 116 and type {16,68}_272 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1088 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_68 isomorphic to its dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^-1 ] Chiral map of genus 35 and type {4,8}_136 not isomorphic to its dual or mirror-dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 35 and type {4,8}_136 not isomorphic to its dual or mirror-dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, Y*X^-1*Y^2*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-1*X*Y*X^-1 ] Chiral map of genus 69 and type {8,8}_68 isomorphic to its dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X^2*Y^2*X^-2*Y^-1*X*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 69 and type {8,8}_68 isomorphic to its dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^2*X*Y^-1*X*Y^-1 ] Chiral map of genus 69 and type {8,8}_68 not isomorphic to its dual or mirror-dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, X^-2*Y*X^-3*Y^4*X*Y^-1 ] Chiral map of genus 103 and type {16,16}_34 isomorphic to its dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-1*X*Y^-2*X*Y^-1*X^-2*Y^2*X^-1*Y*X^-2*Y^-1*X, X^16 ] Chiral map of genus 103 and type {16,16}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, Y*X^6*Y^2*X^-2*Y, (X^-5*Y*X^-2)^2 ] Chiral map of genus 103 and type {16,16}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y^4, Y^2*X^-1*Y*X^2*Y^-2*X*Y, X^2*Y^-1*X^8*Y^-3*X^2 ] Chiral map of genus 103 and type {16,16}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^3*Y^-1*X*Y*X^-1, Y*X*Y^-1*X^4*Y^2*X^-1*Y^2, X*Y^-1*X^9*Y^-2*X*Y^-1*X ] Chiral map of genus 103 and type {16,16}_68 isomorphic to its dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^2*Y^-2*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2 ] Chiral map of genus 103 and type {16,16}_68 not isomorphic to its dual or mirror-dual Automorphism group of order 544 with defining relations: [ (X*Y)^2, Y*X^6*Y^2*X^-2*Y, Y^-1*X^-1*Y*X^4*Y^-2*X*Y^-2 ] .......................... Rotary maps with 273 edges .......................... Orientable map of genus 0 and type {2,273}_546 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^273 ] Non-orientable map of genus 15 and type {3,7}_13 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (c*b)^7, c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 106 and type {6,7}_13 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (c*b)^7, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, b*c*a*b*c*a*b*a*b*c*a*b*a*c*b*a*b*a*c*b*a*c*b*a ] Non-orientable map of genus 181 and type {6,182}_273 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 119 and type {7,7}_7 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, (c*b)^7, (a*b*c*b*c*b*a*b)^2, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*b*a*c*b*a ] Non-orientable map of genus 119 and type {7,7}_7 invariant under all six Wilson transforms Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, (c*b)^7, c*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*a*b*c*b, b*c*b*a*b*c*a*b*a*b*a*c*b*c*b*a*c*b*c*b*a ] Non-orientable map of genus 155 and type {7,13}_13 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, b*c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b*a*c, b*a*b*c*a*b*c*b*a*b*a*c*b*c*b*a*b*a*c*b*c ] Non-orientable map of genus 229 and type {14,78}_273 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 241 and type {26,42}_273 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1092 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 1 and type {3,6}_182 not isomorphic to its dual or mirror-dual Automorphism group of order 546 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^3*X^-1*Y*X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y^-2*X*Y ] Chiral map of genus 1 and type {3,6}_182 not isomorphic to its dual or mirror-dual Automorphism group of order 546 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-1*X*Y^3*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-1 ] Chiral map of genus 79 and type {6,21}_182 not isomorphic to its dual or mirror-dual Automorphism group of order 546 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^-1*Y*X*Y^-1*X^-1*Y*X^3*Y^-1*X*Y*X^-1*Y^-2 ] Chiral map of genus 85 and type {6,39}_182 not isomorphic to its dual or mirror-dual Automorphism group of order 546 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^-1*Y*X^2*Y^-1*X^2*Y^-1*X^2*Y*X^-2*Y*X^-1*Y, Y^-3*X^-1*Y*X*Y^-1*X^2*Y^-1*X^2*Y^-7 ] Chiral map of genus 118 and type {21,42}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 546 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^2, X^-3*Y*X^-2*Y*X^-10*Y*X^-2*Y ] Chiral map of genus 127 and type {39,78}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 546 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, Y^16*X^-3*Y*X^-10*Y^2*X^-3*Y^3*X^-1 ] .......................... Rotary maps with 274 edges .......................... Orientable map of genus 0 and type {2,274}_274 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1096 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^274 ] Non-orientable map of genus 1 and type {2,548}_548 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1096 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_274 isomorphic to its dual Automorphism group of order 548 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X*Y^-1*X ] .......................... Rotary maps with 275 edges .......................... Orientable map of genus 0 and type {2,275}_550 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1100 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^275 ] Orientable map of genus 106 and type {10,55}_110 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1100 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (c*b)^55 ] Non-orientable map of genus 241 and type {22,50}_275 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1100 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 56 and type {5,10}_110 not isomorphic to its dual or mirror-dual Automorphism group of order 550 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y^-1 ] Chiral map of genus 56 and type {5,10}_110 not isomorphic to its dual or mirror-dual Automorphism group of order 550 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y^-3*X*Y^-1*X^-2*Y^-1*X*Y*X^-1*Y^-2 ] Chiral map of genus 122 and type {25,50}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 550 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y^4, X^-2*Y*X^3*Y^-1*X*Y^2, X^-1*Y^7*X^-1*Y*X^-1*Y*X^-10*Y*X^-2 ] Chiral map of genus 122 and type {25,50}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 550 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X*Y^-2*X^2*Y*X^-1*Y^2, Y^6*X^-3*Y*X^-1*Y^2*X^-11*Y ] .......................... Rotary maps with 276 edges .......................... Orientable map of genus 0 and type {2,276}_276 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^276 ] Non-orientable map of genus 1 and type {2,552}_552 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 66 and type {4,69}_138 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^69 ] Non-orientable map of genus 136 and type {4,138}_138 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^138 ] Orientable map of genus 68 and type {4,138}_276 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^138 ] Orientable map of genus 89 and type {6,69}_92 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 90 and type {6,92}_276 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^92 ] Orientable map of genus 110 and type {12,46}_276 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^46 ] Orientable map of genus 113 and type {12,92}_138 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1104 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 277 edges .......................... Orientable map of genus 0 and type {2,277}_554 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1108 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^277 ] .......................... Rotary maps with 278 edges .......................... Orientable map of genus 0 and type {2,278}_278 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1112 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^278 ] Non-orientable map of genus 1 and type {2,556}_556 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1112 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 279 edges .......................... Orientable map of genus 0 and type {2,279}_558 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1116 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^279 ] Orientable map of genus 91 and type {6,93}_186 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1116 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^93 ] Non-orientable map of genus 241 and type {18,62}_279 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1116 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_186 not isomorphic to its dual or mirror-dual Automorphism group of order 558 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-2*X*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y^-2*X*Y^-1 ] Chiral map of genus 94 and type {9,18}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 558 with defining relations: [ (X*Y)^2, X^9, Y*X^4*Y*X^-2, Y^2*X^-3*Y^4, Y*X^-1*Y^3*X*Y^-2*X^-2*Y^-1*X*Y^2*X^-1*Y^2*X^-1*Y ] .......................... Rotary maps with 280 edges .......................... Orientable map of genus 0 and type {2,280}_280 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^280 ] Non-orientable map of genus 1 and type {2,560}_560 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 126 and type {4,35}_35 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (c*b)^35 ] Orientable map of genus 69 and type {4,140}_140 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^140 ] Orientable map of genus 70 and type {4,280}_280 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 102 and type {8,70}_280 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^70 ] Orientable map of genus 104 and type {8,140}_280 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 108 and type {10,56}_280 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^56 ] Orientable map of genus 114 and type {14,40}_280 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^40 ] Orientable map of genus 117 and type {20,28}_140 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^28 ] Orientable map of genus 122 and type {20,56}_280 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 124 and type {28,40}_280 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 129 and type {40,56}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 129 and type {40,56}_140 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1120 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] Chiral map of genus 61 and type {4,28}_140 not isomorphic to its dual or mirror-dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^28 ] Chiral map of genus 101 and type {8,56}_70 not isomorphic to its dual or mirror-dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^2*X*Y^-1*X^-1*Y^2*X*Y^-2*X^-1*Y^7 ] Chiral map of genus 101 and type {8,56}_140 not isomorphic to its dual or mirror-dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y*X^2*Y^-2*X^2*Y^2*X^-1*Y*X^-1, Y^6*X*Y^-2*X*Y^2*X^-1*Y^-2*X*Y^2 ] Chiral map of genus 113 and type {14,35}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, Y^-1*X^-5*Y^3*X^-1*Y^-1 ] Chiral map of genus 121 and type {28,28}_20 isomorphic to its dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, Y^-2*X*Y^-1*X^2*Y^-2*X*Y^-1*X^7*Y^-2*X*Y^-3*X*Y^-1*X^3 ] Chiral map of genus 129 and type {35,70}_4 not isomorphic to its dual or mirror-dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y^3*X^-1, X^-2*Y*X^-18*Y*X^-11*Y^2 ] Chiral map of genus 131 and type {56,56}_10 isomorphic to its dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-1*Y*X^-26*Y^3*X^-1*Y^3*X^-1*Y^2*X^-8*Y*X^-1*Y^2*X^-1*Y*X^-1*Y^3 ] Chiral map of genus 131 and type {56,56}_20 isomorphic to its dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X*Y^-1*X^2*Y^-1*X*Y^2*X^-1, X*Y^-3*X^2*Y^-1*X*Y^-1*X*Y^-1*X^6*Y^-2*X*Y^-3*X*Y^-1*X*Y^-2 ] Chiral map of genus 133 and type {70,70}_4 isomorphic to its mirror-dual Automorphism group of order 560 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-1*Y, X^-54*Y^2*X^-12*Y^2 ] .......................... Rotary maps with 281 edges .......................... Orientable map of genus 0 and type {2,281}_562 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1124 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^281 ] .......................... Rotary maps with 282 edges .......................... Orientable map of genus 0 and type {2,282}_282 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1128 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^282 ] Non-orientable map of genus 1 and type {2,564}_564 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1128 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 139 and type {4,141}_141 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^141 ] Orientable map of genus 92 and type {6,94}_282 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1128 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^94 ] .......................... Rotary maps with 283 edges .......................... Orientable map of genus 0 and type {2,283}_566 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1132 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^283 ] .......................... Rotary maps with 284 edges .......................... Orientable map of genus 0 and type {2,284}_284 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1136 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^284 ] Non-orientable map of genus 1 and type {2,568}_568 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1136 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 70 and type {4,142}_284 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1136 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^142 ] .......................... Rotary maps with 285 edges .......................... Orientable map of genus 0 and type {2,285}_570 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1140 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^285 ] Non-orientable map of genus 189 and type {6,190}_285 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1140 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 225 and type {10,114}_285 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1140 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 253 and type {30,38}_285 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1140 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 77 and type {6,15}_190 not isomorphic to its dual or mirror-dual Automorphism group of order 570 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^-1*Y*X^2*Y^-1*X^-2*Y*X^3*Y^-1*X*Y*X^-1*Y^-2 ] Chiral map of genus 115 and type {15,30}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 570 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, X^-15, Y^-1*X*Y^-2*X*Y^-1*X^-2*Y^3*X^-1*Y*X^-1*Y^-2 ] .......................... Rotary maps with 286 edges .......................... Orientable map of genus 0 and type {2,286}_286 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1144 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^286 ] Non-orientable map of genus 1 and type {2,572}_572 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1144 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 120 and type {22,26}_286 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1144 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, (b*c)^26 ] Chiral map of genus 131 and type {44,44}_26 isomorphic to its dual Automorphism group of order 572 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, X^-2*Y*X^-1*Y^3*X^-1*Y*X^-6*Y^2*X^-1*Y*X^-2*Y ] .......................... Rotary maps with 287 edges .......................... Orientable map of genus 0 and type {2,287}_574 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1148 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^287 ] Non-orientable map of genus 241 and type {14,82}_287 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1148 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 288 edges .......................... Orientable map of genus 0 and type {2,288}_288 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^288 ] Non-orientable map of genus 1 and type {2,576}_576 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 25 and type {3,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^12, c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 25 and type {3,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*c*b*a*c*b, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 37 and type {3,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 1 and type {4,4}_24 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (a*b*c*b)^12 ] Non-orientable map of genus 50 and type {4,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*b*c*a*b*c*a*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*a*c*b, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 37 and type {4,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 37 and type {4,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b*a*b)^3, (b*c)^8, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 37 and type {4,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*c*a*b*c*a*b*c*b*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 82 and type {4,9}_9 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (c*b)^9, b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 55 and type {4,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (a*b*c*b)^6, (b*c)^16 ] Orientable map of genus 55 and type {4,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*a*b*c*b*a*b*c*b*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 57 and type {4,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c*b*a, (b*c)^18 ] Orientable map of genus 57 and type {4,18}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, (b*c)^18 ] Orientable map of genus 65 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^36 ] Non-orientable map of genus 130 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 130 and type {4,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^36 ] Orientable map of genus 65 and type {4,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^36 ] Orientable map of genus 65 and type {4,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 69 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^72 ] Orientable map of genus 69 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 69 and type {4,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^72 ] Orientable map of genus 71 and type {4,144}_144 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 71 and type {4,144}_144 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^144 ] Non-orientable map of genus 142 and type {4,144}_144 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 142 and type {4,144}_144 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^144 ] Orientable map of genus 72 and type {4,288}_288 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {6,6}_6 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b ] Orientable map of genus 49 and type {6,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, (a*b*c*b*c*b*a*b*c*b*a*b)^2 ] Non-orientable map of genus 98 and type {6,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (a*b*c*b)^4, b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*a*c*b*c ] Orientable map of genus 49 and type {6,6}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c ] Orientable map of genus 49 and type {6,6}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (b*c)^6, a*b*c*a*b*a*b*c*a*b*a*b*c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b ] Non-orientable map of genus 122 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, (b*c)^8, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Non-orientable map of genus 122 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (b*c)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b ] Orientable map of genus 73 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, (b*c)^12 ] Orientable map of genus 73 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 73 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*a*b*a*b*c*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, (b*c)^12 ] Orientable map of genus 73 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 73 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, c*a*b*c*a*b*c*b*a*b*a*c*b*a*b*c*b*a*c*b ] Orientable map of genus 73 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*a*b*c*b*c*a*b*c*b*a*c*b*a*c*b*a*b*c*b*c, (b*c)^12 ] Orientable map of genus 73 and type {6,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 85 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (b*c)^24 ] Orientable map of genus 85 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b ] Orientable map of genus 85 and type {6,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, a*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 88 and type {6,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^32 ] Orientable map of genus 94 and type {6,96}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (b*c)^96 ] Orientable map of genus 94 and type {6,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 73 and type {8,8}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 73 and type {8,8}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*c*b*a*b*c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Orientable map of genus 73 and type {8,8}_24 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, (b*c)^8, (a*b*c*b)^6 ] Orientable map of genus 73 and type {8,8}_24 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*c*b*c*a*b*c*b*c*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b*c*b*a ] Orientable map of genus 73 and type {8,8}_24 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^8, a*b*c*a*b*c*a*b*c*a*b*a*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 77 and type {8,9}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (c*b)^9, c*a*b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*b ] Orientable map of genus 91 and type {8,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, a*b*c*b*a*b*c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Orientable map of genus 91 and type {8,16}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, (a*b*c*b)^6 ] Orientable map of genus 93 and type {8,18}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (b*c)^18 ] Non-orientable map of genus 186 and type {8,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*a*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b*c, (b*c)^18 ] Non-orientable map of genus 186 and type {8,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^18 ] Orientable map of genus 93 and type {8,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^18 ] Orientable map of genus 93 and type {8,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 93 and type {8,18}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*a, (b*c)^18 ] Orientable map of genus 101 and type {8,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^36 ] Orientable map of genus 101 and type {8,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 101 and type {8,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, (b*c)^36 ] Orientable map of genus 101 and type {8,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^36 ] Non-orientable map of genus 202 and type {8,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c ] Non-orientable map of genus 202 and type {8,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*a*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 101 and type {8,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^36 ] Orientable map of genus 101 and type {8,36}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 105 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^72 ] Orientable map of genus 105 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {8,72}_72 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 107 and type {8,144}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 214 and type {8,144}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 97 and type {12,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (a*b)^12, (b*c)^12 ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (a*b)^12, (b*c)^12 ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (a*b)^12, (b*c)^12 ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*a*b*a*b*a*b*a*b*a*c*b*c*b*a*c*b*c*b*c, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*c*b, b*c*b*c*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, (a*b)^12 ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*a*c*b*a*c, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, (a*b)^12 ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*c*b*c*b*c*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, (a*b)^12 ] Orientable map of genus 97 and type {12,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, (b*c)^12 ] Orientable map of genus 103 and type {12,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^12, b*c*a*b*a*b*a*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 103 and type {12,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, (b*c)^16 ] Orientable map of genus 109 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, (a*b)^12, (b*c)^24 ] Orientable map of genus 109 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (a*b)^12, b*c*b*c*a*b*c*b*c*b*c*b*c*a^2*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 109 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (a*b)^12, b*c*b*c*a*b*c*b*c*b*c*b*c*a^2*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 109 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (b*c)^24 ] Orientable map of genus 109 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, (a*b)^12 ] Orientable map of genus 109 and type {12,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*a*b*a, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 112 and type {12,32}_32 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*a*b*c*b*c*a*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 115 and type {12,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 115 and type {12,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, (b*c)^48 ] Orientable map of genus 115 and type {12,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, c*b*c*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 115 and type {12,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 118 and type {12,96}_96 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 118 and type {12,96}_96 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 109 and type {16,16}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*a*b*a*b*a*b*a*b*c*b*c*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, b*c*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*c*b*c ] Orientable map of genus 119 and type {16,36}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^36 ] Orientable map of genus 119 and type {16,36}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, (b*c)^36 ] Orientable map of genus 123 and type {16,72}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 123 and type {16,72}_144 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 120 and type {18,32}_288 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^32 ] Orientable map of genus 121 and type {24,24}_24 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b*c*b*a*b, b*c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 121 and type {24,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c, a*b*c*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*a*b*a*b*a*b*c*b ] Orientable map of genus 121 and type {24,24}_24 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 121 and type {24,24}_24 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b*c*b, (b*c)^24 ] Orientable map of genus 121 and type {24,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*c*b*c*b*c*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*c*b*a*b*c*b*c*b ] Orientable map of genus 121 and type {24,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*a*c*b*a*c, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*c*b*a*b*c*b*c*b ] Orientable map of genus 127 and type {24,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 127 and type {24,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 127 and type {24,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*b*c*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*c*b*c*b*c*b, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b*a*b ] Orientable map of genus 128 and type {32,36}_288 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1152 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 37 and type {4,8}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^4, Y^8, Y^2*X^-1*Y*X^-1*Y*X^2*Y^-2*X*Y*X^-1*Y, Y^-1*X^-1*Y^2*X*Y^-1*X*Y^2*X^-1*Y^-2 ] Chiral map of genus 55 and type {4,16}_16 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^4, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^2*X^-1*Y*X*Y^-1*X^-1*Y^2*X^-1*Y^2, Y^16 ] Chiral map of genus 55 and type {4,16}_16 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^4, Y^-2*X^-1*Y*X*Y^-1*X^-1*Y^2*X^-1*Y^-2 ] Chiral map of genus 49 and type {6,6}_12 isomorphic to its dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-1)^4, Y*X^-2*Y*X^3*Y^3*X^-1*Y ] Chiral map of genus 49 and type {6,6}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^3*Y^3*X^-2, (X*Y^-2*X*Y^-1*X)^2, (X*Y^-2)^4, X^-1*Y^2*X*Y^-1*X^-3*Y^-1*X^2*Y^-1*X*Y ] Chiral map of genus 73 and type {8,8}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-3)^2, X^-2*Y*X*Y^-1*X^-2*Y^-1*X^3*Y ] Chiral map of genus 73 and type {8,8}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-3)^2, Y^-1*X^3*Y^-1*X^-4*Y^-1*X*Y^-1 ] Chiral map of genus 73 and type {8,8}_12 isomorphic to its dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, Y^-1*X^3*Y^-1*X^-2*Y^4*X ] Chiral map of genus 73 and type {8,8}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1)^4, Y^-1*X^-2*Y*X^-3*Y^-1*X^3*Y^-1 ] Chiral map of genus 91 and type {8,16}_16 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, Y^-3*X^4*Y^-5, Y*X*Y^-1*X*Y^-1*X^2*Y^-2*X^2*Y, Y*X*Y^-3*X^2*Y^-1*X*Y^3 ] Chiral map of genus 91 and type {8,16}_16 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, Y^-3*X^4*Y^-5, Y*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y*X^-1*Y, Y^-1*X*Y^-3*X^2*Y^-1*X*Y^-3 ] Chiral map of genus 109 and type {16,16}_12 isomorphic to its dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, Y*X^6*Y^2*X^-2*Y, Y*X*Y^-1*X^4*Y*X^-1*Y^3, X^-2*Y*X^4*Y^-1*X*Y*X^-1*Y, X^16 ] Chiral map of genus 109 and type {16,16}_12 isomorphic to its dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, Y*X^6*Y^2*X^-2*Y, X^2*Y^-1*X^4*Y^-1*X*Y*X^-1*Y^-1 ] Chiral map of genus 109 and type {16,16}_24 not isomorphic to its dual or mirror-dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, (X*Y^-2*X)^2, X^2*Y^-1*X^4*Y^-1*X*Y*X^-1*Y^-1 ] Chiral map of genus 113 and type {18,18}_8 isomorphic to its dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y*X^6*Y^5, Y*X*Y^-2*X^3*Y^3*X^-2, X^-2*Y*X^-3*Y*X^-4*Y^4*X^-1*Y^2 ] Chiral map of genus 127 and type {32,32}_6 isomorphic to its dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y*X^5*Y^3*X^-1, Y^-1*X^8*Y^-1*X^5*Y^-1*X^9*Y^-1*X^3*Y^-2*X ] Chiral map of genus 127 and type {32,32}_12 isomorphic to its dual Automorphism group of order 576 with defining relations: [ (X*Y)^2, Y*X^6*Y^2*X^-2*Y, Y*X*Y^-1*X^4*Y*X^-1*Y^3, X^-2*Y*X^4*Y^-1*X*Y*X^-1*Y, X^11*Y^-1*X*Y^-3 ] .......................... Rotary maps with 289 edges .......................... Orientable map of genus 0 and type {2,289}_578 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1156 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^289 ] Orientable map of genus 120 and type {17,34}_34 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1156 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (b*a)^17 ] .......................... Rotary maps with 290 edges .......................... Orientable map of genus 0 and type {2,290}_290 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1160 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^290 ] Non-orientable map of genus 1 and type {2,580}_580 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1160 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 112 and type {10,58}_290 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1160 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^58 ] Chiral map of genus 1 and type {4,4}_290 isomorphic to its dual Automorphism group of order 580 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 1 and type {4,4}_290 isomorphic to its dual Automorphism group of order 580 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^2*X^2*Y^2*X^2*Y^2*X^-2*Y^-2*X^-2 ] Chiral map of genus 117 and type {20,20}_58 isomorphic to its dual Automorphism group of order 580 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-2*X^-1*Y*X*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 141 and type {116,116}_10 isomorphic to its dual Automorphism group of order 580 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^29*X^-2*Y^2*X^-1*Y^3*X^-1*Y^2*X^-8*Y*X^-1*Y^2*X^-1*Y*X^-1*Y^3 ] .......................... Rotary maps with 291 edges .......................... Orientable map of genus 0 and type {2,291}_582 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1164 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^291 ] Non-orientable map of genus 193 and type {6,194}_291 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1164 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_194 not isomorphic to its dual or mirror-dual Automorphism group of order 582 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^-3*X*Y^-1*X*Y^3*X*Y^-2*X^-1*Y^2*X^-1*Y^2*X^-1*Y ] .......................... Rotary maps with 292 edges .......................... Orientable map of genus 0 and type {2,292}_292 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1168 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^292 ] Non-orientable map of genus 1 and type {2,584}_584 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1168 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 72 and type {4,146}_292 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1168 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^146 ] Chiral map of genus 1 and type {4,4}_146 isomorphic to its dual Automorphism group of order 584 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^-1 ] Chiral map of genus 74 and type {8,8}_146 not isomorphic to its dual or mirror-dual Automorphism group of order 584 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, X*Y^-1*X^-1*Y*X^3*Y^-1*X^2*Y^2 ] .......................... Rotary maps with 293 edges .......................... Orientable map of genus 0 and type {2,293}_586 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1172 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^293 ] .......................... Rotary maps with 294 edges .......................... Orientable map of genus 0 and type {2,294}_294 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^294 ] Non-orientable map of genus 1 and type {2,588}_588 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 145 and type {4,147}_147 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^147 ] Orientable map of genus 50 and type {6,6}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^6, c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 96 and type {6,98}_294 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^98 ] Orientable map of genus 99 and type {12,12}_14 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*c*b*c*b, (a*b)^12, c*b*a*b*c*a*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*a*b*a*c*b*a*b ] Orientable map of genus 120 and type {14,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c, (a*b)^14, a*b*a*b*c*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*c*b*c*b ] Orientable map of genus 120 and type {14,42}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1176 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^42 ] Chiral map of genus 50 and type {6,6}_14 isomorphic to its dual Automorphism group of order 588 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^3*Y^3*X^-2, X*Y^-1*X^-2*Y*X^2*Y^3*X*Y^-1 ] Chiral map of genus 50 and type {6,6}_14 isomorphic to its mirror-dual Automorphism group of order 588 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^3*Y^3*X^-2, (X*Y^-2*X*Y^-1*X)^2, Y^-1*X^-1*Y*X*Y^-1*X^2*Y^2*X^-2*Y^-1 ] Chiral map of genus 50 and type {6,6}_98 not isomorphic to its dual or mirror-dual Automorphism group of order 588 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, X^-1*Y*X^-2*Y*X^2*Y^-1*X^2*Y^-1*X^3*Y*X^-2*Y*X^-2*Y^-1*X^2*Y ] Chiral map of genus 92 and type {6,42}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 588 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^2*Y^-1*X^2*Y^-1*X*Y^-1*X^-2*Y^-1*X^2*Y*X^-1*Y, Y^-3*X^-1*Y*X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y^-7 ] Chiral map of genus 92 and type {6,42}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 588 with defining relations: [ (X*Y)^2, X^6, X*Y^-3*X^2*Y*X^-1*Y^-2, Y^-6*X^2*Y^-1*X^2*Y^-7 ] Chiral map of genus 99 and type {12,12}_14 isomorphic to its mirror-dual Automorphism group of order 588 with defining relations: [ (X*Y)^2, (Y^-1*X)^3, X^12, (X*Y^-2*X^3)^2, Y^-1*X^-1*Y*X^4*Y^3*X^-1*Y^-1 ] Chiral map of genus 134 and type {42,42}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 588 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-1*Y*X^-1, X^-1*Y*X^-1*Y^14*X^-2*Y^4*X^-9*Y*X^-1*Y^2*X^-2*Y*X^-1*Y*X^-1 ] .......................... Rotary maps with 295 edges .......................... Orientable map of genus 0 and type {2,295}_590 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1180 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^295 ] Non-orientable map of genus 233 and type {10,118}_295 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1180 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 296 edges .......................... Orientable map of genus 0 and type {2,296}_296 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1184 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^296 ] Non-orientable map of genus 1 and type {2,592}_592 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1184 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 73 and type {4,148}_148 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1184 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^148 ] Orientable map of genus 74 and type {4,296}_296 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1184 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 108 and type {8,74}_296 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1184 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^74 ] Orientable map of genus 110 and type {8,148}_296 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1184 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_148 isomorphic to its dual Automorphism group of order 592 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 75 and type {8,8}_74 isomorphic to its dual Automorphism group of order 592 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^2*X^-2*Y*X^-1*Y^-1*X*Y^-2*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y^2*X^-2 ] Chiral map of genus 75 and type {8,8}_148 isomorphic to its dual Automorphism group of order 592 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X^-1*Y*X^-2*Y*X^-1*Y^-1*X*Y^-2*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2 ] .......................... Rotary maps with 297 edges .......................... Orientable map of genus 0 and type {2,297}_594 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1188 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^297 ] Orientable map of genus 91 and type {6,33}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1188 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^33 ] Orientable map of genus 97 and type {6,99}_198 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1188 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^99 ] Non-orientable map of genus 257 and type {18,66}_99 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1188 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 261 and type {22,54}_297 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1188 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 97 and type {6,99}_198 not isomorphic to its dual or mirror-dual Automorphism group of order 594 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^-17*X^3*Y*X^-1*Y^-15 ] Chiral map of genus 142 and type {66,99}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 594 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, Y*X^-11*Y*X^-1*Y^2*X^-1*Y^2*X^-9*Y^2*X^-2*Y ] .......................... Rotary maps with 298 edges .......................... Orientable map of genus 0 and type {2,298}_298 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1192 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^298 ] Non-orientable map of genus 1 and type {2,596}_596 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1192 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_298 isomorphic to its dual Automorphism group of order 596 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y*X^-1*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y ] .......................... Rotary maps with 299 edges .......................... Orientable map of genus 0 and type {2,299}_598 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1196 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^299 ] Non-orientable map of genus 265 and type {26,46}_299 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1196 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] .......................... Rotary maps with 300 edges .......................... Orientable map of genus 0 and type {2,300}_300 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^300 ] Non-orientable map of genus 1 and type {2,600}_600 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {3,6}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 16 and type {4,5}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, (a*b*c*b)^6, a*b*c*b*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 51 and type {4,12}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^12, a*b*c*a*b*c*b*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 72 and type {4,75}_150 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^75 ] Non-orientable map of genus 148 and type {4,150}_150 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^150 ] Orientable map of genus 74 and type {4,150}_300 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^150 ] Orientable map of genus 41 and type {5,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*a*b*c*b*c*b*a*b*c*b*a*b*c*b*c*b*a*c*b*c*b ] Orientable map of genus 41 and type {5,6}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, (a*b*c*b)^4, c*a*b*c*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 61 and type {5,10}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, (b*c)^10 ] Non-orientable map of genus 142 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a, (b*c)^10, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b ] Orientable map of genus 76 and type {6,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b, a*b*c*a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*a*c*b*c*b*a*b*c*b*c ] Orientable map of genus 76 and type {6,12}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (b*c)^12, a*b*c*a*b*c*a*b*c*a*b*a*b*c*b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*c ] Non-orientable map of genus 182 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, (a*b*c*b*a*b*c*b*a*b)^2, c*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 97 and type {6,75}_100 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 98 and type {6,100}_300 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^100 ] Non-orientable map of genus 182 and type {10,10}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b)^10, (a*b*c*b*c*b*c*b*c*b)^2, (b*c)^10, b*c*a*b*c*b*c*b*a*b*a*b*a*b*a*b*c*b*a*b*a*b*c ] Non-orientable map of genus 182 and type {10,10}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, (a*b)^10, (a*b*c*b*a*b*a*b*a*b)^2, (b*c)^10, c*b*c*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b*a*b ] Orientable map of genus 96 and type {10,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^10, (b*c)^12 ] Orientable map of genus 96 and type {10,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (a*b)^10, (b*c)^12 ] Non-orientable map of genus 212 and type {10,20}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*c*b)^2, (a*b)^10, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (a*b*c*b*a*b*c*b*a*b)^2, a*b*a*b*c*b*a*b*a*b*a*b*c*b*c*b*a*b*a*c*b, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 116 and type {10,60}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^60 ] Orientable map of genus 116 and type {10,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^10, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 120 and type {12,50}_300 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^50 ] Orientable map of genus 123 and type {12,100}_150 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 116 and type {15,20}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, a*b*a*b*c*b*a*b*a*b*a*b*c*b*c*b*c*b*a*b, (b*a)^15 ] Orientable map of genus 126 and type {20,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (b*c)^30 ] Orientable map of genus 126 and type {20,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*b*a*b*a*b*c*b*a*b*a*b*c*b*c*b*c*b*c*b, (a*b)^20 ] Orientable map of genus 126 and type {20,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1200 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^30 ] Chiral map of genus 51 and type {4,12}_6 not isomorphic to its dual or mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, X^4, Y^-1*X^-1*Y*X*Y^-1*X^2*Y^-1*X*Y*X^-1*Y^-1, X*Y^-4*X^-1*Y^2*X^-1*Y^-1*X*Y^-1 ] Chiral map of genus 51 and type {4,12}_150 not isomorphic to its dual or mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^12, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-2*X*Y^2*X^-1*Y^-2 ] Chiral map of genus 71 and type {4,60}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^15*X*Y^-1*X*Y*X^-1*Y^-5*X*Y^8 ] Chiral map of genus 101 and type {12,12}_10 isomorphic to its dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, X^12, Y^-2*X^5*Y^-1*X*Y^-3, Y*X*Y^-1*X^4*Y^3*X^-1*Y, X*Y^-3*X^3*Y^-2*X*Y^-1*X ] Chiral map of genus 101 and type {12,12}_50 isomorphic to its dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, X^-1*Y*X^-1*Y*X^-1*Y*X*Y^-1*X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 111 and type {12,20}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X^12, X*Y^-2*X*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-1, X^-1*Y*X*Y^-2*X^3*Y*X^-1*Y^-6 ] Chiral map of genus 121 and type {12,60}_10 not isomorphic to its dual or mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, X^12, Y^-2*X^5*Y^-3*X*Y^-1, X*Y^-2*X*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-1, Y^4*X*Y^-1*X^2*Y^-2*X*Y^3 ] Chiral map of genus 131 and type {20,60}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, Y*X^-1*Y^3*X^-1*Y*X^-1*Y*X^-7*Y*X^-2*Y ] Chiral map of genus 126 and type {24,24}_10 isomorphic to its mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, Y*X^6*Y^2*X^-2*Y, X*Y^-1*X^5*Y^-1*X^3*Y^-1 ] Chiral map of genus 126 and type {24,24}_10 not isomorphic to its dual or mirror-dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X^2*Y^2*X^-1*Y, X^8*Y^-2*X*Y^-1 ] Chiral map of genus 141 and type {60,60}_10 isomorphic to its dual Automorphism group of order 600 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X^-1*Y^29*X^-2*Y^2*X^-1*Y^3*X^-1*Y^2*X^-8*Y*X^-1*Y^3*X^-1*Y^3*X^-1 ] .......................... Rotary maps with 301 edges .......................... Orientable map of genus 0 and type {2,301}_602 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1204 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^301 ] Non-orientable map of genus 253 and type {14,86}_301 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1204 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 87 and type {7,14}_86 not isomorphic to its dual or mirror-dual Automorphism group of order 602 with defining relations: [ (X*Y)^2, X^7, Y^3*X^-3*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 87 and type {7,14}_86 not isomorphic to its dual or mirror-dual Automorphism group of order 602 with defining relations: [ (X*Y)^2, X^7, X^-2*Y*X^3*Y*X^-1*Y^-2 ] Chiral map of genus 87 and type {7,14}_86 not isomorphic to its dual or mirror-dual Automorphism group of order 602 with defining relations: [ (X*Y)^2, X^7, Y*X*Y^-1*X^3*Y*X^-2*Y ] .......................... Rotary maps with 302 edges .......................... Orientable map of genus 0 and type {2,302}_302 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1208 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^302 ] Non-orientable map of genus 1 and type {2,604}_604 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1208 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 303 edges .......................... Orientable map of genus 0 and type {2,303}_606 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1212 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^303 ] Non-orientable map of genus 201 and type {6,202}_303 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1212 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 304 edges .......................... Orientable map of genus 0 and type {2,304}_304 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^304 ] Non-orientable map of genus 1 and type {2,608}_608 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 73 and type {4,76}_76 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^76 ] Orientable map of genus 75 and type {4,152}_152 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 75 and type {4,152}_152 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^152 ] Orientable map of genus 76 and type {4,304}_304 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 111 and type {8,76}_152 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^76 ] Orientable map of genus 111 and type {8,76}_152 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^76 ] Orientable map of genus 126 and type {16,38}_304 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^38 ] Orientable map of genus 130 and type {16,76}_304 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1216 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 305 edges .......................... Orientable map of genus 0 and type {2,305}_610 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1220 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^305 ] Non-orientable map of genus 241 and type {10,122}_305 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1220 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 62 and type {5,10}_122 not isomorphic to its dual or mirror-dual Automorphism group of order 610 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y^-1*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X^2*Y^-1 ] Chiral map of genus 62 and type {5,10}_122 not isomorphic to its dual or mirror-dual Automorphism group of order 610 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y^-1*X^-1*Y*X*Y^-1*X^-2*Y^-2*X*Y^-3 ] .......................... Rotary maps with 306 edges .......................... Orientable map of genus 0 and type {2,306}_306 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1224 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^306 ] Non-orientable map of genus 1 and type {2,612}_612 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1224 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 151 and type {4,153}_153 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^153 ] Non-orientable map of genus 197 and type {6,68}_68 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 100 and type {6,102}_102 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 100 and type {6,102}_102 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^102 ] Orientable map of genus 128 and type {18,34}_306 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1224 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^34 ] Chiral map of genus 1 and type {4,4}_102 isomorphic to its dual Automorphism group of order 612 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 137 and type {36,36}_34 isomorphic to its dual Automorphism group of order 612 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-1*X*Y^-2*X*Y^-1*X^-2*Y^2*X^-1*Y*X^-2*Y^-1*X, Y^-1*X*Y^-1*X*Y^-1*X*Y^-2*X^4*Y^-2*X*Y^-2*X ] .......................... Rotary maps with 307 edges .......................... Orientable map of genus 0 and type {2,307}_614 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1228 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^307 ] .......................... Rotary maps with 308 edges .......................... Orientable map of genus 0 and type {2,308}_308 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1232 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^308 ] Non-orientable map of genus 1 and type {2,616}_616 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1232 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 76 and type {4,154}_308 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1232 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^154 ] Orientable map of genus 126 and type {14,44}_308 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1232 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^44 ] Orientable map of genus 130 and type {22,28}_308 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1232 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, (b*c)^28 ] Orientable map of genus 137 and type {28,44}_154 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1232 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 147 and type {77,77}_4 isomorphic to its mirror-dual Automorphism group of order 616 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^-2*Y^58*X^-1*Y*X^-15 ] .......................... Rotary maps with 309 edges .......................... Orientable map of genus 0 and type {2,309}_618 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1236 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^309 ] Non-orientable map of genus 205 and type {6,206}_309 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1236 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_206 not isomorphic to its dual or mirror-dual Automorphism group of order 618 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^3*X*Y^-2*X*Y^-1*X*Y^-2*X*Y^2*X^-1*Y ] .......................... Rotary maps with 310 edges .......................... Orientable map of genus 0 and type {2,310}_310 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1240 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^310 ] Non-orientable map of genus 1 and type {2,620}_620 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1240 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 120 and type {10,62}_310 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1240 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^62 ] Chiral map of genus 94 and type {10,10}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 620 with defining relations: [ (X*Y)^2, X^10, (X*Y^-2*X^2)^2, X^-2*Y*X^3*Y*X^-1*Y^-2 ] Chiral map of genus 94 and type {10,10}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 620 with defining relations: [ (X*Y)^2, X^10, (X*Y^-2*X^2)^2, (X*Y^-1*X*Y^-1*X)^2, Y^10, Y*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 151 and type {124,124}_10 isomorphic to its dual Automorphism group of order 620 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^33*X^-2*Y^2*X^-1*Y^3*X^-1*Y^2*X^-9*Y*X^-3*Y^4*X^-1 ] .......................... Rotary maps with 311 edges .......................... Orientable map of genus 0 and type {2,311}_622 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1244 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^311 ] .......................... Rotary maps with 312 edges .......................... Orientable map of genus 0 and type {2,312}_312 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^312 ] Non-orientable map of genus 1 and type {2,624}_624 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 75 and type {4,78}_78 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^78 ] Orientable map of genus 77 and type {4,156}_156 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^156 ] Non-orientable map of genus 154 and type {4,156}_156 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 154 and type {4,156}_156 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^156 ] Orientable map of genus 78 and type {4,312}_312 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 99 and type {6,52}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 102 and type {6,104}_312 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^104 ] Orientable map of genus 110 and type {8,39}_156 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (c*b)^39 ] Orientable map of genus 114 and type {8,78}_156 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 114 and type {8,78}_312 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^78 ] Orientable map of genus 116 and type {8,156}_312 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 123 and type {12,39}_104 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, b*c*b*c*b*c*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 125 and type {12,52}_156 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^52 ] Orientable map of genus 127 and type {12,78}_104 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 128 and type {12,104}_312 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 132 and type {24,26}_312 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^24, (b*c)^26 ] Orientable map of genus 138 and type {24,52}_312 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^24, b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 140 and type {24,78}_104 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 141 and type {24,104}_156 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1248 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 27 and type {3,12}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^3, (X*Y^-5)^2, Y*X^-1*Y^2*X*Y^-2*X*Y^-2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y ] Chiral map of genus 53 and type {4,12}_156 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^12, X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X^-1*Y*X^2*Y^-1*X*Y*X^-1*Y*X^-1*Y^2 ] Chiral map of genus 53 and type {6,6}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X^-1*Y*X^-3*Y*X^-2*Y^-1*X^2*Y^-2*X^-2*Y*X^-1 ] Chiral map of genus 79 and type {6,12}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^6, (X*Y^-1*X)^2, Y^-4*X^3*Y^-2, Y*X*Y^-2*X^-1*Y^2*X^-1*Y^2*X*Y^-1*X*Y^2*X^-1*Y^-2*X*Y^-1*X*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 92 and type {6,24}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-4*X^2*Y^-1*X^3*Y*X^-2*Y*X^-1*Y^-1 ] Chiral map of genus 92 and type {6,24}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^6, X^-1*Y*X^-2*Y*X^3*Y*X^-2*Y, Y^2*X^2*Y^-1*X^-1*Y*X^-1*Y^-1*X^2*Y, Y^-2*X^2*Y^-1*X^2*Y^-5, X*Y^-3*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 105 and type {8,24}_78 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-2*X^2*Y^-1*X*Y^2*X^-1*Y^-1 ] Chiral map of genus 105 and type {8,24}_156 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-2*X ] Chiral map of genus 105 and type {12,12}_52 isomorphic to its dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X^-1*Y*X*Y^-1*X^2*Y^-2*X*Y^-1, X^12 ] Chiral map of genus 105 and type {12,12}_52 isomorphic to its dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, Y*X^-1*Y^-2*X^-1*Y*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2*X^2*Y*X^-1 ] Chiral map of genus 105 and type {12,12}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-2*X^2*Y^3*X^-1, X^12, Y^12, Y*X*Y^-1*X^-1*Y*X^3*Y*X^-2*Y^-1*X*Y ] Chiral map of genus 105 and type {12,12}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, (Y^-1*X)^3, X^12, (X*Y^-2*X^3)^2, X^-2*Y*X^5*Y*X^-1*Y^-1*X*Y*X^-1 ] Chiral map of genus 105 and type {12,12}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y^2*X^-1*Y*X^2*Y^-2*X*Y, X^12, Y^-1*X^6*Y^-3*X^2 ] Chiral map of genus 118 and type {12,24}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-2*X^2*Y^3*X^-1, X^12, X^-1*Y*X^2*Y^-1*X^3*Y^-1*X*Y*X^-1*Y^-2 ] Chiral map of genus 118 and type {12,24}_104 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, X*Y^-2*X^3*Y*X^-1*Y^-1*X, Y^-3*X^4*Y*X^-2*Y^-2, Y^-1*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^-2 ] Chiral map of genus 131 and type {24,24}_26 isomorphic to its dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, X^-1*Y^2*X^-1*Y^3*X^-1*Y^2*X^-8*Y^2*X^-1*Y^3 ] Chiral map of genus 131 and type {24,24}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^3*Y*X^-2*Y*X^-1, Y^-2*X*Y^-1*X*Y^-2*X^10*Y^-2*X*Y^-1*X*Y^-2 ] Chiral map of genus 131 and type {24,24}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^3*Y*X^-2*Y^-1, Y^3*X^3*Y^-1*X*Y^2, X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y^2*X^-10*Y^3 ] Chiral map of genus 131 and type {24,24}_52 isomorphic to its dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X*Y^-1*X*Y^-2*X^2*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 131 and type {24,24}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-2*X^2*Y^3*X^-1, Y^-1*X^6*Y^-5, Y^-1*X^2*Y^-1*X^3*Y^-1*X*Y^-1*X^2 ] Chiral map of genus 131 and type {24,24}_52 not isomorphic to its dual or mirror-dual Automorphism group of order 624 with defining relations: [ (X*Y)^2, Y^2*X^-1*Y*X^2*Y^-2*X*Y, Y*X^6*Y*X^-2*Y^2, X*Y^-1*X^5*Y^-1*X^2*Y^-2 ] .......................... Rotary maps with 313 edges .......................... Orientable map of genus 0 and type {2,313}_626 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1252 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^313 ] .......................... Rotary maps with 314 edges .......................... Orientable map of genus 0 and type {2,314}_314 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1256 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^314 ] Non-orientable map of genus 1 and type {2,628}_628 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1256 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_314 isomorphic to its dual Automorphism group of order 628 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X ] .......................... Rotary maps with 315 edges .......................... Orientable map of genus 0 and type {2,315}_630 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1260 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^315 ] Orientable map of genus 103 and type {6,105}_210 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1260 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^105 ] Non-orientable map of genus 249 and type {10,126}_315 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1260 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 265 and type {14,90}_315 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1260 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 273 and type {18,70}_315 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1260 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 281 and type {30,42}_105 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1260 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] Chiral map of genus 85 and type {6,15}_210 not isomorphic to its dual or mirror-dual Automorphism group of order 630 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^2*Y^-1*X^2*Y^-1*X*Y^-1*X^3*Y^-1*X^2*Y^2, Y^-15 ] Chiral map of genus 127 and type {15,30}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 630 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, X^-15, Y^2*X*Y^-2*X*Y^-2*X^-2*Y^-1*X*Y^2*X^-1*Y ] Chiral map of genus 134 and type {18,45}_70 not isomorphic to its dual or mirror-dual Automorphism group of order 630 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-2*X^2*Y^3*X^-1, X^-2*Y*X^-4*Y*X^-1*Y^-1*X*Y^2 ] Chiral map of genus 148 and type {45,90}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 630 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, Y^18*X^-1*Y^6*X^-1*Y*X^-9*Y*X^-3*Y^4*X^-1 ] .......................... Rotary maps with 316 edges .......................... Orientable map of genus 0 and type {2,316}_316 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1264 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^316 ] Non-orientable map of genus 1 and type {2,632}_632 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1264 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 78 and type {4,158}_316 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1264 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^158 ] .......................... Rotary maps with 317 edges .......................... Orientable map of genus 0 and type {2,317}_634 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1268 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^317 ] .......................... Rotary maps with 318 edges .......................... Orientable map of genus 0 and type {2,318}_318 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1272 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^318 ] Non-orientable map of genus 1 and type {2,636}_636 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1272 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 157 and type {4,159}_159 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1272 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^159 ] Orientable map of genus 104 and type {6,106}_318 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1272 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^106 ] Chiral map of genus 107 and type {12,12}_106 isomorphic to its dual Automorphism group of order 636 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, Y^2*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-2*X^2*Y*X^-1 ] .......................... Rotary maps with 319 edges .......................... Orientable map of genus 0 and type {2,319}_638 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1276 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^319 ] Non-orientable map of genus 281 and type {22,58}_319 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1276 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] .......................... Rotary maps with 320 edges .......................... Orientable map of genus 0 and type {2,320}_320 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^320 ] Non-orientable map of genus 1 and type {2,640}_640 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {4,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^10, b*c*a*b*c*b*a*b*c*b*c*a*b*c*b*c*b*a*b*c*b*c ] Orientable map of genus 49 and type {4,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (b*c)^10, a*b*c*a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {4,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, (b*c)^10, a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c ] Orientable map of genus 65 and type {4,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, (b*c)^20 ] Orientable map of genus 65 and type {4,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*a*b*c*b*a*b*c*b*c*a*b*c*b*c*b*a*b*c*b*c, c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 65 and type {4,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*b*c*b*c, (b*c)^20 ] Orientable map of genus 73 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*b*c*b*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 73 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^40 ] Non-orientable map of genus 146 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c, c*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 146 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c, c*b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*c*b ] Non-orientable map of genus 146 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 146 and type {4,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (b*c)^40 ] Orientable map of genus 77 and type {4,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 77 and type {4,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^80 ] Orientable map of genus 79 and type {4,160}_160 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 79 and type {4,160}_160 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^160 ] Orientable map of genus 80 and type {4,320}_320 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 57 and type {5,8}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*a*b*c*b*a*b*c*a*b*a*c*b*a*b*c*b*a*b*c ] Orientable map of genus 89 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (a*b*c*b*c*b*c*b*c*b)^2, (b*c)^10 ] Orientable map of genus 89 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (b*c)^10, c*b*c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*a*b ] Orientable map of genus 89 and type {8,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, (b*c)^10 ] Orientable map of genus 89 and type {8,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (b*c)^10, b*c*a*b*c*b*a*b*c*b*c*a*b*c*b*c*b*a*b*c*b*c ] Orientable map of genus 89 and type {8,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*b*a*b*c*b*a*c*b*c*b*c*b*a*c*b ] Orientable map of genus 89 and type {8,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c, a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c ] Orientable map of genus 89 and type {8,10}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b*c*b)^2, (b*c)^10, a*b*c*b*a*b*c*a*b*a*b*a*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (b*c)^20 ] Orientable map of genus 105 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (a*b*c*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 105 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, c*b*c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*a*b, c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 210 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (a*b*c*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 210 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (a*b*c*b*c*b*c*b*c*b)^2, c*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 210 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (b*c)^20 ] Non-orientable map of genus 210 and type {8,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, (b*c)^20 ] Orientable map of genus 105 and type {8,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^20 ] Orientable map of genus 105 and type {8,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*c*b*c, (b*c)^20 ] Orientable map of genus 105 and type {8,20}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, (b*c)^20 ] Orientable map of genus 113 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 113 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^40 ] Orientable map of genus 113 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 113 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^40 ] Orientable map of genus 113 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 226 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 226 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2, c*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 226 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 226 and type {8,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 117 and type {8,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 117 and type {8,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 117 and type {8,80}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 117 and type {8,80}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^80 ] Orientable map of genus 117 and type {8,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 117 and type {8,80}_80 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 119 and type {8,160}_160 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 124 and type {10,64}_320 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^64 ] Orientable map of genus 125 and type {16,20}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^16, (b*c)^20 ] Orientable map of genus 125 and type {16,20}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*a*c, (b*c)^20 ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^40 ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, (b*c)^40 ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (b*c)^40 ] Orientable map of genus 133 and type {16,40}_80 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, (b*c)^40 ] Orientable map of genus 135 and type {20,32}_160 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c, (a*b)^20 ] Orientable map of genus 135 and type {20,32}_160 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^32 ] Orientable map of genus 140 and type {20,64}_320 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c ] Orientable map of genus 143 and type {32,40}_160 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 143 and type {32,40}_160 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1280 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*c*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^-1*X*Y^-1 ] Chiral map of genus 41 and type {4,8}_10 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^8, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^3*X*Y^-2*X^-1*Y*X^-1*Y^4*X^-1 ] Chiral map of genus 41 and type {4,8}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^8, X^-1*Y^-4*X^2*Y^4*X^-1, Y^-1*X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y*X^-1*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 41 and type {4,8}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^8, Y^-3*X*Y^-1*X^-1*Y*X^-1*Y^-1*X*Y^-1*X ] Chiral map of genus 41 and type {4,8}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^8, (Y^-1*X)^5, X^-1*Y^-4*X*Y^-1*X^-2*Y^4*X^2*Y, Y^-3*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^4*X ] Chiral map of genus 41 and type {4,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, X^2*Y^-2*X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-1*X*Y^2 ] Chiral map of genus 41 and type {4,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^8, X^-1*Y^-4*X^2*Y^4*X^-1, Y^-1*X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y*X^-1*Y^-1 ] Chiral map of genus 41 and type {4,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, Y^8, (X*Y^-3)^2, Y*X^-1*Y^2*X*Y^-1*X^-1*Y*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-1*X*Y*X^-1 ] Chiral map of genus 61 and type {4,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^-1*X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y*X^-1*Y^-1*X*Y^-1, Y^16 ] Chiral map of genus 61 and type {4,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^-2*X^-1*Y^2*X*Y^-2*X^-2*Y^-1*X*Y*X^-1*Y^-1*X*Y^-1*X ] Chiral map of genus 71 and type {4,32}_160 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^-1*X^-1*Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y*X^-1*Y^-1*X*Y^-1, Y^4*X*Y^-2*X^-1*Y^2*X^-2*Y*X^-1*Y^-1*X*Y^6 ] Chiral map of genus 71 and type {4,32}_160 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^32 ] Chiral map of genus 81 and type {8,8}_10 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X*Y^-2*X^3*Y*X^-2*Y^2, (X*Y^-1*X)^4 ] Chiral map of genus 81 and type {8,8}_10 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X*Y^-1*X^3*Y^-3*X ] Chiral map of genus 81 and type {8,8}_10 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-3*X^3*Y^-2*X^2 ] Chiral map of genus 81 and type {8,8}_20 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^2*X^-1*Y*X^-1*Y ] Chiral map of genus 81 and type {8,8}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, Y^3*X^3*Y^3*X^-1, X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2 ] Chiral map of genus 81 and type {8,8}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-2*X^-2*Y*X^-1*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 81 and type {8,8}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X^-1*Y^2*X*Y^-1*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y^-1*X*Y^-1*X*Y^-1*X*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 81 and type {8,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X^2*Y^-2*X^-1*Y*X^-2*Y^-1*X*Y^2*X^-1*Y*X^-1*Y ] Chiral map of genus 81 and type {8,8}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-1*X^2)^2, Y^3*X^3*Y^3*X^-1, X^-1*Y*X^2*Y^-2*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2 ] Chiral map of genus 81 and type {8,8}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, X*Y^-1*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y^-1*X*Y^-1*X*Y^-1*X*Y*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y^-2*X*Y^3 ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1, Y^16 ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-3*X^4*Y^-5, Y^-1*X*Y^-1*X*Y^-2*X^-2*Y*X^-1*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-3*X^4*Y^-5, X^2*Y^-2*X^-1*Y*X^-2*Y^-1*X*Y^2*X^-1*Y*X^-1*Y ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y*X*Y^-3*X*Y^4, Y^-1*X^3*Y^-1*X^-2*Y^-1*X^3*Y^-1, Y*X^2*Y^-1*X^3*Y^2*X^-1*Y^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y*X^-1*Y^-1 ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, Y*X*Y^-3*X*Y^4, Y^-1*X^3*Y^-1*X^-2*Y^-1*X^3*Y^-1, Y*X^2*Y^-1*X^3*Y^2*X^-1*Y^2, Y*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X^-2*Y^2*X*Y^-1*X^2*Y^-2*X*Y^3 ] Chiral map of genus 101 and type {8,16}_80 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^16 ] Chiral map of genus 111 and type {8,32}_160 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^2*X*Y^-5*X^-1*Y^2*X^-1*Y^-5*X*Y^2 ] Chiral map of genus 111 and type {8,32}_160 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1, Y^2*X*Y^-5*X^-1*Y^2*X^-1*Y^-5*X*Y^2 ] Chiral map of genus 121 and type {16,16}_20 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2, X^16 ] Chiral map of genus 121 and type {16,16}_20 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y^-1*X^4*Y^-3, Y^-1*X^2*Y^-1*X^3*Y*X^-1*Y^-1*X^2, X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2 ] Chiral map of genus 121 and type {16,16}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 121 and type {16,16}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-2*X^2*Y^-1 ] Chiral map of genus 121 and type {16,16}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1, Y^-2*X^-8*Y^-6 ] Chiral map of genus 121 and type {16,16}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X*Y^-1*X^-2*Y*X^3*Y*X^-1*Y^2*X^-1*Y, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y^-2*X*Y^3 ] Chiral map of genus 121 and type {16,16}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^2*Y^-1*X*Y^-2*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2 ] Chiral map of genus 121 and type {16,16}_40 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y^-1*X^4*Y^-3, Y^-1*X^2*Y^-1*X^3*Y*X^-1*Y^-1*X^2, X^2*Y^-1*X*Y^-2*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2 ] Chiral map of genus 121 and type {16,16}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y*X*Y^-3*X*Y^4, Y*X^2*Y^-1*X^3*Y^2*X^-1*Y^2, Y*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y, X^16 ] Chiral map of genus 121 and type {16,16}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y*X*Y^-3*X*Y^4, Y*X^2*Y^-1*X^3*Y^2*X^-1*Y^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y*X^-1*Y^-1 ] Chiral map of genus 137 and type {16,80}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-1)^4, (X*Y^-3)^2, Y^-1*X^6*Y*X^-1*Y^-1*X*Y^-1, Y^10*X^2*Y*X^-2*Y^9 ] Chiral map of genus 141 and type {32,32}_20 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-1*X*Y^-1*X*Y^2, Y^-1*X*Y^-1*X^6*Y^-1*X*Y^-2*X*Y^-1*X ] Chiral map of genus 141 and type {32,32}_20 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, Y^3*X^-2*Y*X^-1*Y^3*X^-1*Y^2*X^-10*Y^9 ] Chiral map of genus 141 and type {32,32}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y*X*Y^-3*X*Y^4, Y*X^2*Y^-1*X^3*Y^2*X^-1*Y^2, Y*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y, X^12*Y^-4 ] Chiral map of genus 151 and type {64,64}_10 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, X^-1*Y^36*X^-1*Y*X^-1*Y^3*X^-1*Y^2*X^-9*Y*X^-3*Y^5 ] Chiral map of genus 151 and type {64,64}_20 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, Y^-1*X*Y^-1*X*Y^-6*X^10*Y^-2*X*Y^-3*X*Y^-1*X^4 ] Chiral map of genus 153 and type {80,80}_8 isomorphic to its dual Automorphism group of order 640 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y, Y*X^6*Y*X^-1*Y^2*X^-1, Y^3*X*Y^-1*X^2*Y^-1*X*Y^3, Y^3*X^-3*Y^2*X^-5*Y^3*X^-4 ] .......................... Rotary maps with 321 edges .......................... Orientable map of genus 0 and type {2,321}_642 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1284 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^321 ] Non-orientable map of genus 213 and type {6,214}_321 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1284 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 322 edges .......................... Orientable map of genus 0 and type {2,322}_322 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1288 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^322 ] Non-orientable map of genus 1 and type {2,644}_644 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1288 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 132 and type {14,46}_322 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1288 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^46 ] .......................... Rotary maps with 323 edges .......................... Orientable map of genus 0 and type {2,323}_646 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1292 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^323 ] Non-orientable map of genus 289 and type {34,38}_323 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1292 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b ] .......................... Rotary maps with 324 edges .......................... Orientable map of genus 0 and type {2,324}_324 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^324 ] Non-orientable map of genus 1 and type {2,648}_648 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {3,6}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 28 and type {3,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^12, c*b*c*a*b*c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b, c*a*b*c*a*b*c*a*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 28 and type {3,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*b*c*a*b*c*b*c*b*c*a*b*a^2*c*b*a*c*b*c*b*c*b*a*c*b, (b*c)^12 ] Orientable map of genus 1 and type {4,4}_18 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 56 and type {4,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, a*b*c*b*a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Non-orientable map of genus 56 and type {4,6}_9 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (a*b*c*b)^4, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 28 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (a*b*c*b)^6, a*b*c*a*b*c*b*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*b*c*b*c ] Orientable map of genus 46 and type {4,9}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^9, b*c*a*b*c*b*c*a*b*c*a*b*a*b*c*b*c*b*a*c*b*c*b*a, a*b*c*a*b*c*a*b*c*b*a*b*c*b*c*b*c*b*a*b*c*b*a*c*b*c ] Non-orientable map of genus 128 and type {4,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, a*b*c*b*a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Orientable map of genus 64 and type {4,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (a*b*c*b)^6, (b*c)^18 ] Orientable map of genus 78 and type {4,81}_162 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^81 ] Non-orientable map of genus 160 and type {4,162}_162 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^162 ] Orientable map of genus 80 and type {4,162}_324 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^162 ] Orientable map of genus 55 and type {6,6}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (c*b*a*b)^3, (b*c)^6, c*b*c*a*b*a*b*c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b*a*c*b ] Non-orientable map of genus 137 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^8, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, a*b*c*b*a*b*a*b*c*a*b*a*b*a*b*c*b*a*b*a*b*c*b*a*b ] Orientable map of genus 73 and type {6,9}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*a*c*b*c*b*c*b, b*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*b*c, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c*a*b*c ] Orientable map of genus 73 and type {6,9}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (c*b)^9, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 73 and type {6,9}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (c*b)^9, b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 73 and type {6,9}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (c*b)^9, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 73 and type {6,9}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (c*b)^9, a*b*c*a*b*c*a*b*c*a*b*a*b*c*b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 82 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^12 ] Orientable map of genus 82 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, (b*c)^12 ] Orientable map of genus 82 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, (b*c)^12 ] Orientable map of genus 82 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (a*b*c*b*a*b*c*b*a*b)^2, (b*c)^12 ] Orientable map of genus 82 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, (a*b*c*b*a*b)^4 ] Orientable map of genus 82 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, b*c*a*b*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*c ] Orientable map of genus 82 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, b*c*a*b*a*b*c*b*a*b*a*b*c*b*c*b*a*c*b*c*b*a ] Non-orientable map of genus 164 and type {6,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, c*b*c*b*c*a*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*a*c*b, (b*c)^12, a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 82 and type {6,12}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, (b*c)^12, a*b*c*a*b*a*b*c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b ] Orientable map of genus 82 and type {6,12}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^6, (b*c)^12 ] Orientable map of genus 82 and type {6,12}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*a, (b*c)^12 ] Orientable map of genus 82 and type {6,12}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 97 and type {6,27}_108 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (c*b)^27 ] Orientable map of genus 100 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^36 ] Orientable map of genus 100 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^6, c*b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 100 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, (b*c)^36 ] Orientable map of genus 100 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^36 ] Orientable map of genus 100 and type {6,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (a*b*c*b*a*b*c*b*a*b)^2, c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 106 and type {6,108}_108 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^108 ] Orientable map of genus 100 and type {9,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b, (b*c)^12 ] Orientable map of genus 100 and type {9,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (b*a)^9, c*a*b*c*a*b*c*a*b*a*c*b*c*b*a*b*c*b, (b*c)^12 ] Orientable map of genus 100 and type {9,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (b*a)^9, (b*c*b*a*b*c)^3 ] Orientable map of genus 109 and type {9,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^9, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 109 and type {12,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*c*b*a*c*b*c*b*c*b, c*a*b*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b, (a*b)^12, a*b*c*a*b*a*b*c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b ] Orientable map of genus 109 and type {12,12}_18 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*a*b*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 236 and type {12,18}_18 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, b*c*a*b*c*a*b*a*b*a*c*b*c*b*c*b*a*b*c, (a*b*c*b*c*b*c*b*a*b)^2 ] Orientable map of genus 118 and type {12,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (a*b*c*b*c*b*c*b*a*b)^2, (a*b)^12 ] Orientable map of genus 118 and type {12,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, (a*b)^12, (b*c)^18 ] Orientable map of genus 118 and type {12,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, (b*c)^18 ] Orientable map of genus 118 and type {12,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, b*c*b*a*b*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*a*c ] Orientable map of genus 118 and type {12,18}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, (a*b)^12, (b*c)^18 ] Orientable map of genus 124 and type {12,27}_54 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^27 ] Orientable map of genus 130 and type {12,54}_108 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^54 ] Orientable map of genus 130 and type {12,54}_108 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, (b*c)^54 ] Orientable map of genus 136 and type {18,36}_36 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^36 ] Orientable map of genus 136 and type {18,36}_36 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1296 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (a*b)^18 ] Chiral map of genus 55 and type {6,6}_12 isomorphic to its dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, X^6, Y^6, Y*X*Y^-1*X^2*Y*X^-1*Y, Y^-1*X^-3*Y^-3*X^3*Y^3*X^3*Y^-2 ] Chiral map of genus 97 and type {6,27}_108 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-2*X^-1*Y*X*Y^-1*X^-1*Y*X^-3*Y^-1*X^2*Y^-3 ] Chiral map of genus 100 and type {6,36}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, X^6, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y^2*X^2*Y^-1*X^-1*Y*X^-1*Y^-1*X^2*Y, Y^2*X*Y^-4*X^-2*Y^-2*X*Y^4 ] Chiral map of genus 106 and type {6,108}_108 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^18*X*Y^-1*X*Y^5*X^-1*Y^-1*X*Y^11 ] Chiral map of genus 82 and type {8,8}_18 isomorphic to its dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, Y^-1*X^-1*Y*X*Y^-1*X^-3*Y^-1*X^3*Y^-1*X ] Chiral map of genus 109 and type {9,18}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, X^9, Y*X*Y^-1*X^3*Y^2*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y^-2*X*Y^-2*X^-2*Y^-1*X*Y^-2*X*Y^-1 ] Chiral map of genus 118 and type {9,36}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, X^9, Y*X*Y^-1*X^3*Y^2*X^-2, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y, Y^-1*X*Y^-1*X*Y^-1*X^-2*Y^-1*X*Y^-4 ] Chiral map of genus 118 and type {12,18}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^-1*Y*X*Y^-1*X^2*Y^-4, X^12 ] Chiral map of genus 124 and type {12,27}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, X^12, X*Y^-4*X^-5*Y*X^-1*Y^-4*X ] Chiral map of genus 127 and type {12,36}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^12, (X*Y^-1*X^4)^2, X*Y^-2*X^4*Y^-4*X ] Chiral map of genus 130 and type {12,54}_108 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^12, Y^9*X^2*Y*X^-1*Y^-5*X*Y^3 ] Chiral map of genus 133 and type {12,108}_54 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^12, Y^9*X^2*Y^4*X^-1*Y^-2*X*Y^3 ] Chiral map of genus 136 and type {18,36}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y^2*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-1*X*Y^-1*X*Y^2*X^-1*Y, X*Y^-1*X^-8*Y^-1*X^3*Y^-2, X^7*Y^-1*X^3*Y^-1*X^3*Y^-1*X*Y^-1 ] Chiral map of genus 136 and type {18,36}_36 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y^4*X*Y^-1*X^-2*Y^-5*X*Y^2, (X^4*Y^-2*X^3)^2 ] Chiral map of genus 136 and type {24,24}_6 isomorphic to its dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y^-2*X^5*Y^-1*X^2*Y^-2, Y^-1*X^-1*Y*X^4*Y*X^-3*Y^-1 ] Chiral map of genus 145 and type {36,36}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X^5*Y^3*X^-1, Y*X*Y^-1*X^3*Y^2*X^-2, X^-2*Y*X^-10*Y*X^-1*Y^2*X^-1*Y*X^-2*Y*X^-8*Y^2*X^-1*Y*X^-1*Y ] Chiral map of genus 154 and type {72,72}_6 isomorphic to its dual Automorphism group of order 648 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X^5*Y*X^-1*Y^2, Y^-1*X^13*Y^-5*X^3*Y^-1*X^8*Y^-2*X^3 ] .......................... Rotary maps with 325 edges .......................... Orientable map of genus 0 and type {2,325}_650 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1300 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^325 ] Orientable map of genus 126 and type {10,65}_130 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1300 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (c*b)^65 ] Non-orientable map of genus 289 and type {26,50}_325 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1300 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] .......................... Rotary maps with 326 edges .......................... Orientable map of genus 0 and type {2,326}_326 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1304 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^326 ] Non-orientable map of genus 1 and type {2,652}_652 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1304 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 327 edges .......................... Orientable map of genus 0 and type {2,327}_654 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1308 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^327 ] Non-orientable map of genus 217 and type {6,218}_327 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1308 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_218 not isomorphic to its dual or mirror-dual Automorphism group of order 654 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y^-3*X*Y^-1*X*Y^3*X*Y^-2*X*Y^-1*X*Y^-2*X*Y^2*X^-1*Y^-2 ] .......................... Rotary maps with 328 edges .......................... Orientable map of genus 0 and type {2,328}_328 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1312 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^328 ] Non-orientable map of genus 1 and type {2,656}_656 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1312 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {4,164}_164 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1312 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^164 ] Orientable map of genus 82 and type {4,328}_328 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1312 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 120 and type {8,82}_328 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1312 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^82 ] Orientable map of genus 122 and type {8,164}_328 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1312 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_164 isomorphic to its dual Automorphism group of order 656 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y ] Chiral map of genus 83 and type {8,8}_82 isomorphic to its dual Automorphism group of order 656 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y*X^-1*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 83 and type {8,8}_82 not isomorphic to its dual or mirror-dual Automorphism group of order 656 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, Y^-2*X*Y^-1*X^-2*Y^4*X*Y^-1 ] Chiral map of genus 83 and type {8,8}_164 isomorphic to its dual Automorphism group of order 656 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^-2*Y^-1*X*Y^-1*X*Y^-1*X ] .......................... Rotary maps with 329 edges .......................... Orientable map of genus 0 and type {2,329}_658 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1316 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^329 ] Non-orientable map of genus 277 and type {14,94}_329 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1316 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 330 edges .......................... Orientable map of genus 0 and type {2,330}_330 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^330 ] Non-orientable map of genus 1 and type {2,660}_660 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 46 and type {3,10}_11 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^10, b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 46 and type {3,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^10, b*c*b*c*a*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*c, c*b*c*a*b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 57 and type {3,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b, (b*c)^12, b*c*b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Non-orientable map of genus 35 and type {4,5}_11 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, a*b*c*b*a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b, (c*b*a*b*c*b*c*b*a*b)^3 ] Non-orientable map of genus 35 and type {4,5}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Non-orientable map of genus 57 and type {4,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b, b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 101 and type {4,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b*a*b)^3, (b*c)^10, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 163 and type {4,165}_165 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^165 ] Orientable map of genus 34 and type {5,5}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, a*b*c*a*b*c*b*a*b*c*b*c*a*b*a*c*b*a*b*c*b*a*b*c ] Orientable map of genus 34 and type {5,5}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (c*b)^5, b*c*a*b*a*b*c*b*c*b*a*b*a*b*c*b*c*b*a*b*a*c*b*c ] Orientable map of genus 45 and type {5,6}_6 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, (c*b*a*b)^5 ] Non-orientable map of genus 90 and type {5,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*b*c*a*b*a*b*c*b*a*b*a*c*b*c*b*a*b*a*c*b*a*b ] Orientable map of genus 45 and type {5,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, b*c*b*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c ] Non-orientable map of genus 134 and type {5,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a ] Non-orientable map of genus 134 and type {5,10}_11 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, (b*c)^10, b*c*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*c*b*a ] Non-orientable map of genus 134 and type {5,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b)^4, a*b*a*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 112 and type {6,6}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (b*a*b*a*b*c)^3, b*c*a*b*c*b*c*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c ] Non-orientable map of genus 112 and type {6,6}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (c*b*a*b)^5, b*c*a*b*c*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*c ] Orientable map of genus 56 and type {6,6}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (b*a*b*a*b*c)^3, (b*c*b*a*b*c)^3, (c*b*a*b)^5 ] Non-orientable map of genus 156 and type {6,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, (b*c)^10, b*c*b*c*a*b*c*b*a*b*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 81 and type {6,11}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (c*b*a*b)^3, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, (c*b)^11 ] Non-orientable map of genus 210 and type {6,55}_55 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 108 and type {6,110}_330 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^110 ] Non-orientable map of genus 200 and type {10,10}_10 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, a*b*c*a*b*a*b*a*c*b*a*b*a*c*b, (a*b)^10, (c*b*a*b)^5, (b*c)^10, a*b*c*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 200 and type {10,10}_10 invariant under all six Wilson transforms Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 211 and type {10,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*b*a*b*a*b*a*b*c*b*c*b*a*c*b, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b ] Non-orientable map of genus 246 and type {10,33}_55 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^10, b*c*a*b*c*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*c*b*a, c*a*b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 128 and type {10,66}_330 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^66 ] Orientable map of genus 106 and type {11,11}_12 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*c*b*a*b*a*c*b*c*b*a*b*c*b, c*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*c*b*c*b, (b*a)^11, b*a*b*a*b*c*b*a*b*a*b*a*c*b*a*c*b*a*c*b*a*c ] Orientable map of genus 140 and type {22,30}_330 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, (b*c)^30 ] Orientable map of genus 150 and type {30,66}_110 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1320 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 122 and type {10,30}_66 not isomorphic to its dual or mirror-dual Automorphism group of order 660 with defining relations: [ (X*Y)^2, X^10, (X*Y^-2*X^2)^2, (X*Y^-1*X*Y^-1*X)^2, Y^-1*X^-1*Y^2*X^2*Y*X^-1*Y^-2 ] Chiral map of genus 122 and type {10,30}_66 not isomorphic to its dual or mirror-dual Automorphism group of order 660 with defining relations: [ (X*Y)^2, X^10, (X*Y^-2*X^2)^2, (X*Y^-1*X*Y^-1*X)^2, Y^-1*X^-1*Y*X^4*Y^3*X^-1*Y^-1 ] Chiral map of genus 122 and type {10,30}_66 not isomorphic to its dual or mirror-dual Automorphism group of order 660 with defining relations: [ (X*Y)^2, X^10, Y*X*Y^-1*X^3*Y^4 ] Chiral map of genus 122 and type {10,30}_66 not isomorphic to its dual or mirror-dual Automorphism group of order 660 with defining relations: [ (X*Y)^2, X^10, X*Y^-2*X^3*Y^-1*X^2*Y^-1, (X*Y^-3*X)^2 ] Chiral map of genus 144 and type {30,30}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 660 with defining relations: [ (X*Y)^2, Y*X^5*Y^3*X^-1, Y*X*Y^-1*X^3*Y*X^-1*Y*X^-1, Y^-1*X^5*Y^-1*X^2*Y^-1*X^2*Y^-1*X*Y^-1*X^8*Y^-2*X^2*Y^-1*X^2 ] Chiral map of genus 144 and type {30,30}_22 not isomorphic to its dual or mirror-dual Automorphism group of order 660 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, Y^-1*X^8*Y^-1*X*Y^-2*X^2*Y^-1*X*Y^-1*X^8*Y^-4 ] Chiral map of genus 161 and type {132,132}_10 isomorphic to its dual Automorphism group of order 660 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X^-1*Y^35*X^-3*Y^2*X^-1*Y*X^-1*Y*X^-10*Y*X^-1*Y^3*X^-1*Y^3*X^-1 ] .......................... Rotary maps with 331 edges .......................... Orientable map of genus 0 and type {2,331}_662 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1324 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^331 ] .......................... Rotary maps with 332 edges .......................... Orientable map of genus 0 and type {2,332}_332 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1328 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^332 ] Non-orientable map of genus 1 and type {2,664}_664 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1328 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 82 and type {4,166}_332 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1328 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^166 ] .......................... Rotary maps with 333 edges .......................... Orientable map of genus 0 and type {2,333}_666 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1332 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^333 ] Orientable map of genus 109 and type {6,111}_222 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1332 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^111 ] Non-orientable map of genus 289 and type {18,74}_333 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1332 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_222 not isomorphic to its dual or mirror-dual Automorphism group of order 666 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X*Y^-1*X*Y^3*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y ] Chiral map of genus 112 and type {9,18}_74 not isomorphic to its dual or mirror-dual Automorphism group of order 666 with defining relations: [ (X*Y)^2, X^9, Y*X^4*Y*X^-2, Y^2*X^-3*Y^4, Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^3*X^-1*Y*X^-1*Y^-1*X*Y*X^-1*Y ] Chiral map of genus 112 and type {9,18}_74 not isomorphic to its dual or mirror-dual Automorphism group of order 666 with defining relations: [ (X*Y)^2, X^9, (Y*X^-1*Y)^3, Y*X^2*Y^-1*X^3*Y^4*X^-1, Y*X*Y^-2*X^3*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 112 and type {9,18}_74 not isomorphic to its dual or mirror-dual Automorphism group of order 666 with defining relations: [ (X*Y)^2, X^9, (Y*X^-1*Y)^3, Y^3*X^3*Y^-1*X*Y^2 ] Chiral map of genus 112 and type {9,18}_74 not isomorphic to its dual or mirror-dual Automorphism group of order 666 with defining relations: [ (X*Y)^2, X^9, (Y*X^-1*Y)^3, Y*X*Y^-1*X^4*Y*X^-1*Y*X^-2 ] .......................... Rotary maps with 334 edges .......................... Orientable map of genus 0 and type {2,334}_334 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1336 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^334 ] Non-orientable map of genus 1 and type {2,668}_668 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1336 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 335 edges .......................... Orientable map of genus 0 and type {2,335}_670 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1340 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^335 ] Non-orientable map of genus 265 and type {10,134}_335 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1340 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 336 edges .......................... Orientable map of genus 0 and type {2,336}_336 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^336 ] Non-orientable map of genus 1 and type {2,672}_672 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 36 and type {3,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 36 and type {3,16}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 29 and type {4,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b, b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 86 and type {4,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, b*c*a*b*c*b*c*b*a*b*c*b*a*b*c*b*c*b*a*c*b*a*c ] Non-orientable map of genus 86 and type {4,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, b*c*a*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*a*b*c*b*c*b*c ] Orientable map of genus 43 and type {4,8}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, (a*b*c*b*c*b*a*b*c*b)^2, b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 86 and type {4,8}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, a*b*c*b*a*b*a*c*b*a*b*c*b, (b*c)^8 ] Non-orientable map of genus 86 and type {4,8}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, (a*b*c*b*c*b*a*b*c*b)^2, b*c*a*b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Non-orientable map of genus 154 and type {4,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, (b*c)^42 ] Orientable map of genus 77 and type {4,42}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^42 ] Orientable map of genus 81 and type {4,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^84 ] Orientable map of genus 81 and type {4,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^84 ] Orientable map of genus 83 and type {4,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 83 and type {4,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^168 ] Non-orientable map of genus 166 and type {4,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 166 and type {4,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^168 ] Orientable map of genus 84 and type {4,336}_336 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 57 and type {6,6}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (a*b*c*b)^4, a*b*c*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*a*b, c*a*b*a*b*c*b*c*b*a*b*a*c*b*a*b*c*b*c*b*a*b ] Orientable map of genus 65 and type {6,7}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (c*b)^7, (a*b*c*b*a*b*c*b*a*b)^2, b*c*a*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b*c ] Orientable map of genus 71 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b ] Non-orientable map of genus 142 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^8, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*c*b*a*b*c*b*a*c*b, c*b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*c*b ] Non-orientable map of genus 142 and type {6,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^8, c*a*b*c*b*a*b*a*b*a*c*b*c*b*a*b*a*b, c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*c*b*a*b*c*b*a*c*b, b*c*a*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*a*b*c*b*c*b*c ] Non-orientable map of genus 142 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (b*c)^8, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b ] Non-orientable map of genus 142 and type {6,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^8, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, a*b*c*a*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b*c, c*a*b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*b*c*b*a*c*b ] Orientable map of genus 71 and type {6,8}_14 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, b*c*b*c*a*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 71 and type {6,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, (b*a*b*a*b*c)^3 ] Orientable map of genus 71 and type {6,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, c*b*a*b*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b ] Orientable map of genus 89 and type {6,14}_14 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*a*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, a*b*c*a*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {6,14}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b*c*b*a*b)^2, a*b*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*c*b*c, b*c*b*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c ] Orientable map of genus 92 and type {6,16}_16 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c, c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 92 and type {6,16}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c, c*b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*a*b*c*b*c*b*c*b*a*c*b*c*b ] Orientable map of genus 97 and type {6,21}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*c*a*b*c*b*a*b*a*b*c*b*a*b*a*b*c*b*a*b*a*b*c*b*a*c*b*c ] Non-orientable map of genus 202 and type {6,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*a*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*b*c*b*c*b*a*b*c*b*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c ] Non-orientable map of genus 202 and type {6,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*a*b*a*b*a*c*b*a*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 101 and type {6,28}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, (b*c)^28 ] Orientable map of genus 105 and type {6,42}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 107 and type {6,56}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 110 and type {6,112}_336 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^112 ] Orientable map of genus 79 and type {7,8}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b*a*c*b ] Orientable map of genus 93 and type {7,12}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, c*a*b*c*b*c*b*a*c*b*c*b*c*b, b*a*b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*a*b*c*b*a*b*c, a*b*c*a*b*a*b*c*b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*c ] Orientable map of genus 85 and type {8,8}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (b*c)^8, b*c*b*c*b*a*b*a*b*a*b*a*c*b*c*b*a*b*a*c*b*a, c*a*b*c*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*c*b, c*a*b*c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*c*b*c*b ] Orientable map of genus 85 and type {8,8}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (c*b*a*b)^3, (a*b)^8, (b*c)^8, c*a*b*c*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*c*b ] Orientable map of genus 85 and type {8,8}_8 invariant under all six Wilson transforms Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (b*c)^8, (a*b*c*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b*a*b)^2 ] Non-orientable map of genus 198 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*c*b*a*b*a*b)^2, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, a*b*a*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 198 and type {8,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, b*c*a*b*c*a*b*c*b*c*a*b*a*b*c*b*c*b*a*b*c*b*c ] Non-orientable map of genus 198 and type {8,12}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, b*c*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a*c, (b*c)^12 ] Non-orientable map of genus 198 and type {8,12}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, c*b*a*b*a*b*c*b*a*b*a*b*c*b*a*b*a*c*b*a*b ] Orientable map of genus 103 and type {8,14}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*c, c*a*b*c*b*a*b*c*b*a*b*a*c*b*c*b*a*b*c*b*a*b ] Orientable map of genus 106 and type {8,16}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*a*b*c*b)^2, c*b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b, c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*a*c*b*a*b*a*c*b ] Orientable map of genus 106 and type {8,16}_28 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*a*b*c*b)^2, c*b*c*b*c*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b, c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*a*b*c*b ] Orientable map of genus 111 and type {8,21}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^21 ] Orientable map of genus 119 and type {8,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, (b*c)^42 ] Orientable map of genus 119 and type {8,42}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^42 ] Orientable map of genus 123 and type {8,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 123 and type {8,84}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^84 ] Orientable map of genus 123 and type {8,84}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^84 ] Non-orientable map of genus 250 and type {8,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 250 and type {8,168}_168 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 117 and type {12,14}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*a*b*a*b, b*c*a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c*b*c, c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*c*b*a*b*c*b*a*c*b ] Orientable map of genus 129 and type {12,28}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, (a*b)^12, c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 129 and type {12,28}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^12, (b*c)^28 ] Orientable map of genus 129 and type {12,28}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, (a*b)^12, b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 133 and type {12,42}_56 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 135 and type {12,56}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b*c*b*c*b)^2, c*b*c*b*c*a*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 135 and type {12,56}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 135 and type {12,56}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^56 ] Orientable map of genus 138 and type {12,112}_336 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 138 and type {14,48}_336 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^48 ] Orientable map of genus 140 and type {16,42}_336 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^42 ] Orientable map of genus 144 and type {16,84}_336 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 143 and type {24,28}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^24, (b*c)^28 ] Orientable map of genus 143 and type {24,28}_168 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, (b*c)^28 ] Orientable map of genus 149 and type {24,56}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 149 and type {24,56}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^24, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 150 and type {28,48}_336 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 154 and type {42,48}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b*a*b*a*b)^2, a*b*a*b*c*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 158 and type {48,84}_112 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1344 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 1 and type {3,6}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X*Y^-2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y ] Chiral map of genus 57 and type {6,6}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^2*Y^3*X^-1, X^-1*Y*X^2*Y^-1*X^2*Y^-1*X^-3*Y*X^-2*Y^-1*X^2*Y ] Chiral map of genus 85 and type {6,12}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^12, X^-1*Y*X*Y^-1*X^-1*Y*X^-2*Y*X^3*Y*X^-2*Y*X^-2*Y^-2 ] Chiral map of genus 85 and type {6,12}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^6, Y^-1*X^2*Y^-1*X^-2*Y^-1*X^2*Y^-1, Y*X^2*Y^-1*X^2*Y^4, Y^-1*X^-1*Y^2*X^-1*Y^2*X*Y^-1*X*Y^3*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 85 and type {6,12}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^6, Y*X*Y^-2*X*Y^3, Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y^-1*X^2*Y, X^-1*Y*X^2*Y^-1*X^2*Y^-1*X^-3*Y^-1*X^2*Y*X^-2*Y ] Chiral map of genus 85 and type {6,12}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^6, (X*Y^-1*X)^2, (X*Y^-5)^2, Y*X*Y^-2*X^-1*Y^2*X*Y^-1*X*Y^3*X^-1*Y^2*X^-1*Y ] Chiral map of genus 106 and type {6,48}_112 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^2*Y^-1*X^2*Y^-1*X*Y^-1*X^3*Y^-1*X^2*Y^2, Y*X*Y^-1*X^-1*Y^6*X^-2*Y*X^-2*Y^7 ] Chiral map of genus 106 and type {6,48}_112 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^6, X*Y^-3*X^2*Y*X^-1*Y^-2, Y^7*X^-2*Y*X^2*Y*X^-2*Y^7 ] Chiral map of genus 113 and type {12,12}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y*X^-2*Y, X^12, Y^-1*X^6*Y^-1*X*Y^-2*X ] Chiral map of genus 113 and type {12,12}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, X^12, X^-1*Y*X^-1*Y^-2*X^2*Y^-1*X^-3*Y*X^-2*Y^-1*X^2*Y^-2*X^-1 ] Chiral map of genus 113 and type {12,12}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, (X*Y^-2)^2, X^12, Y^-1*X^6*Y^-5, X^-1*Y^-1*X*Y^-1*X^2*Y^-1*X^-3*Y*X^-2*Y*X^-1*Y*X^-2 ] Chiral map of genus 127 and type {12,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-2*X^2*Y^3*X^-1, X^12, Y*X*Y^-1*X^-1*Y*X^3*Y^-1*X*Y^4 ] Chiral map of genus 127 and type {12,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^12, Y^-1*X^6*Y^-1*X*Y^-2*X, Y^-2*X^5*Y^-3*X*Y^-1, X^2*Y^-1*X^4*Y^-2*X^2*Y^-1 ] Chiral map of genus 127 and type {12,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^12, (X*Y^-1*X^4)^2, Y^-1*X*Y^-1*X^4*Y^-2*X*Y^-2, Y^-2*X^2*Y^-1*X^2*Y^-5 ] Chiral map of genus 127 and type {12,24}_56 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y^2*X^-2, Y*X^2*Y^-1*X^2*Y^4, X^12, Y^-1*X*Y^-1*X^4*Y^-2*X*Y^-2 ] Chiral map of genus 134 and type {12,48}_112 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-2*X^2*Y^3*X^-1, X^12, Y*X*Y^-1*X^-1*Y*X^3*Y^-4*X*Y ] Chiral map of genus 134 and type {12,48}_112 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, X^12, (X*Y^-1*X^4)^2, Y^-1*X*Y^-1*X^4*Y^-2*X*Y^-2, Y^2*X*Y^-2*X^2*Y^-3*X*Y ] Chiral map of genus 137 and type {14,42}_12 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y^3*X^3*Y^-1*X*Y^2, Y*X*Y^-1*X^4*Y^3*X^-1*Y, X^14 ] Chiral map of genus 137 and type {21,21}_4 isomorphic to its mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^6*Y^2*X^-3, X^2*Y^-2*X*Y^-2*X*Y^-2*X^8*Y^-1*X*Y^-1 ] Chiral map of genus 141 and type {24,24}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, Y*X^-2*Y^4*X^-2*Y*X^-7*Y^2*X^-5 ] Chiral map of genus 141 and type {24,24}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y*X^-2*Y, X^7*Y^-2*X*Y^-2 ] Chiral map of genus 153 and type {42,42}_4 isomorphic to its mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y*X^-1*Y^2, X^-4*Y^23*X^-2*Y*X^-9*Y*X^-1*Y ] Chiral map of genus 155 and type {48,48}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^3*Y^-15*X^3*Y^-1*X*Y^-1*X*Y^-1*X*Y^-2*X^8*Y^-2*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 155 and type {48,48}_28 not isomorphic to its dual or mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, Y^2*X^-3*Y*X^-1*Y^2*X^-8*Y^2*X^-4*Y ] Chiral map of genus 161 and type {84,84}_4 isomorphic to its mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y*X^-1*Y^2, X^-4*Y^23*X^-2*Y*X^-8*Y*X^-3 ] Chiral map of genus 161 and type {84,84}_4 isomorphic to its mirror-dual Automorphism group of order 672 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-1*Y, X^-68*Y^2*X^-12*Y^2 ] .......................... Rotary maps with 337 edges .......................... Orientable map of genus 0 and type {2,337}_674 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1348 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^337 ] .......................... Rotary maps with 338 edges .......................... Orientable map of genus 0 and type {2,338}_338 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1352 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^338 ] Non-orientable map of genus 1 and type {2,676}_676 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1352 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 1 and type {4,4}_26 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1352 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^4, (c*b*a*b)^13 ] Orientable map of genus 144 and type {26,26}_26 plus image(s) under Wilson transforms [ D, Opp ] Automorphism group of order 1352 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (b*c)^26 ] Chiral map of genus 1 and type {4,4}_338 isomorphic to its dual Automorphism group of order 676 with defining relations: [ (X*Y)^2, X^4, Y^4, X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^-1 ] Chiral map of genus 157 and type {52,52}_26 isomorphic to its dual Automorphism group of order 676 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, X^3*Y^-3*X*Y^-1*X^10*Y^-6*X*Y^-1 ] .......................... Rotary maps with 339 edges .......................... Orientable map of genus 0 and type {2,339}_678 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1356 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^339 ] Non-orientable map of genus 225 and type {6,226}_339 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1356 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 340 edges .......................... Orientable map of genus 0 and type {2,340}_340 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1360 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^340 ] Non-orientable map of genus 1 and type {2,680}_680 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1360 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 84 and type {4,170}_340 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^170 ] Orientable map of genus 132 and type {10,68}_340 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^68 ] Orientable map of genus 144 and type {20,34}_340 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^34 ] Orientable map of genus 149 and type {20,68}_170 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1360 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_170 isomorphic to its dual Automorphism group of order 680 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X ] Chiral map of genus 1 and type {4,4}_170 isomorphic to its dual Automorphism group of order 680 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^2*X^2*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 69 and type {4,20}_170 not isomorphic to its dual or mirror-dual Automorphism group of order 680 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^-2*X^-1*Y*X*Y^-1*X^-1*Y*X^-2*Y*X^-1*Y^-1*X*Y^2*X^-1*Y^-1 ] Chiral map of genus 81 and type {4,68}_170 not isomorphic to its dual or mirror-dual Automorphism group of order 680 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^17*X*Y^-1*X*Y*X^-1*Y^-5*X*Y^10 ] Chiral map of genus 137 and type {20,20}_34 isomorphic to its dual Automorphism group of order 680 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^-1*Y*X^-1*Y*X*Y^-1*X^-2*Y^-1*X*Y^-2*X^2*Y^2, X^-4*Y^2*X^-8*Y*X^-1*Y^3*X^-1 ] Chiral map of genus 154 and type {40,40}_34 not isomorphic to its dual or mirror-dual Automorphism group of order 680 with defining relations: [ (X*Y)^2, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, Y*X^6*Y^2*X^-2*Y, X^-2*Y^3*X^-2*Y*X^-7*Y^5 ] Chiral map of genus 161 and type {68,68}_10 isomorphic to its dual Automorphism group of order 680 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X^2*Y*X^-1*Y, Y^-1*X*Y^-33*X^2*Y^-5*X^3*Y^-1*X^10*Y^-1*X*Y^-1*X^2*Y^-4*X*Y^-2 ] .......................... Rotary maps with 341 edges .......................... Orientable map of genus 0 and type {2,341}_682 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1364 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^341 ] Non-orientable map of genus 301 and type {22,62}_341 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1364 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b ] .......................... Rotary maps with 342 edges .......................... Orientable map of genus 0 and type {2,342}_342 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1368 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^342 ] Non-orientable map of genus 1 and type {2,684}_684 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1368 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 169 and type {4,171}_171 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1368 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^171 ] Non-orientable map of genus 221 and type {6,76}_76 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1368 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 112 and type {6,114}_114 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1368 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 112 and type {6,114}_114 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1368 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^114 ] Orientable map of genus 144 and type {18,38}_342 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1368 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^38 ] Chiral map of genus 58 and type {6,6}_114 not isomorphic to its dual or mirror-dual Automorphism group of order 684 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^3*Y^3*X^-2, X^-1*Y^-3*X*Y^-1*X*Y^3*X^-1*Y, Y^-1*X^-2*Y*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X^2*Y^-1*X ] Chiral map of genus 58 and type {6,6}_114 not isomorphic to its dual or mirror-dual Automorphism group of order 684 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, Y^-1*X^2*Y^2*X^2*Y^-1*X^2*Y^-1*X^2*Y*X^-2*Y^-1*X^2*Y*X^-1*Y*X^-1*Y*X^2 ] Chiral map of genus 134 and type {18,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 684 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, X*Y^-1*X^-1*Y*X*Y^-1*X^-3*Y*X^-2*Y^-1*X*Y^-1*X, Y*X^-1*Y*X^-2*Y^2*X^-3*Y^2*X^-2*Y*X^-1*Y*X^-1 ] Chiral map of genus 134 and type {18,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 684 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y^2*X^2*Y*X^-1*Y^-2, Y*X^6*Y^2*X^-1*Y*X^-1, X^-1*Y*X^-1*Y*X^-1*Y*X^-7*Y^2*X^-1*Y*X^-1 ] Chiral map of genus 134 and type {18,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 684 with defining relations: [ (X*Y)^2, X^-2*Y*X^3*Y^-1*X*Y^2, Y*X*Y^-2*X^2*Y^2*X^-1*Y, Y^3*X^-9*Y*X^-3*Y^2 ] Chiral map of genus 134 and type {18,18}_38 not isomorphic to its dual or mirror-dual Automorphism group of order 684 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y*X^6*Y^3*X^-2, X^-1*Y^2*X^-1*Y*X^-5*Y*X^-2*Y*X^-3*Y ] .......................... Rotary maps with 343 edges .......................... Orientable map of genus 0 and type {2,343}_686 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1372 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^343 ] Orientable map of genus 99 and type {7,14}_14 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1372 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^7, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b ] Orientable map of genus 141 and type {14,49}_98 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1372 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^14, (c*b)^49 ] Chiral map of genus 141 and type {14,49}_98 not isomorphic to its dual or mirror-dual Automorphism group of order 686 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y^3*X^-3*Y^-1*X*Y^3 ] Chiral map of genus 141 and type {14,49}_98 not isomorphic to its dual or mirror-dual Automorphism group of order 686 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X*Y^-3*X^-2*Y^-4*X ] Chiral map of genus 141 and type {14,49}_98 not isomorphic to its dual or mirror-dual Automorphism group of order 686 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, X^2*Y^-2*X^-2*Y^-5 ] .......................... Rotary maps with 344 edges .......................... Orientable map of genus 0 and type {2,344}_344 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1376 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^344 ] Non-orientable map of genus 1 and type {2,688}_688 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1376 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 85 and type {4,172}_172 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1376 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^172 ] Orientable map of genus 86 and type {4,344}_344 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1376 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 126 and type {8,86}_344 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1376 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^86 ] Orientable map of genus 128 and type {8,172}_344 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1376 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 345 edges .......................... Orientable map of genus 0 and type {2,345}_690 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1380 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^345 ] Non-orientable map of genus 229 and type {6,230}_345 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1380 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 273 and type {10,138}_345 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1380 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 309 and type {30,46}_345 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1380 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] .......................... Rotary maps with 346 edges .......................... Orientable map of genus 0 and type {2,346}_346 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1384 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^346 ] Non-orientable map of genus 1 and type {2,692}_692 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1384 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_346 isomorphic to its dual Automorphism group of order 692 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X ] .......................... Rotary maps with 347 edges .......................... Orientable map of genus 0 and type {2,347}_694 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1388 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^347 ] .......................... Rotary maps with 348 edges .......................... Orientable map of genus 0 and type {2,348}_348 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^348 ] Non-orientable map of genus 1 and type {2,696}_696 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 84 and type {4,87}_174 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^87 ] Non-orientable map of genus 172 and type {4,174}_174 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^174 ] Orientable map of genus 86 and type {4,174}_348 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^174 ] Orientable map of genus 113 and type {6,87}_116 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 114 and type {6,116}_348 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^116 ] Orientable map of genus 140 and type {12,58}_348 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^58 ] Orientable map of genus 143 and type {12,116}_174 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1392 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 59 and type {4,12}_174 not isomorphic to its dual or mirror-dual Automorphism group of order 696 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, Y^12, X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X^-1*Y*X^2*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2 ] Chiral map of genus 117 and type {12,12}_58 isomorphic to its dual Automorphism group of order 696 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, Y^2*X^-2*Y^2*X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1 ] .......................... Rotary maps with 349 edges .......................... Orientable map of genus 0 and type {2,349}_698 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1396 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^349 ] .......................... Rotary maps with 350 edges .......................... Orientable map of genus 0 and type {2,350}_350 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1400 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^350 ] Non-orientable map of genus 1 and type {2,700}_700 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1400 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 257 and type {10,28}_28 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^10, c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 136 and type {10,70}_70 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^10, b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 136 and type {10,70}_70 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^70 ] Orientable map of genus 144 and type {14,50}_350 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1400 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^50 ] Chiral map of genus 151 and type {28,28}_50 isomorphic to its dual Automorphism group of order 700 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-2*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 171 and type {140,140}_10 isomorphic to its dual Automorphism group of order 700 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X^-1*Y^39*X^-3*Y^2*X^-4*Y^2*X^-8*Y*X^-1*Y^3*X^-1*Y^3*X^-1 ] .......................... Rotary maps with 351 edges .......................... Orientable map of genus 0 and type {2,351}_702 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1404 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^351 ] Orientable map of genus 109 and type {6,39}_78 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1404 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (c*b)^39 ] Orientable map of genus 115 and type {6,117}_234 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1404 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^117 ] Non-orientable map of genus 305 and type {18,78}_117 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1404 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 313 and type {26,54}_351 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1404 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^26, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 1 and type {3,6}_78 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, X^3, Y^6, Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X^-1*Y^2*X*Y^-1*X*Y^3*X*Y^-2*X*Y^-1*X*Y^-2*X*Y^3*X^-1*Y ] Chiral map of genus 79 and type {6,9}_234 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, X^6, Y^9, (X*Y^-2)^2, X^2*Y^-1*X*Y^-1*X^-2*Y*X^2*Y^-1*X^-3*Y^-1*X^2*Y^-1*X^2*Y^2 ] Chiral map of genus 79 and type {6,9}_234 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, X^6, Y^9, (X*Y^-2)^2, X^2*Y^2*X*Y^-1*X^-2*Y*X^3*Y*X^-2*Y^-1*X^2*Y*X^-1*Y*X^-1*Y ] Chiral map of genus 79 and type {6,9}_234 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, X^6, Y^9, (X*Y^-2)^2, Y*X^-2*Y*X^-2*Y*X^2*Y^-1*X^-3*Y^-1*X^2*Y^-1*X^2*Y*X^-1 ] Chiral map of genus 115 and type {6,117}_234 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^-20*X*Y*X^-1*Y^-1*X*Y^5*X^-1*Y^-12 ] Chiral map of genus 118 and type {9,18}_78 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, X^9, Y*X^4*Y*X^-2, Y^2*X^-3*Y^4, Y^-1*X*Y^-1*X^-1*Y*X*Y^-2*X*Y^-2*X^-1*Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^-2 ] Chiral map of genus 136 and type {13,26}_6 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^3*Y^-1*X*Y*X^-1, Y*X*Y^-3*X^2*Y*X^-1*Y^3, X^-13 ] Chiral map of genus 136 and type {13,26}_6 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^3*Y*X^-2*Y, Y*X^6*Y^2*X^-1*Y*X^-1, X^-13 ] Chiral map of genus 157 and type {27,54}_26 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X^-1*Y^2*X*Y^-1*X*Y^-2*X*Y^2, X^2*Y^-3*X^3*Y^-1*X^9*Y^-8*X ] Chiral map of genus 169 and type {78,117}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 702 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, Y^-2*X*Y^-1*X*Y^-11*X*Y^-1*X^2*Y^-2*X^10*Y^-2*X^3*Y^-2 ] .......................... Rotary maps with 352 edges .......................... Orientable map of genus 0 and type {2,352}_352 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^352 ] Non-orientable map of genus 1 and type {2,704}_704 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 81 and type {4,44}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^44 ] Orientable map of genus 85 and type {4,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^88 ] Orientable map of genus 87 and type {4,176}_176 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 87 and type {4,176}_176 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^176 ] Orientable map of genus 88 and type {4,352}_352 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 125 and type {8,44}_44 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^44 ] Orientable map of genus 125 and type {8,44}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (b*c)^44 ] Orientable map of genus 129 and type {8,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 129 and type {8,88}_88 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^88 ] Orientable map of genus 129 and type {8,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 129 and type {8,88}_88 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^8, (a*b*c*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 131 and type {8,176}_176 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 147 and type {16,44}_176 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, (b*c)^44 ] Orientable map of genus 147 and type {16,44}_176 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^44 ] Orientable map of genus 151 and type {16,88}_176 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 151 and type {16,88}_176 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, b*a*b*a*b*a*b*a*b*a*b*a*c*b*a*b*a*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 150 and type {22,32}_352 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, (b*c)^32 ] Orientable map of genus 158 and type {32,44}_352 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1408 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c ] .......................... Rotary maps with 353 edges .......................... Orientable map of genus 0 and type {2,353}_706 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1412 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^353 ] .......................... Rotary maps with 354 edges .......................... Orientable map of genus 0 and type {2,354}_354 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1416 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^354 ] Non-orientable map of genus 1 and type {2,708}_708 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1416 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 175 and type {4,177}_177 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1416 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^177 ] Orientable map of genus 116 and type {6,118}_354 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1416 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^118 ] .......................... Rotary maps with 355 edges .......................... Orientable map of genus 0 and type {2,355}_710 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1420 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^355 ] Non-orientable map of genus 281 and type {10,142}_355 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1420 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 72 and type {5,10}_142 not isomorphic to its dual or mirror-dual Automorphism group of order 710 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y*X*Y^-1*X*Y^-1*X^-2*Y^4*X^-1*Y ] Chiral map of genus 72 and type {5,10}_142 not isomorphic to its dual or mirror-dual Automorphism group of order 710 with defining relations: [ (X*Y)^2, X^5, (X*Y^-3*X)^2, (X*Y^-2*X*Y^-1)^2, Y^-1*X*Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-4 ] .......................... Rotary maps with 356 edges .......................... Orientable map of genus 0 and type {2,356}_356 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1424 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^356 ] Non-orientable map of genus 1 and type {2,712}_712 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1424 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 88 and type {4,178}_356 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1424 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^178 ] Chiral map of genus 1 and type {4,4}_178 isomorphic to its dual Automorphism group of order 712 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 90 and type {8,8}_178 not isomorphic to its dual or mirror-dual Automorphism group of order 712 with defining relations: [ (X*Y)^2, X^8, Y^8, (X*Y^-2*X)^2, (X*Y^-1)^4, X^3*Y^-1*X^3*Y^-3*X*Y^-1 ] .......................... Rotary maps with 357 edges .......................... Orientable map of genus 0 and type {2,357}_714 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1428 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^357 ] Non-orientable map of genus 237 and type {6,238}_357 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1428 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 301 and type {14,102}_357 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1428 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Non-orientable map of genus 321 and type {34,42}_357 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1428 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c ] Chiral map of genus 113 and type {6,51}_238 not isomorphic to its dual or mirror-dual Automorphism group of order 714 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X*Y^-1*X^-2*Y*X^2*Y^-1*X^-2*Y*X^-2*Y*X^-1*Y, Y^-7*X^-1*Y*X*Y^-1*X^-1*Y*X^-2*Y^6*X^-1*Y^-1 ] Chiral map of genus 169 and type {51,102}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 714 with defining relations: [ (X*Y)^2, Y*X^4*Y*X^-2, Y*X^2*Y^-1*X^2*Y^4, Y*X*Y^-2*X^2*Y^2*X^-1*Y, X^2*Y^-1*X^17*Y^-1*X*Y^-5*X^3*Y^-1*X^9*Y^-5*X*Y^-5 ] .......................... Rotary maps with 358 edges .......................... Orientable map of genus 0 and type {2,358}_358 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1432 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^358 ] Non-orientable map of genus 1 and type {2,716}_716 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1432 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 359 edges .......................... Orientable map of genus 0 and type {2,359}_718 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1436 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^359 ] .......................... Rotary maps with 360 edges .......................... Orientable map of genus 0 and type {2,360}_360 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^360 ] Non-orientable map of genus 1 and type {2,720}_720 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 16 and type {3,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b, c*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*a*b*c*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 37 and type {3,15}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c, (c*b)^15 ] Orientable map of genus 43 and type {3,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*a*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 19 and type {4,5}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (c*b)^5, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 62 and type {4,6}_8 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b, b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*a*c*b*c ] Orientable map of genus 31 and type {4,6}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*b*a*b*c*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 92 and type {4,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Orientable map of genus 46 and type {4,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (b*c)^8, (c*b*c*b*a*b*c*b)^3, c*b*c*b*a*b*c*a*b*c*b*a*b*a*c*b*c*b*a*b*c*b*c*b*a*b ] Non-orientable map of genus 92 and type {4,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b, c*b*a*b*c*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b ] Orientable map of genus 46 and type {4,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^8, c*a*b*c*b*c*b*a*b*c*b*a*b*c*b*a*b*c*b*c*b*a*c*b ] Orientable map of genus 55 and type {4,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c*b*a*b*c)^3, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Non-orientable map of genus 110 and type {4,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, (b*c)^10 ] Non-orientable map of genus 110 and type {4,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b, (b*c)^10, b*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c*b*c ] Orientable map of genus 73 and type {4,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (a*b*c*b)^6, (b*c)^20 ] Non-orientable map of genus 166 and type {4,45}_45 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, a*b*c*a*b*c*b*a*b*a*c*b*c*b*c*b*a*b*c, (c*b)^45 ] Orientable map of genus 87 and type {4,90}_90 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (b*c)^90 ] Orientable map of genus 89 and type {4,180}_180 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^180 ] Non-orientable map of genus 178 and type {4,180}_180 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 178 and type {4,180}_180 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^180 ] Orientable map of genus 90 and type {4,360}_360 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 49 and type {5,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b ] Orientable map of genus 64 and type {5,8}_8 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (b*c)^8, (b*c*b*a*b*c)^3, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c*b, b*a*b*c*a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 73 and type {5,10}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^5, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b)^2 ] Orientable map of genus 61 and type {6,6}_6 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, c*a*b*c*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b*c*b ] Non-orientable map of genus 122 and type {6,6}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (a*b*c*b)^4, a*b*c*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*a*b*c ] Orientable map of genus 61 and type {6,6}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (b*c)^6, (a*b*c*b)^4, c*a*b*a*b*c*b*a*b*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 152 and type {6,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b ] Non-orientable map of genus 152 and type {6,8}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^8, b*c*a*b*c*b*c*b*a*b*c*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Non-orientable map of genus 152 and type {6,8}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*c*b*c*b*c ] Non-orientable map of genus 152 and type {6,8}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (b*c)^8, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*a ] Orientable map of genus 85 and type {6,10}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*a*b)^2, (b*c)^10 ] Orientable map of genus 85 and type {6,10}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, (b*c)^10, c*a*b*c*a*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 182 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b*c*b*a*b)^2, b*c*b*c*a*b*c*b*a*b*a*b*c*b*c*b*c*b*a*b*a, b*c*a*b*c*a*b*c*b*c*a*b*a*b*c*b*a*b*c*b*c*b*c ] Non-orientable map of genus 182 and type {6,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*b*a*c*b*c*b*a*c*b*a*b, (a*b*c*b*a*b*c*b*a*b)^2, (b*c)^12 ] Orientable map of genus 91 and type {6,12}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, a*b*c*b*c*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*a*b ] Orientable map of genus 97 and type {6,15}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*a*b*a*b*c*b*a*b*a*c*b*c*b*a*b*a*b*c ] Orientable map of genus 103 and type {6,20}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*a*b)^2, b*c*b*c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b*c, c*a*b*c*a*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 212 and type {6,24}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, b*a*b*c*b*a*b*a*b*a*c*b*a*b*a*b*c*b*a, b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*a*c ] Orientable map of genus 109 and type {6,30}_30 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, c*a*b*c*b*c*b*a*b*a*b*a*c*b*c*b*c*b*a*b*a*b ] Orientable map of genus 109 and type {6,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, c*a*b*c*b*c*b*a*b*c*b*a*c*b*c*b*c*b*a*b*c*b, c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*b*c*b*a*c*b*a*c*b ] Orientable map of genus 109 and type {6,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (b*c)^30 ] Orientable map of genus 112 and type {6,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (b*c)^40 ] Non-orientable map of genus 230 and type {6,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b*c*b*c*b*c*b*c*b)^2 ] Non-orientable map of genus 230 and type {6,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*a, c*a*b*a*b*c*b*a*b*a*b*a*c*b*a*b*c*b*a*b*a*b, b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 118 and type {6,120}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (b*c)^120 ] Orientable map of genus 118 and type {6,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 91 and type {8,8}_8 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b)^4, (b*c)^8, c*a*b*c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*c*b*c*b, c*a*b*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*c*b*c*b*c*b ] Orientable map of genus 91 and type {8,8}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (c*b*a*b)^3, (a*b)^8, (b*c)^8, b*c*a*b*c*b*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*c*b*a ] Non-orientable map of genus 182 and type {8,8}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (b*c)^8, (a*b*c*b*a*b*c*b*a*b)^2, (a*b*c*b*c*b*a*b*c*b)^2, b*c*a*b*c*b*a*b*a*b*a*c*b*a*c*b*c*b*c*b*a ] Orientable map of genus 91 and type {8,8}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (b*c)^8, c*a*b*a*b*c*b*a*b*a*c*b*c*b*a*b*c*b, c*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*c*b*c*b ] Orientable map of genus 100 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (c*b*a*b)^3, (a*b)^8, (a*b*c*b*c*b*a*b*a*b)^2, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b ] Non-orientable map of genus 200 and type {8,10}_10 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, c*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, c*a*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*a*c*b, (b*c)^10 ] Orientable map of genus 124 and type {8,30}_40 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 127 and type {8,40}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (a*b*c*b*c*b*c*b)^2, a*b*c*b*a*b*c*b*a*b*c*a*b*a*b*a*c*b*a*b*c*b*a*b*c*b, a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 128 and type {8,45}_180 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, (c*b)^45 ] Orientable map of genus 132 and type {8,90}_180 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^8, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 132 and type {8,90}_360 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^90 ] Orientable map of genus 134 and type {8,180}_360 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 109 and type {10,10}_10 plus image(s) under Wilson transforms [ P, Opp ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, c*a*b*a*b*a*b*a*b*a*c*b*c*b*c*b*c*b, (a*b)^10 ] Non-orientable map of genus 230 and type {10,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (a*b*c*b*c*b*c*b)^2, (a*b)^10, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b ] Non-orientable map of genus 230 and type {10,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*c*b)^2, (a*b)^10, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, (a*b*c*b*a*b*c*b*a*b)^2, a*b*a*b*c*b*a*b*a*b*a*b*c*b*c*b*a*b*a*c*b, (b*c)^12 ] Non-orientable map of genus 230 and type {10,12}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^10, c*b*c*a*b*c*a*b*a*b*a*b*a*c*b*a*b*a*b*a*c*b*a*c*b ] Non-orientable map of genus 230 and type {10,12}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^10, b*c*a*b*a*b*a*b*a*b*c*b*a*c*b*a*b*a*c*b*a*b*a, (b*c)^12 ] Orientable map of genus 140 and type {10,72}_360 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^72 ] Non-orientable map of genus 254 and type {12,15}_15 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, b*a*b*a*b*c*b*a*b*a*b*a*b*c*b*c*b*c*b*c*b*a, (a*b)^12 ] Orientable map of genus 127 and type {12,15}_20 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*b*a*c*b*a*b*a*b, c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b, b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 127 and type {12,15}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*b*c*b*a*b*a*b*a*b*a*c*b*a*b*a*c*b*c*b, c*b*c*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b*a*b*a*c*b ] Orientable map of genus 127 and type {12,15}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, (c*b)^15 ] Orientable map of genus 133 and type {12,20}_20 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, (b*c)^20 ] Non-orientable map of genus 266 and type {12,20}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, (a*b)^12, a*b*c*b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b, a*b*c*a*b*c*b*c*b*c*a*b*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 139 and type {12,30}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b*a*b)^2, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (a*b*c*b)^4, (b*c)^30 ] Orientable map of genus 139 and type {12,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, a*b*a*b*c*b*a*b*a*c*b*c*b*c*b*c ] Orientable map of genus 139 and type {12,30}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*b*a*b*c*b*a*b*a*c*b*a*b, b*c*b*c*b*c*b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 142 and type {12,40}_40 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, b*c*b*c*b*a*b*a*c*b*a*c*b*a, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 145 and type {12,60}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, (b*c)^60 ] Orientable map of genus 145 and type {12,60}_60 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 148 and type {12,120}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 148 and type {12,120}_120 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b)^12, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 142 and type {15,24}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*a*b)^2, c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b, (b*a)^15 ] Orientable map of genus 143 and type {18,20}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, c*a*b*c*b*a*b*a*b*a*b*c*b*a*c*b*a*b, b*c*a*b*c*a*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c, (a*b)^18 ] Orientable map of genus 152 and type {18,40}_360 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^40 ] Orientable map of genus 153 and type {20,36}_180 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^36 ] Orientable map of genus 158 and type {20,72}_360 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 154 and type {24,30}_60 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, b*c*a*b*c*a*b*c*b*c*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 154 and type {24,30}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, (b*c)^30 ] Orientable map of genus 154 and type {24,30}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^24, (b*c)^30 ] Orientable map of genus 154 and type {24,30}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b, (a*b)^24 ] Orientable map of genus 160 and type {24,60}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, c*a*b*a*b*a*b*a*b*a*c*b*a*b*a*b*a*b, a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 160 and type {24,60}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^24, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Orientable map of genus 160 and type {24,60}_120 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*a*b*a*b*c*a*b*a*c*b*a*b*a*b*c*b*c*b*a*c*b*c*a ] Non-orientable map of genus 324 and type {36,40}_45 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*c*b)^2, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, c*b*c*b*a*b*a*b*a*b*a*b*a*c*b*a*c*b*a*b*a*b*a*c*b ] Non-orientable map of genus 324 and type {36,40}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b*c*b)^2, c*a*b*c*a*b*c*b*a*b*a*c*b*a*c*b*c*b*a*b, b*c*a*b*c*a*b*a*b*a*b*c*a*b*a*b*a*b*a*c*b*a*c ] Orientable map of genus 162 and type {36,40}_360 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 167 and type {40,72}_90 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b ] Orientable map of genus 167 and type {40,72}_180 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1440 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b)^2, c*b*c*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b ] Chiral map of genus 1 and type {4,4}_60 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^4, Y^4, X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y*X^-1*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y ] Chiral map of genus 61 and type {4,12}_20 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^4, Y^3*X*Y^-1*X^-1*Y^2*X^-1*Y^-1*X*Y, Y^12, X*Y^-1*X*Y^-1*X*Y^-1*X^-2*Y^2*X^-1*Y^-3 ] Chiral map of genus 81 and type {4,36}_180 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^36 ] Chiral map of genus 82 and type {4,40}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^4, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^2*X^-1*Y*X*Y^-1*X^-1*Y^2*X^-1*Y^2, Y^-10*X^2*Y^-2*X*Y^4*X^-1*Y^-4 ] Chiral map of genus 61 and type {6,6}_8 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^6, Y^6, (Y^-1*X)^5, Y^-1*X^-1*Y*X*Y^-1*X^2*Y^-1*X*Y^-2*X ] Chiral map of genus 91 and type {8,8}_30 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^3*Y^-1*X^-2*Y^4*X, Y*X*Y^-2*X^3*Y*X^-2*Y^2, X*Y^-1*X^-1*Y*X^3*Y^-2*X*Y^-2 ] Chiral map of genus 91 and type {8,8}_30 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, Y^8, Y*X*Y^-1*X^2*Y*X^-1*Y, Y^-2*X^-1*Y*X^3*Y^2*X^-2*Y^-1 ] Chiral map of genus 91 and type {8,8}_30 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y*X^-1*Y*X^-1*Y^2*X^-2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 91 and type {8,8}_60 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, Y^8, Y^-1*X^4*Y^-3, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-2*Y^2*X^-2*Y^-2*X ] Chiral map of genus 118 and type {8,20}_40 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, (X*Y^-3)^2, Y^-1*X^3*Y^-1*X^-4*Y^-1*X*Y^-1, Y^-2*X^-1*Y*X*Y^-1*X^-3*Y*X^-1*Y^-5 ] Chiral map of genus 127 and type {8,40}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1)^4, Y^-1*X^-2*Y*X^-3*Y^-1*X^3*Y^-1, Y*X*Y^-3*X^3*Y^6 ] Chiral map of genus 131 and type {8,72}_90 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y^-1*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y^-1, Y^-5*X^-1*Y^2*X*Y^-2*X^2*Y^-9 ] Chiral map of genus 131 and type {8,72}_180 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, X^8, (X*Y^-1*X^2)^2, (X*Y^-3)^2, Y*X^2*Y^-2*X^2*Y^2*X^-1*Y*X^-1, Y^5*X*Y^-2*X^-1*Y^2*X^2*Y^9 ] Chiral map of genus 121 and type {12,12}_60 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X^12, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^-2*Y^-1, Y^12 ] Chiral map of genus 121 and type {12,12}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, X^12, Y^-2*X^5*Y^-3*X*Y^-1, Y^-1*X*Y^-1*X*Y^-1*X^2*Y^-1*X*Y^-2*X, Y^12 ] Chiral map of genus 154 and type {20,40}_8 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y^-1*X*Y^-2*X^2*Y^-3*X ] Chiral map of genus 151 and type {24,24}_30 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X^5*Y*X^-3, Y^-2*X^-1*Y*X^2*Y^2*X^-1*Y^-1, X^-4*Y*X^-2*Y^2*X^-2*Y*X^-8*Y^2*X^-2 ] Chiral map of genus 151 and type {24,24}_30 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X^2*Y^-2*X^3*Y*X^-1*Y^-3 ] Chiral map of genus 151 and type {24,24}_60 not isomorphic to its dual or mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X*Y^-3*X*Y^4, Y^-1*X^6*Y^-1*X*Y^-1*X*Y^-1 ] Chiral map of genus 151 and type {24,24}_60 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, (X*Y^-1*X^2)^2, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X^3*Y^-2*X*Y^2 ] Chiral map of genus 161 and type {36,36}_20 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X*Y^-1*X^2*Y*X^-1*Y^2*X^-1, Y^-1*X*Y^-4*X^5*Y^-2*X*Y^-1*X^8*Y^-2*X^4*Y^-2*X^2*Y^-2*X ] Chiral map of genus 161 and type {36,36}_20 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X^-1*Y*X^2*Y^-1*X*Y, Y*X*Y^-1*X^4*Y*X^-1*Y^3, X^-2*Y^2*X^3*Y*X^-1*Y^-3, Y^3*X^-9*Y*X^-2*Y*X^-2 ] Chiral map of genus 163 and type {40,40}_6 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X*Y^-1*X^2*Y*X^-1*Y, Y*X^5*Y^3*X^-1, X^18*Y^-1*X^2*Y^-2*X*Y^-2*X^9*Y^-1*X^4 ] Chiral map of genus 165 and type {45,45}_4 isomorphic to its mirror-dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y*X^2*Y*X^-1*Y^-1, Y*X^5*Y^2*X^-2, X^-2*Y^29*X^-11*Y^2*X^-1 ] Chiral map of genus 171 and type {72,72}_10 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^44*X^-2*Y^2*X^-4*Y^2*X^-10*Y^8 ] Chiral map of genus 171 and type {72,72}_20 isomorphic to its dual Automorphism group of order 720 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X*Y^-1*X^2*Y^-1*X*Y^2*X^-1, Y^-1*X^2*Y^-11*X^10*Y^-2*X^4*Y^-3*X^2*Y^-1 ] .......................... Rotary maps with 361 edges .......................... Orientable map of genus 0 and type {2,361}_722 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1444 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^361 ] Orientable map of genus 153 and type {19,38}_38 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1444 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*c*b*c*b, (b*a)^19 ] .......................... Rotary maps with 362 edges .......................... Orientable map of genus 0 and type {2,362}_362 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1448 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^362 ] Non-orientable map of genus 1 and type {2,724}_724 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1448 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {4,4}_362 isomorphic to its dual Automorphism group of order 724 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^-2*Y^2*X^2*Y^2*X^2*Y^2*X^-2*Y^-2*X^-2*Y^-1*X ] .......................... Rotary maps with 363 edges .......................... Orientable map of genus 0 and type {2,363}_726 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1452 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^363 ] Orientable map of genus 1 and type {3,6}_22 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1452 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^6, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Non-orientable map of genus 241 and type {6,242}_363 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1452 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 155 and type {22,33}_66 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1452 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, a*b*c*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*c*b, (c*b)^33 ] .......................... Rotary maps with 364 edges .......................... Orientable map of genus 0 and type {2,364}_364 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1456 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^364 ] Non-orientable map of genus 1 and type {2,728}_728 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1456 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 90 and type {4,182}_364 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1456 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^182 ] Orientable map of genus 150 and type {14,52}_364 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1456 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^52 ] Orientable map of genus 156 and type {26,28}_364 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1456 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^26, (b*c)^28 ] Orientable map of genus 163 and type {28,52}_182 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1456 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c ] Chiral map of genus 79 and type {4,28}_182 not isomorphic to its dual or mirror-dual Automorphism group of order 728 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X^-1*Y*X*Y^-1*X*Y^-1*X*Y^-1*X^-1*Y*X^2*Y^-1*X*Y*X^-1*Y*X^-1*Y^2, X*Y^-6*X^-1*Y*X^-2*Y^2*X^-1*Y^-2*X*Y^3 ] Chiral map of genus 157 and type {28,28}_26 isomorphic to its dual Automorphism group of order 728 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y, X*Y^-4*X^12*Y^-2*X^4*Y^-2*X^3 ] Chiral map of genus 175 and type {91,91}_4 isomorphic to its mirror-dual Automorphism group of order 728 with defining relations: [ (X*Y)^2, Y*X^4*Y^2*X^-1, X^-2*Y^72*X^-1*Y*X^-15 ] .......................... Rotary maps with 365 edges .......................... Orientable map of genus 0 and type {2,365}_730 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1460 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^365 ] Non-orientable map of genus 289 and type {10,146}_365 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1460 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 366 edges .......................... Orientable map of genus 0 and type {2,366}_366 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1464 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^366 ] Non-orientable map of genus 1 and type {2,732}_732 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1464 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 181 and type {4,183}_183 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1464 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^183 ] Orientable map of genus 120 and type {6,122}_366 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1464 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^122 ] Chiral map of genus 62 and type {6,6}_122 not isomorphic to its dual or mirror-dual Automorphism group of order 732 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-1*X)^2, Y^2*X*Y^-1*X*Y^2*X^-1*Y^-3*X*Y^-1*X^-2*Y^3*X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y ] Chiral map of genus 123 and type {12,12}_122 not isomorphic to its dual or mirror-dual Automorphism group of order 732 with defining relations: [ (X*Y)^2, (Y^-1*X)^3, X^12, (X*Y^-2*X^3)^2, X^-1*Y*X^6*Y^-1*X*Y*X^-1*Y^-2 ] Chiral map of genus 123 and type {12,12}_122 isomorphic to its dual Automorphism group of order 732 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, X^12, X*Y^-2*X*Y^-1*X*Y^-1*X^-2*Y*X^-1*Y*X^-1*Y^-1*X*Y^-2*X^-1*Y*X^2*Y^-1 ] .......................... Rotary maps with 367 edges .......................... Orientable map of genus 0 and type {2,367}_734 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1468 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^367 ] .......................... Rotary maps with 368 edges .......................... Orientable map of genus 0 and type {2,368}_368 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^368 ] Non-orientable map of genus 1 and type {2,736}_736 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {4,92}_92 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^92 ] Orientable map of genus 91 and type {4,184}_184 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*a*b*a*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 91 and type {4,184}_184 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^184 ] Orientable map of genus 92 and type {4,368}_368 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 135 and type {8,92}_184 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^92 ] Orientable map of genus 135 and type {8,92}_184 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^8, (b*c)^92 ] Orientable map of genus 154 and type {16,46}_368 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, (b*c)^46 ] Orientable map of genus 158 and type {16,92}_368 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1472 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^16, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 369 edges .......................... Orientable map of genus 0 and type {2,369}_738 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1476 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^369 ] Orientable map of genus 121 and type {6,123}_246 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1476 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^6, (c*b)^123 ] Non-orientable map of genus 321 and type {18,82}_369 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1476 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 370 edges .......................... Orientable map of genus 0 and type {2,370}_370 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1480 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^370 ] Non-orientable map of genus 1 and type {2,740}_740 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1480 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 144 and type {10,74}_370 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1480 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^74 ] Chiral map of genus 1 and type {4,4}_370 isomorphic to its dual Automorphism group of order 740 with defining relations: [ (X*Y)^2, X^4, Y^4, Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X*Y^-1*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X*Y^-1*X*Y^-1*X ] Chiral map of genus 1 and type {4,4}_370 isomorphic to its dual Automorphism group of order 740 with defining relations: [ (X*Y)^2, X^4, Y^4, Y*X^-1*Y*X^-1*Y*X^2*Y^-2*X^-2*Y^-2*X^-2*Y^-2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^2*Y^2*X^-1 ] Chiral map of genus 149 and type {20,20}_74 isomorphic to its dual Automorphism group of order 740 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-1*X*Y^-2*X^-1*Y*X^2*Y^-1*X*Y^-1*X*Y^-1*X ] Chiral map of genus 181 and type {148,148}_10 isomorphic to its dual Automorphism group of order 740 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X^-1*Y*X^2*Y^-1*X*Y, Y^-1*X^42*Y^-1*X^2*Y^-5*X^14*Y^-1*X*Y^-1*X*Y^-2*X*Y^-2 ] .......................... Rotary maps with 371 edges .......................... Orientable map of genus 0 and type {2,371}_742 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1484 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^371 ] Non-orientable map of genus 313 and type {14,106}_371 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1484 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] .......................... Rotary maps with 372 edges .......................... Orientable map of genus 0 and type {2,372}_372 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^372 ] Non-orientable map of genus 1 and type {2,744}_744 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 90 and type {4,93}_186 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b)^2, (c*b)^93 ] Non-orientable map of genus 184 and type {4,186}_186 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (b*c)^186 ] Orientable map of genus 92 and type {4,186}_372 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^186 ] Orientable map of genus 121 and type {6,93}_124 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b)^2, c*a*b*a*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 122 and type {6,124}_372 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^124 ] Orientable map of genus 150 and type {12,62}_372 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, (b*c)^62 ] Orientable map of genus 153 and type {12,124}_186 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1488 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^12, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 1 and type {3,6}_124 not isomorphic to its dual or mirror-dual Automorphism group of order 744 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-2*X*Y^-2*X^-1*Y*X^-1*Y^3*X*Y^-2*X^-1*Y*X^-1*Y^-3*X*Y^-2*X*Y^-1 ] Chiral map of genus 94 and type {6,12}_124 not isomorphic to its dual or mirror-dual Automorphism group of order 744 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^12, Y*X^-2*Y*X^-2*Y*X^3*Y*X^-1*Y*X^-2*Y*X^-2 ] Chiral map of genus 94 and type {6,12}_124 not isomorphic to its dual or mirror-dual Automorphism group of order 744 with defining relations: [ (X*Y)^2, X^6, Y^-1*X^2*Y^-1*X^-2*Y^-1*X^2*Y^-1, Y*X^2*Y^-1*X^2*Y^4, Y^-1*X*Y^-2*X*Y^-2*X^-1*Y*X^-1*Y^2*X^-1*Y^2*X^-1*Y^-2 ] Chiral map of genus 125 and type {12,12}_62 not isomorphic to its dual or mirror-dual Automorphism group of order 744 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, X^12, X*Y*X^-1*Y^-1*X*Y^-1*X*Y^-1*X^-3*Y*X^-1*Y*X^-2*Y^-1*X*Y^-1*X ] .......................... Rotary maps with 373 edges .......................... Orientable map of genus 0 and type {2,373}_746 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1492 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^373 ] .......................... Rotary maps with 374 edges .......................... Orientable map of genus 0 and type {2,374}_374 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1496 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^374 ] Non-orientable map of genus 1 and type {2,748}_748 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1496 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 160 and type {22,34}_374 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1496 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^22, (b*c)^34 ] Chiral map of genus 171 and type {44,44}_34 isomorphic to its dual Automorphism group of order 748 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y^-2*X^-1*Y*X*Y^-1*X*Y^-1*X^-1*Y*X^-1*Y*X^-2*Y^-1*X, Y*X^-1*Y*X^-1*Y^3*X^-1*Y*X^-7*Y*X^-1*Y*X^-1*Y*X^-1 ] .......................... Rotary maps with 375 edges .......................... Orientable map of genus 0 and type {2,375}_750 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^375 ] Orientable map of genus 26 and type {3,10}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^10, c*a*b*c*a*b*c*a*b*c*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b ] Non-orientable map of genus 177 and type {6,10}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, (b*c)^10, c*b*c*b*c*a*b*c*b*c*b*a*b*c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b*a*b ] Non-orientable map of genus 177 and type {6,10}_15 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*c*a*b*a*c*b*c*b*a*c*b, (b*c)^10, b*c*a*b*c*b*c*b*c*a*b*a*b*a*c*b*a*b*a*c*b*a*b*a*c*b*a ] Non-orientable map of genus 249 and type {6,250}_375 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 126 and type {10,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*b*c*b*a*b, (a*b)^10, a*b*c*b*a*b*a*b*a*b*a*b*c*b*a*b*c*b*c*b, (c*b)^15 ] Orientable map of genus 126 and type {10,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, b*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*b*c, (a*b)^10, (c*b)^15 ] Orientable map of genus 126 and type {10,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, c*a*b*a*b*c*b*a*b*a*c*b*a*c*b*a*c*b, (a*b)^10 ] Orientable map of genus 126 and type {10,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (a*b)^10, b*c*b*a*b*a*b*c*b*a*b*a*b*c*b*a*c*b*c*b*a*c, c*a*b*c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*c*b*c*b*c*b ] Orientable map of genus 126 and type {10,15}_30 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b*c*b)^2, (b*a*b*a*b*c)^3, (a*b)^10 ] Orientable map of genus 146 and type {10,75}_150 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*a*b*a*c*b*a*b, (a*b)^10, (c*b)^75 ] Non-orientable map of genus 337 and type {30,50}_75 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1500 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Chiral map of genus 146 and type {10,75}_150 not isomorphic to its dual or mirror-dual Automorphism group of order 750 with defining relations: [ (X*Y)^2, X^10, X*Y^-1*X^4*Y^-1*X*Y^-2, Y^3*X*Y^-1*X^-1*Y^3*X^-2*Y^8 ] Chiral map of genus 146 and type {10,75}_150 not isomorphic to its dual or mirror-dual Automorphism group of order 750 with defining relations: [ (X*Y)^2, X^10, X*Y^-1*X^4*Y^-1*X*Y^-2, Y^-6*X^2*Y^-2*X^-2*Y^-7 ] Chiral map of genus 171 and type {30,75}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 750 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y*X^6*Y*X^-1*Y^2*X^-1, Y*X*Y^-1*X^4*Y^3*X^-1*Y, Y^3*X*Y^-2*X^2*Y^-1*X*Y^4, X^-8*Y*X^-2*Y^4 ] Chiral map of genus 171 and type {30,75}_50 not isomorphic to its dual or mirror-dual Automorphism group of order 750 with defining relations: [ (X*Y)^2, Y*X^2*Y^-1*X^2*Y*X^-1*Y*X^-1, Y*X^6*Y*X^-1*Y^2*X^-1, Y*X*Y^-1*X^4*Y^3*X^-1*Y, Y*X*Y^-3*X^3*Y^6, X^-8*Y^3*X^-2*Y^2 ] .......................... Rotary maps with 376 edges .......................... Orientable map of genus 0 and type {2,376}_376 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1504 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^376 ] Non-orientable map of genus 1 and type {2,752}_752 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1504 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 93 and type {4,188}_188 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^188 ] Orientable map of genus 94 and type {4,376}_376 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 138 and type {8,94}_376 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, (b*c)^94 ] Orientable map of genus 140 and type {8,188}_376 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1504 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^8, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 377 edges .......................... Orientable map of genus 0 and type {2,377}_754 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1508 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^377 ] Non-orientable map of genus 337 and type {26,58}_377 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1508 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^26, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*a*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] .......................... Rotary maps with 378 edges .......................... Orientable map of genus 0 and type {2,378}_378 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^378 ] Non-orientable map of genus 1 and type {2,756}_756 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 187 and type {4,189}_189 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*a*b*a*c*b*a*b, (c*b)^189 ] Non-orientable map of genus 227 and type {6,28}_84 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (a*b*c*b*a*b*c*b*a*b)^2, c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 118 and type {6,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*c*b*a*c*b*c*b*a*b*c*b, c*a*b*c*b*c*a*b*a*b*a*c*b*c*b*a*c*b*a*b, c*b*c*b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Orientable map of genus 118 and type {6,42}_42 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*a*b*a*b*a*c*b*a*c*b*a*b, c*b*a*b*c*b*a*b*a*b*c*b*a*b*c*b, (b*c)^42 ] Orientable map of genus 118 and type {6,42}_42 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (b*c)^42 ] Non-orientable map of genus 245 and type {6,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, b*c*b*c*b*a*b*a*c*b*a*c*b*a, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Non-orientable map of genus 245 and type {6,84}_84 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^6, (a*b*c*b*c*b*c*b)^2, (a*b*c*b*a*b*c*b*a*b)^2, c*b*c*b*c*a*b*c*b*c*a*b*c*b*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 124 and type {6,126}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, (b*c)^126 ] Orientable map of genus 156 and type {14,54}_378 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^14, (b*c)^54 ] Orientable map of genus 160 and type {18,42}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, c*a*b*c*b*a*b*a*c*b*c*b*a*b, (a*b*c*b*a*b*a*b*a*b*a*b)^2, b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c, (a*b)^18 ] Orientable map of genus 160 and type {18,42}_126 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1512 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^18, (b*c)^42 ] Chiral map of genus 64 and type {6,6}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^3*Y^3*X^-2, (X*Y^-2*X*Y^-1*X)^2, Y*X*Y^-1*X^-1*Y*X^2*Y^-1*X*Y^2*X^-1 ] Chiral map of genus 64 and type {6,6}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, Y^6, (X*Y^-2)^2, X*Y*X^-1*Y^-1*X*Y*X^-1*Y^-2*X^2*Y^-1*X^-2*Y*X^3*Y*X^-2*Y^-1*X^2*Y^2*X^2*Y^-1*X ] Chiral map of genus 64 and type {6,6}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, Y^6, X^-1*Y^-3*X^3*Y^3*X^-2, X^-1*Y^-3*X*Y^-1*X*Y^3*X^-1*Y, X*Y^-1*X^-2*Y*X^2*Y^-1*X^-2*Y*X^-2*Y*X^-1*Y ] Chiral map of genus 106 and type {6,18}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, Y^-1*X^-1*Y^2*X^2*Y*X^-1*Y^-2 ] Chiral map of genus 106 and type {6,18}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, Y^2*X^2*Y^-1*X^-1*Y*X^-1*Y^-1*X^2*Y, (X*Y^-2*X*Y^-1*X)^2, X^-1*Y^2*X*Y^-1*X^2*Y*X^-1*Y^-1*X*Y, X*Y^-4*X^2*Y^-3*X*Y^-1 ] Chiral map of genus 106 and type {6,18}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, X*Y^-3*X^2*Y*X^-1*Y^-2, Y^18 ] Chiral map of genus 106 and type {6,18}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X*Y^-1*X^-2*Y*X^-2*Y^-1*X^2*Y^-1*X, Y^18 ] Chiral map of genus 106 and type {6,18}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X^-2*Y*X^-2*Y*X^-2*Y*X^-2*Y*X^-1*Y^-1*X*Y ] Chiral map of genus 106 and type {6,18}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, X*Y^-1*X^-1*Y*X^2*Y^-1*X^3*Y^-1*X*Y*X^-1*Y^-1*X*Y^2 ] Chiral map of genus 124 and type {6,126}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, X^6, (X*Y^-2)^2, Y^-1*X^2*Y^-1*X^2*Y*X^-1*Y^-1*X, Y^21*X^2*Y*X^-2*Y^20 ] Chiral map of genus 148 and type {18,18}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, Y^-1*X^-1*Y^2*X^2*Y*X^-1*Y^-2, Y*X^6*Y^5, X^-1*Y*X^-1*Y^4*X^-8*Y^3 ] Chiral map of genus 148 and type {18,18}_42 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, X^-1*Y*X^2*Y^-1*X*Y^-1*X^-3*Y^-1*X^2*Y*X^-1*Y, X^-1*Y^2*X^-2*Y^2*X^-7*Y^4 ] Chiral map of genus 160 and type {18,42}_126 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, Y^-2*X^4*Y*X^-1*Y^-1*X, Y^-6*X^2*Y^-1*X^2*Y^-7 ] Chiral map of genus 178 and type {42,126}_18 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y^4, Y^-19*X*Y^-4*X^3*Y^-2*X^9*Y^-1*X*Y^-2 ] Chiral map of genus 176 and type {54,54}_14 not isomorphic to its dual or mirror-dual Automorphism group of order 756 with defining relations: [ (X*Y)^2, Y*X*Y^-2*X*Y^3, Y*X^5*Y^2*X^-1*Y, Y*X*Y^-1*X^3*Y*X^-2*Y, X^3*Y^-20*X^3*Y^-1*X^2*Y^-1*X^2*Y^-1*X^10*Y^-2*X*Y^-1*X*Y^-4*X^2 ] .......................... Rotary maps with 379 edges .......................... Orientable map of genus 0 and type {2,379}_758 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1516 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^379 ] .......................... Rotary maps with 380 edges .......................... Orientable map of genus 0 and type {2,380}_380 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1520 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^380 ] Non-orientable map of genus 1 and type {2,760}_760 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1520 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 94 and type {4,190}_380 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1520 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^2, (b*c)^190 ] Orientable map of genus 148 and type {10,76}_380 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1520 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^10, (b*c)^76 ] Orientable map of genus 162 and type {20,38}_380 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1520 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, (b*c)^38 ] Orientable map of genus 167 and type {20,76}_190 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1520 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^20, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Chiral map of genus 91 and type {4,76}_190 not isomorphic to its dual or mirror-dual Automorphism group of order 760 with defining relations: [ (X*Y)^2, X^4, (X*Y^-3)^2, X*Y^-1*X^-1*Y*X*Y^-1*X^2*Y*X^-1*Y^-2, Y^19*X*Y^-1*X*Y*X^-1*Y^-5*X*Y^12 ] Chiral map of genus 181 and type {76,76}_10 isomorphic to its dual Automorphism group of order 760 with defining relations: [ (X*Y)^2, Y*X^4*Y^3, Y*X*Y^-1*X^2*Y*X^-1*Y, X*Y^-43*X^4*Y^-5*X^12*Y^-1*X*Y^-3*X*Y^-2*X^3 ] .......................... Rotary maps with 381 edges .......................... Orientable map of genus 0 and type {2,381}_762 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1524 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^381 ] Non-orientable map of genus 253 and type {6,254}_381 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1524 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b*c*b)^2, (a*b)^6, c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b ] Chiral map of genus 1 and type {3,6}_254 not isomorphic to its dual or mirror-dual Automorphism group of order 762 with defining relations: [ (X*Y)^2, X^3, Y^6, Y^-1*X*Y^-3*X^-1*Y^2*X^-1*Y*X^-1*Y^2*X^-1*Y^-3*X^-1*Y*X^-1*Y^3*X*Y^-2*X*Y^-1*X*Y^-2*X*Y^2*X^-1*Y^-2*X*Y^-1 ] .......................... Rotary maps with 382 edges .......................... Orientable map of genus 0 and type {2,382}_382 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1528 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^382 ] Non-orientable map of genus 1 and type {2,764}_764 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1528 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] .......................... Rotary maps with 383 edges .......................... Orientable map of genus 0 and type {2,383}_766 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1532 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (c*b)^383 ] .......................... Rotary maps with 384 edges .......................... Orientable map of genus 0 and type {2,384}_384 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, (b*c)^384 ] Non-orientable map of genus 1 and type {2,768}_768 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*b)^2, (a*c)^2, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 17 and type {3,8}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, (b*c)^8, b*c*a*b*c*a*b*c*b*c*a*b*c*a*b*c*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 33 and type {3,12}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, b*c*a*b*c*a*b*c*b*c*a*b*c*b*a*c*b*a*c*b*c*b*a*c*b*c, (b*c)^12 ] Orientable map of genus 33 and type {3,12}_16 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (b*a)^3, c*a*b*c*b*c*b*c*b*c*b*a*b*c*b*c*b*c*b*c*b*a*c*b, c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b*a*c*b ] Orientable map of genus 33 and type {4,6}_6 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, c*a*b*c*a*b*c*a*b*a*c*b*a*c*b*a*c*b, b*c*a*b*c*b*c*a*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c ] Orientable map of genus 33 and type {4,6}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (a*b*c*b*c*b)^4, b*a*b*c*a*b*c*b*a*b*c*a*b*c*a*b*a*b*c*b*a*c*b*a*b*c*b*c ] Orientable map of genus 33 and type {4,6}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, b*c*b*c*b*a*b*c*b*c*a*b*a*b*c*b*c*b*a*b*c*b*a*c*b*a ] Orientable map of genus 33 and type {4,6}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (b*c)^6, (a*b*c*b)^4, b*c*a*b*c*a*b*c*b*c*a*b*c*a*b*c*a^2*b*a*c*b*a*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 65 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c*b, (b*c)^12 ] Orientable map of genus 65 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b*c*b)^2, (b*c)^12 ] Orientable map of genus 65 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*b*a*b*c*b*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c, (a*b*c*b*c*b)^4 ] Orientable map of genus 65 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c*b*a, (a*b*c*b*c*b)^4, (b*c)^12 ] Orientable map of genus 65 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*a*b*c*b*c*a*b*c*a*b*a*b*c*b*c*b*a*c*b*c*b*a, (a*b*c*b*c*b)^4, (b*c)^12 ] Non-orientable map of genus 130 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*a*b*c*b*a*c*b*c*b*a*c*b, (b*c)^12 ] Non-orientable map of genus 130 and type {4,12}_12 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b)^4, (b*c)^12, b*c*b*c*b*c*b*c*b*c*b*a*b*a*c*b*c*b*a*c*b*c*b*a*c*b*a ] Orientable map of genus 65 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b)^4, (b*c)^12, b*c*b*c*b*a*b*c*a*b*c*a*b*c*b*a*c*b*a*c*b*a*b*c*b*c*b*c ] Orientable map of genus 65 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*b*a*b*c*b*a*c*b*c*b*c*b*a*b*c*b, (b*c)^12 ] Orientable map of genus 65 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*b*a*b*c*b*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c, b*c*b*c*b*a*b*c*b*c*a*b*a*b*c*b*c*b*a*b*c*b*a*c*b*a ] Orientable map of genus 65 and type {4,12}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b*c*b)^2, (b*c)^12, c*b*c*b*c*a*b*c*b*c*b*a*b*c*b*c*b*a*b*c*b*c*b*a*c*b ] Orientable map of genus 65 and type {4,12}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^12, (a*b*c*b)^8 ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*b*c*b*c, (b*c)^24 ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*c*b*a*b*a*c*b*c*b*c*b*c*b*a*b, (b*c)^24 ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c*b, (b*c)^24 ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c*b, b*c*b*c*a*b*c*b*c*b*c*b*c*b*a*c*b*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*b*a*b*c*b*a*c*b*c*b*c*b*a*b*c*b, c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*c*b*c*b*a*c*b ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*b*a*b*c*b*a*c*b*c*b*c*b*a*b*c*b, b*c*a*b*c*a*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*a*c*b*a*c*b*c ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, c*a*b*c*b*c*b*a*b*a*c*b*c*b*c*b*a*b, (b*c)^24 ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b)^4, (a*b*c*b*c*b*c*b*c*b*c*b)^2, b*c*a*b*c*a*b*c*a*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c*b*a, (b*c)^24 ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*a*b*c*b*c*b*c*b*a*b*a*c*b*a*c*b*a*c*b*c*b*a, (a*b*c*b*c*b)^4, b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 81 and type {4,24}_24 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, b*c*a*b*c*b*c*a*b*c*a*b*a*b*c*b*c*b*a*c*b*c*b*a, (a*b*c*b*c*b)^4, b*c*a*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*c*b*c*b*a*c*b*c ] Orientable map of genus 81 and type {4,24}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*c*a*b*c*b*c*b*c*a*b*c*b*a*c*b*a*c*b*a*c*b*a*c*b*c ] Orientable map of genus 89 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P, Opp, DP, PD ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b*c*b*c*b)^2, a*b*c*a*b*c*b*a*b*c*a*b*a*c*b*a*c*b*a*c*b*a*b*c*b*c, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*a*c*b*c*b*a*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*a*b*c*b*c*b*c*b*a*b*a*c*b*c*b*c*b*c*b*a*b, b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*a*b*c*b*c*b*c*b*a*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c*b*c ] Orientable map of genus 89 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, (a*b*c*b*c*b*c*b)^2, (b*c)^48 ] Orientable map of genus 89 and type {4,48}_48 plus image(s) under Wilson transforms [ D, P ] Automorphism group of order 1536 with defining relations: [ a^2, b^2, c^2, (a*c)^2, (a*b)^4, (a*b*c*b)^4, c*b*c*b*a*b*c*b*c*a*b*a*c*b*c*b*a*b*c*b*c*b, b*c*b*c*b*c*b*c*b*c* | 426,931 | 1,044,816 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2013-48 | latest | en | 0.900933 |
https://ch.mathworks.com/matlabcentral/cody/problems/1515-procrustean-bed/solutions/1215289 | 1,597,096,882,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738699.68/warc/CC-MAIN-20200810205824-20200810235824-00520.warc.gz | 254,157,743 | 15,617 | Cody
# Problem 1515. Procrustean bed
Solution 1215289
Submitted on 18 Jun 2017
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Fail
x=[2 -16 384 -18432 1474560]; n=8; y=[2 -16 384 -18432 1474560 0 0 0]; assert(isequal(procrustes(x,n),y))
Error in solution Line: 4 Column: 4 Unbalanced or unexpected parenthesis or bracket.
2 Fail
x=[8 -96 3072 -184320 17694720]; n=0; assert(isempty(procrustes(x,n)))
Error in solution Line: 4 Column: 4 Unbalanced or unexpected parenthesis or bracket.
3 Fail
x='0.314 arcseconds'; n=12; y='0.314 arcsec'; assert(isequal(procrustes(x,n),y))
Error in solution Line: 4 Column: 4 Unbalanced or unexpected parenthesis or bracket.
4 Fail
x='credible fishers'; n=20; y='credible fishers '; assert(isequal(procrustes(x,n),y))
Error in solution Line: 4 Column: 4 Unbalanced or unexpected parenthesis or bracket. | 302 | 967 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2020-34 | latest | en | 0.428725 |
https://jp.maplesoft.com/support/help/maplesim/view.aspx?path=networks(deprecated)%2Fpetersen | 1,716,335,233,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058522.2/warc/CC-MAIN-20240521214515-20240522004515-00382.warc.gz | 281,684,433 | 21,733 | networks(deprecated)/petersen - Maple Help
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Home : Support : Online Help : networks(deprecated)/petersen
networks
petersen
creates the petersen graph
Calling Sequence G:=petersen()
Parameters
G - is returned as the petersen
Description
• Important: The networks package has been deprecated.Use the superseding command GraphTheory[SpecialGraphs][PetersenGraph] instead.
• The petersen graph is constructed. This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[petersen]().
Examples
Important: The networks package has been deprecated.Use the superseding command GraphTheory[SpecialGraphs][PetersenGraph] instead.
> $\mathrm{with}\left(\mathrm{networks}\right):$
> $G≔\mathrm{petersen}\left(\right):$
> $\mathrm{degreeseq}\left(G\right)$
$\left[{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}{,}{3}\right]$ (1)
> $\mathrm{nops}\left(\mathrm{vertices}\left(G\right)\right)$
${10}$ (2)
> $\mathrm{nops}\left(\mathrm{edges}\left(G\right)\right)$
${15}$ (3) | 328 | 1,142 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-22 | latest | en | 0.458887 |
http://www.mathisfunforum.com/viewtopic.php?pid=128793 | 1,394,471,658,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394010914773/warc/CC-MAIN-20140305091514-00067-ip-10-183-142-35.ec2.internal.warc.gz | 419,571,539 | 11,514 | Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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#1 2009-10-01 17:03:22
bobbym
Online
Is this cool with you?
Hi;
How would you judge this answer? And why?
Last edited by bobbym (2009-10-01 17:05:12)
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#2 2009-10-02 17:15:16
bobbym
Online
Re: Is this cool with you?
Hi;
Show that there are at least 3 real roots in [-2,2] for the function:
f(x) = x^5 - 3x -1
Here is how he does it:
Look at these values:
f(-2) = -27
f(-1) = 1
f(0) = - 1
f(1) = - 3
f(2) = 25
Look at the values of f(-2) and f(-1) they went from negative to positive (crossed the x axis). So somewhere between -2 and -1 is a root.
Look at the values of f(-1) and f(0) they went from + to - (crossed the x axis). So somewhere between -1 and 0 is a root.
Look at the values of f(1) and f(2) they went from - to + (crossed the x axis). So somewhere between 1 and 2 is a root.
So there are 3 or more real roots between -2 and 2.
Last edited by bobbym (2009-10-02 22:35:51)
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#3 2010-01-01 13:48:34
bobbym
Online
Re: Is this cool with you?
Hi;
#3)
A person reduces the assertion that there is always a square between n and 2n inclusive for all n to this inequality:
She manipulates this to:
She says proved:
Someone else says that you must use induction, presumably on the inequality. Who is right?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#4 2010-01-02 02:34:48
JaneFairfax
Legendary Member
Offline
Re: Is this cool with you?
bobbym wrote:
Hi;
How would you judge this answer? And why?
Last edited by JaneFairfax (2010-01-02 02:44:46)
Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?
#5 2010-01-02 02:47:27
JaneFairfax
Legendary Member
Offline
Re: Is this cool with you?
bobbym wrote:
A person reduces the assertion that there is always a square between n and 2n inclusive for all n to this inequality:
That would be looking for a square between
and
. It does not imply that there is a square between
and
.
Correct proof of #3.
If the statement were false, there would exist a natural number
and a natural number
satisfying
With some simple algebraic manipulation, we should arrive at
It can be easily checked that there are no natural numbers
satisfying
for
or
and so we have a contradiction.
Last edited by JaneFairfax (2010-01-02 12:22:14)
Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?
#6 2010-01-05 01:01:09
bobbym
Online
Re: Is this cool with you?
OK.
Congratulations on your deep sense of knowing how to perplex me.
With some simple algebraic manipulation, we should arrive at
What did you do here?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#7 2010-01-05 01:16:26
mathsyperson
Moderator
Offline
Re: Is this cool with you?
She removed the n's by doubling the first inequality and combining them.
2k² < (k+1)²
From there it's simple manipulation.
Why did the vector cross the road?
It wanted to be normal.
#8 2010-01-05 01:24:12
bobbym
Online
Re: Is this cool with you?
Hi mathsyperson;
Thanks, clear now, it is my first blind spot of the year.
Nice proof Jane. Happy New year to you.
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#9 2010-01-09 22:17:48
scientia
Full Member
Offline
Re: Is this cool with you?
bobbym wrote:
Hi;
How would you judge this answer? And why?
The first step is invalid because in order to split the limit of a sum as the sum of limits, you have to make sure all the limits you are taking exist. In this case, none of the three limits exists. The rest of the proof is treating ∞ as a number, which it is not.
The second problem looks fine to me.
The third problem can also be proved this way. Note that
JaneFairfax wrote:
can be written
since n is positive. There are n+1 integers from n to 2n inclusive and so there are at least n+1 integers between k² and (k+1)². Hence these two integers must differ by at least n+2:
Combining with k² < n gives
Last edited by scientia (2010-01-10 00:53:46)
#10 2010-01-10 03:10:12
bobbym
Online
Re: Is this cool with you?
Hi Jane and scientia;
1) I agree that the way that guy does that limit has many holes in it.
2) That is a perfectly acceptable method to look for roots, just keep in mind not all roots cross the x axis so that idea will miss some.
3) This was the trickiest one of all. Very pretty ideas were given to prove that equality.The question has not been answered and here is why.
A person reduces the assertion that there is always a square between n and 2n inclusive for all n to this inequality:
She manipulates this to:
She says proved:
The question was, is her manipulation a proof. Do you like where she stops? Do you find her proof valid? Is more required? When does algebraic manipulation constitute a proof?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#11 2010-01-10 04:32:17
scientia
Full Member
Offline
Re: Is this cool with you?
bobbym wrote:
She manipulates this to:
She says proved:
The question was, is her manipulation a proof. Do you like where she stops? Do you find her proof valid? Is more required? When does algebraic manipulation constitute a proof?
So you just want to prove
for all natural numbers n (even though this is the wrong way to go about solving the original question of finding a square between n and 2n)?
I don’t know what the person did, but if we want to use her method, we should proceed as follows. Start by noting that for all integers n ≥ 1,
Hence for all natural numbers n,
and the proof is completed by adding n² throughout.
The wrong way to go about it is to start with [1] and get [2]. This would be assuming what you want to prove to be true already, and would therefore prove nothing – yet this is an all too common mistake among students (and sometimes even teachers).
So what did the person do? Did she start from [1] and get [2] (which would be incorrect) or did she start with [2] and get [1]?
Last edited by scientia (2010-01-10 04:32:58)
#12 2010-01-10 06:00:18
bobbym
Online
Re: Is this cool with you?
Hi scientia;
So what did the person do? Did she start from [1] and get [2] (which would be incorrect) or did she start with [2] and get [1]?
I can't say, I don't know.
Jane wrote:
That would be looking for a square between
and
. It does not imply that there is a square between
and
.
I obviously forgot what you and Jane already know, that the first statement in her proof is wrong.
I think you have both solved the problem. Good job! Sorry to have continued to beat a dead horse.
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#13 2010-01-27 19:24:14
bobbym
Online
Re: Is this cool with you?
This prob came up somewhere else:
A coin with probability p of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is {2,4,6,8,10...} is 2/5, then find p:
B solves it like this:
The chance that a head comes up on an even toss is:
Now sum that series:
Set the sum to 2/5 and solve for p.
Solve the equation any way you can, to get p = 1/3
Has B solved the problem?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#14 2010-01-28 09:46:33
mathsyperson
Moderator
Offline
Re: Is this cool with you?
Just want to point out that to prove #2 like that, you need to observe that the function is continuous.
Otherwise you could use that proof to say that f(x) = 1/x has a root in [-1,1], for example.
Why did the vector cross the road?
It wanted to be normal.
#15 2010-01-28 13:09:04
bobbym
Online
Re: Is this cool with you?
Hi;
True, but since he/she is using it on a polynomial it is OK.
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#16 2010-02-02 03:26:39
bobbym
Online
Re: Is this cool with you?
Hi;
There is a 60 percent chance of snow on Tuesday, If there is a 45 percent of chance of snow on both Tuesday and Wednesday, and a 16 percent chance that it will not snow on both Tuesday and Wednesday, what is the probability of snow on Wednesday?
A says 75%
B says 69%
C says who cares, I have boots.
Who is right? (Please don't pick C)
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#17 2010-02-02 10:44:28
mathsyperson
Moderator
Offline
Re: Is this cool with you?
I agree with B.
P(T) = 0.6 and P(T n W) = 0.45, so P(T n ¬W) = 0.15.
Also, P(¬T n ¬W) = 0.16.
The remaining event is ¬T n W, and the probability of this must be 0.24.
Therefore, P(W) = 0.45 + 0.24 = 0.69 = 69%.
Why did the vector cross the road?
It wanted to be normal.
#18 2010-02-02 13:40:58
bobbym
Online
Re: Is this cool with you?
Hi mathsyperson;
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#19 2010-02-09 23:05:56
bobbym
Online
Re: Is this cool with you?
How many integer values can a have?
B says just substitute into the inequalities.
Supposing a = 1 then 1 < b and b <= 1 + 3b is true.
Supposing a = 2 then 2 < b and 2b <= 2 + 3b is true.
Supposing a = 3 then 3 < b and 3b <= 3 + 3b is true.
Supposing a = 4 then 4 < b and 4b <= 4 + 3b is not true when b>4.
The same is true for a=5,6,7...
So a can take positive values of 1,2,3 and nothing greater.
Did you like this?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#20 2010-02-17 08:06:20
bobbym
Online
Re: Is this cool with you?
How many ways can you arrange 5 A's, 7 B's and 4 C's so there are 3 CA pairs?
A) Says there are:
B) Says the magic number: 87120 ways.
Who is right?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#21 2010-02-19 06:26:59
bobbym
Online
Re: Is this cool with you?
Exasperating:
Let a, b, and c be real numbers such that a-7b+8c=4 and 8a+4b-c=7. What is a^2-b^2+c^2?
(a) 0
(b) 1
(c) 4
(d) 7
(e) 8
B) Says:
Looks like all you need to do is the algebra. It's tedious but...
Solve these simultaneously by multiplying the top equation by 8 and subtracting the bottom.
You get:
plug back in: You get another 2x2:
Solve for a:
Plug into the a^2-b^2+c^2
Which equals 1 so option b) 1 is the answer.
A says start by just setting a=0 and then solve from there. Because there are 3 variables and two equations, there are an infinite number of ordered triplets (a,b,c) that can satisfy the two equations. However, while the variables change, the value of a^2-b^2+c^2 stays constant. In one of these triplets, a=0. So if we set a to 0, we still get the same value of a^2-b^2+c^2 as in any other triplet.
Which method do you prefer?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#22 2010-02-26 06:14:08
bobbym
Online
Re: Is this cool with you?
Hi;
4 checkers are randomly placed on a chessboard, what is the probability that no checker is in the same row or column as any other?
A) says:
B) says:
What do you like?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#23 2010-02-26 07:55:05
mathsyperson
Moderator
Offline
Re: Is this cool with you?
I like the value of the second answer, but I like the reasoning of the first.
Even though it's wrong, at least it explained itself a bit.
Why did the vector cross the road?
It wanted to be normal.
#24 2010-02-27 02:58:23
bobbym
Online
Re: Is this cool with you?
Hi mathsyperson;
Maybe B) doesn't like that forum he posted on so he was purposely being enigmatic. My guess is that he used a standard formula for the rook polynomials. For an 8 x 8 board the generating function is:
Each power of x represents how many non attacking rooks. The coefficient represents the number of ways. The coefficient of x^4 is 117600. That is the number of ways to place 4 non attacking rooks on an 8x8 board.
Since the rook polys are used for derangements. I suspect that you could use the principle of inclusion and exclusion but that looks tedious.
Claude Tardif on another forum solved it in this manner:
(8*8*7*7*6*6*5*5)/4! = (117600)
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
#25 2010-03-02 20:52:19
bobbym
Online
Re: Is this cool with you?
Hi;
has 4 real roots:
A says when -27 < k < 5;
B says when 5 < k < 27;
C says when -5 < k < 0.
D says never.
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort. | 4,134 | 14,674 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2014-10 | longest | en | 0.933647 |
https://www.codezclub.com/cpp-calculate-sum-average-three-numbers/ | 1,723,514,383,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641054522.78/warc/CC-MAIN-20240813012759-20240813042759-00491.warc.gz | 540,308,179 | 22,169 | By | 24.12.2016
# Sum and Average of three numbers
Write a C++ Program to Find Sum and Average of three numbers. Here’s simple C++ Program to Find Sum and Average of three numbers in C++ Programming Language.
Here is source code of the C++ Program to Find Sum and Average of three numbers. The C++ program is successfully compiled and run(on Codeblocks) on a Windows system. The program output is also shown in below.
## SOURCE CODE : :
/* C++ Program to Find Sum and Average of three numbers */
#include<iostream>
using namespace std;
int main()
{
float a,b,c,sum,avg;
cout<<"Enter 1st number :: ";
cin>>a;
cout<<"\nEnter 2nd number :: ";
cin>>b;
cout<<"\nEnter 3rd number :: ";
cin>>c;
sum=a+b+c;
avg=sum/3;
cout<<"\nThe SUM of 3 Numbers [ "<<a<<" + "<<b<<" + "<<c<<" ] = "<<sum<<"\n";
cout<<"\nThe AVERAGE of 3 Numbers [ "<<a<<", "<<b<<", "<<c<<" ] = "<<avg<<"\n";
return 0;
}
### OUTPUT : :
/* C++ Program to Find Sum and Average of three numbers */
Enter 1st number :: 3
Enter 2nd number :: 4
Enter 3rd number :: 5
The SUM of 3 Numbers [ 3 + 4 + 5 ] = 12
The AVERAGE of 3 Numbers [ 3, 4, 5 ] = 4
Process returned 0
Above is the source code for C++ Program to Find Sum and Avg. of three numbers which is successfully compiled and run on Windows System.The Output of the program is shown above .
If you found any error or any queries related to the above program or any questions or reviews , you wanna to ask from us ,you may Contact Us through our contact Page or you can also comment below in the comment section.We will try our best to reach up to you in short interval.
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Inline Feedbacks | 504 | 1,956 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2024-33 | latest | en | 0.839001 |
https://penelopethemovie.com/what-is-symmetric-relation-in-discrete-mathematics/ | 1,660,653,478,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572304.13/warc/CC-MAIN-20220816120802-20220816150802-00029.warc.gz | 405,007,136 | 15,035 | # What is symmetric relation in discrete mathematics?
## What is symmetric relation in discrete mathematics?
In discrete mathematics, a symmetric relation between two or more elements of a set is such that if the first element is related to the second element, then the second element is also related to the first element as defined by the relation.
### What do you mean by symmetric relation?
Symmetric Relation In a symmetric relation, if a=b is true then b=a is also true. In other words, a relation R is symmetric only if (b, a) ∈ R is true when (a,b) ∈ R. An example of symmetric relation will be R = {(1, 2), (2, 1)} for a set A = {1, 2}. So, for a symmetric relation, aRb ⇒ bRa, ∀ a, b ∈ A.
#### What are relations in discrete mathematics?
In discrete mathematics, the relation can be described as a collection of ordered pairs. It is used to relate an object from one set to the other set, and the sets must be non-empty. The relation can contain two or more than two sets. Suppose there are two sets, A and B for instance.
How do you find the number of symmetric relations?
Total number of symmetric relations is 2n(n+1)/2.
Can relations be symmetric and antisymmetric?
There is at most one edge between distinct vertices. Some notes on Symmetric and Antisymmetric: • A relation can be both symmetric and antisymmetric. A relation can be neither symmetric nor antisymmetric.
## What is not symmetric relation?
Relation R on a set A is asymmetric if(a,b)∈R but (b,a)∉ R. Relation R of a set A is antisymmetric if (a,b) ∈ R and (b,a) ∈ R, then a=b. “Is equal to” is a symmetric relation, such as 3 = 2+1 and 1+2=3. “Is less than” is an asymmetric, such as 7<15 but 15 is not less than 7.
### What is symmetric relationship in math?
Symmetric Relation. Any relation R in a set A is said to be symmetric if (a, b) ∈ R. This implies that \\[(b, a) ∈ R\\] In other words, a relation R in a set A is said to be in a symmetric relationship only if every value of a,b ∈ A, (a, b) ∈ R then it should be (b, a) ∈ R.
#### What is relations in discrete mathematics?
Discrete Mathematics – Relations. Whenever sets are being discussed, the relationship between the elements of the sets is the next thing that comes up.
What is antisymmetric relation in Discrete Math?
Antisymmetric Relation — Discrete Math #5 — Transitive Relation If R is a relation on A, then R is transitive if (a,b) and (b,c) then (a,c) are in R. In other words, for every undirected path joining three vertices a,b, and c, in that order, there is also a directed line joining a to c.
How to find the number of symmetric relations on a set?
The number of symmetric relations on a set with the ‘n’ number of elements is given by N = 2n(n+1)/2, where N is the number of symmetric relations and n is the number of elements in the set.
Begin typing your search term above and press enter to search. Press ESC to cancel. | 727 | 2,902 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.625 | 5 | CC-MAIN-2022-33 | latest | en | 0.933909 |
https://math.stackexchange.com/questions/2548066/newb-question-about-limits-and-probability-distribution-functions | 1,723,278,587,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640790444.57/warc/CC-MAIN-20240810061945-20240810091945-00262.warc.gz | 308,125,379 | 37,461 | # Newb question about limits and probability distribution functions
Background: I'm a newbie trying to learn about joint distribution functions. This is from Sheldon Ross's book (which is fantastic).
Question A: Why is it not kosher/acceptable to go from step 2 to step 6? [see below in red]
Question B: If someone went from step 2 to step 4, would this be seen as a totally newb maneuver? What is the logic behind these steps?
The transition from Step $3$ to Step $4$ is based on the Third Axiom of Probability which is generally stated in terms of countable unions of events but has an equivalent formulation:
This principle is used to go from the $\displaystyle P\big(\lim_{b\to \infty} (X \leq a, Y \leq b)\big)$ of Step $3$ to the $\displaystyle \lim_{b\to\infty} P(X\leq a, Y \leq b)$ of Step $4$.
Similarly, the $F(a,\infty)$ of Step $6$ is pretty meaningless since $F(\cdot, \cdot)$ is a function of real variables and so you cannot just substitute $\infty$ for one of them. It is, of course, quite common to define $F(a,\infty)$ as the symbol used as shorthand for the more elaborate $\displaystyle \lim_{b\to\infty} F(a,b)$ of Step $5$. Thus, jumping directly from Step $2$ directly to Step $6$ is not quite kosher (as you call it) until you have defined some notation at the very least. Ross is being very careful to cross the i's and dot the t's in his development of the material; just as well in light of the recent controversy over on stats.SE over one of his proofs in Chapter $2$ (where also Ross is perfectly correct in what he says). | 407 | 1,556 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2024-33 | latest | en | 0.954667 |
https://oeis.org/A078458 | 1,653,295,008,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662556725.76/warc/CC-MAIN-20220523071517-20220523101517-00094.warc.gz | 488,541,643 | 4,801 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A078458 Total number of factors in a factorization of n into Gaussian primes. 15
0, 2, 1, 4, 2, 3, 1, 6, 2, 4, 1, 5, 2, 3, 3, 8, 2, 4, 1, 6, 2, 3, 1, 7, 4, 4, 3, 5, 2, 5, 1, 10, 2, 4, 3, 6, 2, 3, 3, 8, 2, 4, 1, 5, 4, 3, 1, 9, 2, 6, 3, 6, 2, 5, 3, 7, 2, 4, 1, 7, 2, 3, 3, 12, 4, 4, 1, 6, 2, 5, 1, 8, 2, 4, 5, 5, 2, 5, 1, 10, 4, 4, 1, 6, 4, 3, 3, 7, 2, 6, 3, 5, 2, 3, 3, 11, 2, 4, 3, 8, 2, 5, 1, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS a(n)+1 is also the total number of factors in a factorization of n+n*i into Gaussian primes. - Jason Kimberley, Dec 17 2011 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Eric W. Weisstein, MathWorld: Gaussian Prime FORMULA Fully additive with a(p)=2 if p=2 or p mod 4=1 and a(p)=1 if p mod 4=3. - Vladeta Jovovic, Jan 20 2003 a(n) depends on the number of primes of the forms 4k+1 (A083025) and 4k-1 (A065339) and on the highest power of 2 dividing n (A007814): a(n) = 2*A007814(n) + 2*A083025(n) + A065339(n) - T. D. Noe, Jul 14 2003 EXAMPLE 2 = (1+i)*(1-i), so a(2) = 2; 9 = 3*3, so a(9) = 2. a(1006655265000) = a(2^3*3^2*5^4*7^5*11^3) = 3*a(2)+2*a(3)+4*a(5)+5*a(7)+3*a(11) = 3*2+2*1+4*2+5*1+3*1 = 24. - Vladeta Jovovic, Jan 20 2003 MATHEMATICA Join[{0}, Table[f = FactorInteger[n, GaussianIntegers -> True]; cnt = Total[Transpose[f][[2]]]; If[MemberQ[{-1, I, -I}, f[[1, 1]]], cnt--]; cnt, {n, 2, 100}]] (* T. D. Noe, Mar 31 2014 *) PROG (PARI) a(n)=my(f=factor(n)); sum(i=1, #f~, if(f[i, 1]%4==3, 1, 2)*f[i, 2]) \\ Charles R Greathouse IV, Mar 31 2014 CROSSREFS Cf. A078908-A078911, A007814, A065339, A083025, A086275 (number of distinct Gaussian primes in the factorization of n). Cf. A239626, A239627 (including units). Sequence in context: A130584 A339046 A265911 * A033317 A183200 A326732 Adjacent sequences: A078455 A078456 A078457 * A078459 A078460 A078461 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jan 11 2003 EXTENSIONS More terms from Vladeta Jovovic, Jan 12 2003 STATUS approved
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Last modified May 23 04:06 EDT 2022. Contains 353959 sequences. (Running on oeis4.) | 1,095 | 2,452 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2022-21 | latest | en | 0.571069 |
https://discuss.interviewbit.com/t/why-for-input-3-1-there-is-only-one-path/16811 | 1,610,776,821,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703500028.5/warc/CC-MAIN-20210116044418-20210116074418-00518.warc.gz | 313,474,656 | 3,201 | # Why for input "3 1" there is only one path?
#1
As far as I understand there should be three different paths:
(0, 0) -> (0, 1) -> (1, 1) -> (2, 1) -> (3, 1)
(0, 0) -> (1, 0) -> (1, 1) -> (2, 1) -> (3, 1)
(0, 0) -> (1, 0) -> (2, 0) -> (2, 1) -> (3, 1)
Can someone explain this to me?
Thanks!
#2
for this input it means you have 3 rows and 1 column. so you only have cells (0,0),(1,0),(2,0) so u can only have one path which s going down | 189 | 441 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2021-04 | latest | en | 0.93012 |
https://stats.stackexchange.com/questions/348880/how-to-set-up-a-linear-system-to-interpolate-the-train-data-perfectly-with-gradi/348898 | 1,643,386,873,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320306301.52/warc/CC-MAIN-20220128152530-20220128182530-00284.warc.gz | 593,729,648 | 36,912 | # How to set up a linear system to interpolate the train data perfectly with Gradient Descent?
Consider a (consistent) regression problem (i.e. we are trying to predict a real valued function and we don't have inconsistencies in the way we map x's to y).
I am trying to perfectly fit/interpolate the (train) data set with Gradient Descent (to understand academically Gradient Descent better) with fixed step size:
$$w^{(t+1)} = w^{(t)} - \eta \nabla_w L(w^{(t)})$$
I've tried things empirically by minimizing L2 loss:
$$L(w) = \| Xw - y \|^2$$
I noticed that sometimes its hard to find the right step size such that the loss value $L(w)$ is zero within machine precision (fit/interpolate data in this sense https://arxiv.org/abs/1712.06559). I suspect that its highly dependent on the basis/kernels I use since the gradient and hessian are:
$$\nabla L(w) = 2(X^T X w - y)$$
$$\nabla^2 L(w) = X$$
I wanted to only use 1st order methods to solve this problem so I am wondering, how do I figure out a good step size and/or basis/feature matrix $X$ given that I want to solve this problem with first order method?
If I decide to use say, Hermitian polynomials, why would that be better than other polynomials for example if I want to fit/interpolate the data perfect?
What if I used a Gaussian Kernel or Lapacian Kernel? How would $X = K$ kernel matrix change and how would Gradient Descent be affected? How does the curvature change/get affected as I change the kernel matrix? How can I set up the problem so the optimization via (S)GD fits the data perfectly?
• Maybe I'm confused by your notation, but I don't think your equations are correct. The first one should have some term involving 'w' , else the second partials wrt w will be zero, meaning that nabla squared is zero. In the end the loss function should be quadratic in the w's and gradient descent should work for most choices of a learning rate.
– meh
May 30 '18 at 2:48
• @aginensky oh yea there was a typo, ooops! May 30 '18 at 16:57
• Incidentally, using the second derivative matrix allows one to use Newton
– meh
May 30 '18 at 17:22
• @aginensky yea I know I don't want to use Newton. This is an academic question of GD and least squares. May 30 '18 at 21:38
I think you may be overthinking this a little bit, basis functions need not to enter into the problem and will only confuse the issue if your goal is to understand gradient descent. If your goal is understanding kernels and basis functions, I think you'll be able to find a better problem. Off the bat, your gradient is incorrect which is probably the source of the issue that has you asking this question.
Let's take it from the top. The system is consistent so that we have $y=Xw$ for some weight vector $w$. For academic interest we decide to use gradient descent to minimize the $L_2$ distance between the vectors,
$\arg\min_w(L) =\arg\min_w \frac{1}{2}\|Xw-y \|_2^2$, and $\nabla_w L= X^T(Xw-y)$.
Our gradient descent recursion is as follows:
$w_{k+1} = w_k - \eta \nabla_w L$.
For a generic function L (ie not just least squares problems), you can calculate the optimal stepsize, as described in this informative answer. At the end of the day, provided $0<\eta < \frac{2}{\gamma}$, where $\gamma$ is the Lipschitz constant of the gradient, gradient descent will converge to a stationary point at a linear rate. Of course, if the function is poorly conditioned the constant could be very small and it may appear not to converge. This is shown formally in most optimization textbooks (Boyd/Vandenberghe, Nocedal/Wright), a quick reference can be found here.
I just read the comments on the other answer. You should note further that the optimality of the result is subject to the convexity of $L$. If it is strongly convex then gradient descent will converge almost surely to the true solution, but if it is nonconvex (ie not a least squares problem) GD may not converge to a global minimum.
You're more than likely not going to be able to interpolate the data perfectly for most function if they aren't smooth and have some noise in them.
1. Typically with Hermitian polynomials, Hermitian polynomials can be utilized to decrease the effects of Gibbs phenomenon.. They sometimes have better spacing I believe.
1. I believe that both of those kernels are ill-conditioned and maybe you'd have problems.
For some reason this isn't formatting right. Some edits here. It is well known that the Gaussian Kernel is ill-conditioned. Generally, the method around this is regularization. You recommended using gradient descent. You realize that gradient descent with ill-conditioning means that the convergence rate would be slow. I think you said SGD which can sometimes help with this.
• what do you mean they would be ill-conditioned? It doesn't matter if there are many solutions, (S)GD chooses the one with minimum norm. May 30 '18 at 16:58
• @Pinocchio (S)GD does no such thing ! It merely finds (approximately) points where the derivative is zero, i.e. local maxima and minima. In the case of least squares, there is a unique minma because the eqns are quadratic. In general, one has no way of knowing if the local extreme found by gradient descent are global extrema. Consider neural nets for example !
– meh
May 30 '18 at 17:21
• I stick by my comment that properly coded gradient descent will work.
– meh
May 30 '18 at 17:24
• I don't think in general it will fit any underlying function. It has to do with whether there is noise or not in the function. The question you're asking is can you learn any type of function with a given set of orthogonal basis functions. Well, it matters what type of basis functions and how. If the function is smooth you can definitely do it.
– user28896
May 30 '18 at 17:38
• @aginensky dude don't bring neural nets, thats not relevant. In the context that of this question. SGD finds minimum norm solution of course. May 30 '18 at 21:40 | 1,467 | 5,921 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2022-05 | latest | en | 0.919512 |
https://www.siyavula.com/read/science/grade-12/electrodynamics/11-electrodynamics-01 | 1,660,524,802,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572089.53/warc/CC-MAIN-20220814234405-20220815024405-00085.warc.gz | 851,897,922 | 9,644 | We think you are located in United States. Is this correct?
# Chapter 11: Electrodynamics
## 11.1 Introduction (ESCQ3)
In Grade 11 you learnt how a magnetic field is generated around a current-carrying conductor. You also learnt how a current is generated in a conductor that moves in a magnetic field or in a stationay conductor in a changing magnetic field. This chapter describes how conductors moving in a magnetic field are applied in the real-world.
Today, currents induced by magnetic fields are essential to our technological society. The ubiquitous generator—found in automobiles, on bicycles, in nuclear power plants, and so on—uses magnetism to generate current. Other devices that use magnetism to induce currents include pickup coils in electric guitars, transformers of every size, certain microphones, airport security gates, and damping mechanisms on sensitive chemical balances. Not so familiar perhaps, but important nevertheless, is that the behavior of AC circuits depends strongly on the effect of magnetic fields on currents.
Electrical machines - generators and motors:
• State the difference between generators and motors.
• Definition of Farady's Law.
• Using Farady's Law for explanations.
• Definition of a generator
• Explaining the principle of an AC and DC generator using words and pictures.
• Explaining the difference between AC and DC generators.
• Explains what happens when a current carrying coil is placed in a magnetic field.
• Explaining the principle of an electric motor using word and pictures.
• Definition of Lorent Force.
• Examples of AC and DC generators and the use of motors.
Alternating current:
• Explaining advantages of alternating current.
• Write different expressions.
• Definition of the root mean square values and explains why they are useful.
• Calculations done on the average power.
• Drawing of graphs.
• Solve different kinds of problems using alternating current.
temp text | 382 | 1,947 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2022-33 | longest | en | 0.887578 |
http://people.hsc.edu/faculty-staff/robbk/Math121/TI-83/TestMeanDiff.html | 1,552,931,385,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912201521.60/warc/CC-MAIN-20190318172016-20190318194016-00356.warc.gz | 158,592,793 | 1,652 | # TI-83 Instructions
## Testing Hypotheses Concerning the Difference between Means using Large Samples
### Method 1 - Data
1. Enter the data from the first sample into a list, say `L1`.
2. Enter the data from the second sample into another list, say `L2`.
3. Press `STAT`. The `STAT` menus appear and the `EDIT` menu title is highlighted.
4. Select the `TESTS` menu title. The `TESTS` menu appears.
5. Select `2-SampZTest`, item #3. A list of options appears.
6. On the first line are two options: `Data` and `Stats`. Use the arrow keys to select `Data`.
7. Press `ENTER`.
8. Press the down arrow once.
9. Enter the standard deviation of the first population, if it is known. Otherwise, enter the standard deviation of the first sample.
10. Press the down arrow once.
11. Enter the standard deviation of the second population, if it is known. Otherwise, enter the standard deviation of the second sample.
12. Press the down arrow once.
13. Enter the name of the list (`L1`) that contains the data from the first sample.
14. Press the down arrow once.
15. Enter the name of the list (`L2`) that contains the data from the second sample.
16. Press the down arrow three times, skipping over the `Freq` options.
17. Select the appropriate alternative hypothesis.
18. Press the down arrow once. The word `Calculate` begins to flash.
19. Press `ENTER`. The calculator will display
• The alternative hypothesis
• The value of the the test statistic z.
• The p-value of the test.
• The means of the two samples.
• The standard deviations of the two samples.
• The sizes of the two samples.
### Method 2 - Statistics
1. Follow Steps 3 - 5 in Method 1 above.
2. Use the arrow keys to select the `Stats` option.
3. Press `ENTER`.
4. Press the down arrow once.
5. Enter the standard deviation of the first population, if it is known. Otherwise, enter the standard deviation of the first sample.
6. Press the down arrow once.
7. Enter the standard deviation of the second population, if it is known. Otherwise, enter the standard deviation of the second sample.
8. Press the down arrow once.
9. Enter the mean of the first sample.
10. Press the down arrow once.
11. Enter the sample size of the first sample.
12. Press the down arrow once.
13. Enter the mean of the second sample.
14. Press the down arrow once.
15. Enter the sample size of the second sample.
16. Press the down arrow once.
17. Follow Steps 17 - 19 in Method 1 above. The calculator will display the information listed in Step 19 of Method 1. | 612 | 2,501 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2019-13 | longest | en | 0.727943 |
https://math.stackexchange.com/questions/1906596/about-pro-p-groups | 1,558,702,433,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232257624.9/warc/CC-MAIN-20190524124534-20190524150534-00437.warc.gz | 549,008,474 | 34,028 | # About pro-$p$ groups
Let $p$ be a prime number. A pro-$p$ group is the inverse limit of an inverse system of discrete finite $p$-groups. (I've just read the definition).
I have two questions:
1. Is it true that a the $p$-part of an abelian profinite group is a pro-$p$ group? (I think so)
2. How is an abelian pro-$p$ group a $\mathbb{Z}_p$-module?
• A pro-$p$-group need not to be commutative: in such a case, it is not a $\Bbb{Z}_p$-module. – Crostul Aug 28 '16 at 18:29
• @Crostul: ok, thanks. – user72870 Aug 28 '16 at 18:36
• You can see an inverse limit as a subgroup of the product of your inverse system (tell me if you need some reference for this). In this case, operations are defined componentwise. If all the groups are abelian, their profinite completion is abelian too. Since the elements of a $p$-group have order a power of $p$, I believe that finite abelian $p$-groups are naturally $\mathbb{Z}_p$-modules (can you guess the action?), so that their profinite completion should be a $\mathbb{Z}_p$-module too, again with componentwise operations. – 57Jimmy Aug 28 '16 at 20:09
• @57Jimmy: If a finite abelian group $A$ is of order $p^m$, then $\mathbb{Z}/p^m\mathbb{Z}$ acts on $A$ trought the rule $(k+p^m\mathbb{Z})a=ka$. And since $\mathbb{Z}_p=\varprojlim \mathbb{Z}/p^m\mathbb{Z}$ this defines also an action of $\mathbb{Z}_p$ on $A$. Right? – user72870 Aug 29 '16 at 9:19
• 1. How do you define "the p-part of a pro-p-group" ? Already for a finite group, you can only define its p-Sylow-subgroups. – nguyen quang do Aug 29 '16 at 12:33
## 1 Answer
EDITED: (I have inserted here at the top an answer to your first question.)
There is a $p$-part of an abelian profinite group $G$, but it’s not what you wanted to define it as. You must define it as $$G_p = \left\lbrace g\in G:\lim_{n\to\infty}g^{p^n}=e_G\right\rbrace\,.$$ You easily check that this $G_p$ is a subgroup of your abelian profinite group. Verification that $G_p$ is closed in $G$, thus compact, thus a profinite group, requires a few more words.
I’ll use additive notation in $G$, and use the letter $U$ for the open subgroups that define the topology of $G$. What is the condition that $g\in G_p$? \begin{align} g\in G_p&\Longleftrightarrow\forall U,\exists n_0\text{ such that }\forall n\ge n_0, p^ng\in U\\ &\Longleftrightarrow\forall U,\exists n\text{ such that }p^ng\in U\\ &\Longleftrightarrow\forall U,\exists n\text{ such that }g\in p^{-n}U\\ &\Longleftrightarrow g\in\bigcap_U\bigcup_np^{-n}U\, \end{align} Now, for a given U, this group $\bigcup_np^{-n}U$ is the total union of an ascending chain of opens, call it $U'$. It’s open, so closed, and we’re taking an intersection of closed subgroups $U'$, and that’s closed. Therefore compact, so a profinite group, and clearly a pro-$p$-group.
ORIGINAL POST FOLLOWS:
Here’s how an abelian pro-$p$-group $G$ is a $\Bbb Z_p$-module:
Let $z\in\Bbb Z_p$, and exhibit $z$ as a $p$-adically convergent sequence of positive integers, $z=\lim_in_i$. (If you like, you can take the $n_i$’s to be the partial sums in the standard representation of $z$ as a “power series in $p$”.) Now, for $g\in G$, define $g^z=\lim_ig^{n_i}$. You need to prove a few things, but they’re easy enough.
Note that the definition of this operation had nothing to do with abelianness of $G$: it’s always defined on a pro-$p$-group. It’s just that you don’t get a module structure without the abelian condition.
• Thank you! Do you think is it positive the answer to the question (1)? So I can accept your answer. – user72870 Sep 1 '16 at 23:17
• How do you define the $p$-part? – Lubin Sep 2 '16 at 2:34
• If $G$ is an abelian group, I define the $p-$part of $G$ as $\{x\in G\mid \exists n\in \mathbb{N}, \text{ord}(x)=p^n\}$ – user72870 Sep 2 '16 at 8:23
• But in a profinite group, most elements are not torsion. Consider $\widehat{\Bbb Z}$, where there is no torsion but your $p$-part is a copy of $\Bbb Z_p$. – Lubin Sep 2 '16 at 13:01
• Are you saying that it makes much more sense to define the $p$−part of a profinite abelian group $G=\varprojlim G_i$ as the inverse limit of the $p-$Sylow of $G_i$? (I know that one should prove the existence of such inverse limit) – user72870 Sep 2 '16 at 18:29 | 1,370 | 4,229 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2019-22 | latest | en | 0.833421 |
https://landgreen.github.io/physics/notes/electromagnetism/charge/ | 1,718,367,797,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861546.27/warc/CC-MAIN-20240614110447-20240614140447-00355.warc.gz | 326,047,755 | 7,459 | # Electric Charge
If you rub two materials together, sometimes the materials get opposite charges. This effect is longer lasting in dry weather because the water in the air allows the charges to return to equilibrium.
Experiment: Try rubbing a balloon on your hair and then putting the balloon near an empty soda can. You are strongly encouraged to setup a race between two balloon powered soda cans.
Experiment: Try sticking two strips of scotch tape together and quickly pealing them apart. The strips should now be oppositely charged. As you bring them near each other, they should be attracted.
Try repeating the experiment again to make 4 strips of tape. Put the newly charged tape near the old and some will repel instead of attract.
Question: After playing with the tape what factors determine the strength of the force?
The force between the tape strips is strong when they are closer.
The force also varies with how much charges is separated. Separating more charge is easier when the humidity is lower.
Some particles have an electric charge. The rules that govern these charges can explain electricity, chemical bonds, magnetism, and light!
Electric charge determines the magnitude and direction of the electrostatic force. Charge has a role in the electrostatic force similar to mass's role in gravity.
opposite charges have an attractive force
negative charges have a repulsive force
positive charges have a repulsive force
neutral charges have no force
Charge can be neutralized. If a positive and negative charge are close together the attractive and repulsive forces mostly cancel each other out. This explains why we don't notice the electrostatic forces from neutral atoms.
Electric charge can't be created or destroyed. Like energy and momentum, electric charge is conserved.
The evidence for this conservation law is based on repeated experiments. No one has ever documented the total charge of a system increasing or decreasing. Charged particles can be created and destroyed, but only when another particle is created or destroyed to balance out the total charge
## Elementary Electric Charge
In 1909 Robert Millikan and Harvey Fletcher performed the oil drop experiment to investigate electric charge. They sprayed a fine mist of oil into a uniform electric field. The electric field produced a force on some of the oil droplets. Based on that force, they found that charge only came in even multiples of about 1.6 × 10−19 C.
This evidence helped build our modern model of the atom: negative electrons bound to a nucleus of positive protons and neutral neutrons. Most charge comes from electrons and protons, but there are also more exotic particles.
electron
charge = −1.602 × 10−19 C
mass = 9.109 × 10−31 kg
proton
charge = +1.602 × 10−19 C
mass = 1.672 × 10−27 kg
Example: These 6 values were recorded for electric charge. Which of the measurements are probably inaccurate? Why?
+3.2 × 10−19 C
−2.4 × 10−19 C
−8.0 × 10−19 C
+1.6 × 10−19 C
+5.2 × 10−19 C
−0.4 × 10−19 C
strategy
Charge only comes in even multiples of ±1.6 × 10−19 C.
You can't have half a charge, but you could have 3 charges.
solution
Charge has only been observed in packets of 1.602 × 10−19 C. Any recorded charge must be a multiple of this value.
$$\frac{3.2 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = 2.0$$
$$\frac{2.4 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = \cancel{1.5}$$
$$\frac{8.0 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = 5.0$$
$$\frac{1.6 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = 1.0$$
$$\frac{5.2 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = \cancel{3.25}$$
$$\frac{0.4 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = \cancel{0.25}$$
Example: How many electrons make up -4.5 C of charge?
solution
Use a conversion fraction with 1 electron and the charge on an electron.
$$-4.5 \, \mathrm{C} \left(\frac{1 \, \mathrm{e^-}}{-1.6 \times 10^{−19} \, \mathrm{C}}\right) = 2.81 \times 10^{19} \, \mathrm{e^-}$$
Example: How much charge would 234 trillion electrons have?
solution $$234 \times 10^{12} \, \mathrm{e^-} \left(\frac{-1.6 \times 10^{−19} \, \mathrm{C}}{1 \, \mathrm{e^-}}\right) = -3.744 \times 10^{-5} \, \mathrm{C}$$
## Conductivity
Conductive materials allow electric charges to easily move through them. If a charge is applied to one part of a conductive material the charge will quickly spread out because like charges repel.
These simulations don't include the nuances of quantum mechanics, they only show a cartoony approximation of conductivity.
In some materials, current is understood as the flow of an electron hole. This model of current helps us understand the semiconductors used in solar panels, LEDs, and transistors.
In chemistry, elements are roughly divided into metals, metalloids and nonmetals. Metals are held together by loosely sharing their outer valence electrons. The cloud of free flowing electrons give metals most of their shared characteristics, like conductivity.
insulators
vacuum, nonmetals: gases, plastics, silk, fur
electrolytes
solvents with dissolved ions:
salt water, tap water, soda water
semi-conductors
metalloids: carbon and silicon
conductors
metals, plasma
superconductors
certain low temperature ceramics
Question: Rank these substances by conductivity:
### air, coca cola, copper, carbon, plastic fork
high conductivity
copper (conductor)
carbon (semi-conductor)
coca cola (electrolyte)
plastic fork (insulator)
air (insulator)
low conductivity
Question: Why are metals more conductive than nonmetals?
In metals some electrons are free to move between atoms. In nonmetals the electrons are locked up in covalent bonds so they resist the electrostatic force.
Another way to make a substance conductive is to heat it up so much that electrons can leave the nucleus. We call this state of matter a plasma.
The positive charges on the left polarize the "atoms" on the right, but not enough to get the negative charges to jump over.
Question: Why can't the negative charges spread out into the positive charge group on the left?
The electrostatic force follows a 1/r² rule, so it is weaker with distance. The negative charges would be more stable if they could join the positive charge, but the nearby positive charges have a stronger force.
Add a conductive for the negative charges.
## Static Electricity
It's easy to separate a couple trillion electrons from their protons by walking with socks on a carpet. Lightning is produced in a similar way when a cloud with rising air ends up with an unbalanced distribution of charge.
Static electricity occurs when there is an imbalance of electrons and protons. A lasting charge separation can only occur in insulating materials, because in conductors positive and negative charges quickly pair up.
Static electricity effects are much stronger and longer lasting in low humidity. This is because water molecules increase the conductivity of air, allowing more separated charges to return.
Play around with this PhET simulation for static electricity.
Question: Which are conductors and which are insulators?
(balloons, sweater, wall, air)
conductors: nothing in this simulation
insulators: balloon, sweater, wall, air
Question: Why do some electrons jump to the balloon from the sweater?
Why not the other way around?
Some materials are better at holding onto extra electrons for complex quantum mechanical reasons.
Question: Why is the balloon attracted to the sweater after it gains some electrons?
After rubbing, the balloon has unpaired negative charge, and the sweater has unpaired positive charge. Opposite charges attract.
Question: Why is the balloon attracted to the wall after it gains some electrons?
After rubbing, the balloon has unpaired negative charge. When charge is near another insulator it repels the electrons enough that they are slightly farther away, but not enough to cause them to leave the nucleus. This charge separation is called polarization.
The polarization of the positive and negative pairs creates an induced charge. The charged balloon causes the wall to polarize, which increases the attraction and decreases the repulsion between the balloon and wall.
A TriboElectric Series lists which materials will become electrically charged after they are rubbed together.
Question: If you rubbed polystyrene foam (styrofoam) on a cat, static electricity would cause them stick together. Which would gain a positive charge? | 2,080 | 8,562 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2024-26 | latest | en | 0.944857 |
https://cheatsheeting.com/show.html?sheet=megabit-to-bit-conversions | 1,674,868,847,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499468.22/warc/CC-MAIN-20230127231443-20230128021443-00180.warc.gz | 186,653,051 | 9,114 | Home > Conversions (Computer data storage) > Conversion tables from/to megabit > Mb to bit Conversion Cheat Sheet (Interactive)
To build or customize your cheat sheet (table below) adjust the values (From, Step, Decimals) in this form and hit the Update button. You could also enter the values to convert and print directly on the table From: Step: Decimals: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[Formula: bit = Mb x 1048576] [Printer friendly] [Bits to Megabits]
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# Megabits to Bits Conversion Table
Mb = 1048576 bit
# How to convert from Megabits to Bits
Since 1 megabit is equal to 1048576 bits, we could say that n megabits are equal to 1048576 times n bits. In other words, we could use the following formula:
bits = megabits x 1048576
For example, let's say that we want to convert 2 megabits to bits. Then, we just replace megabits in the abovementioned formula with 2:
bits = 2 x 1048576
That is, 2 megabits are equal to 2097152.0 bits. | 616 | 1,608 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2023-06 | latest | en | 0.223929 |
https://ebrary.net/60340/computer_science/exercises | 1,631,817,190,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780053717.37/warc/CC-MAIN-20210916174455-20210916204455-00499.warc.gz | 281,630,577 | 8,755 | # EXERCISES
• 1. What is the most probable value under a univariate Gaussian distribution? What is its probability?
• 2. Use the joint probability rule to argue that a multivariate Gaussian with diagonal covariance is nothing but the product of univariate Gaussians.
• 3. Show that the average is also the MLE for the parameter of the Poisson distribution. Explain why this is consistent with what I said about the average of the Gaussian distribution in Chapter 1.
• 4. Fill in the components of the vectors and matrices for the part of the multivariate Gaussian distribution:
• 5. Derive the MLE for the covariance matrix of the multivariate Gaussian (use the matrix calculus tricks I mentioned in the text).
• 6. Why did we need Lagrange multipliers for the multinomial MLEs, but not for the Guassian MLEs?
• 7. Notice that I left out the terms involving factorials from the multinomial distribution when I calculated the LRT. Show/explain why these terms won’t end up contributing to the statistic. | 229 | 1,006 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2021-39 | latest | en | 0.892258 |
https://crypto.stackexchange.com/questions/44216/determine-whether-bit-sequence-is-hash | 1,701,694,897,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100529.8/warc/CC-MAIN-20231204115419-20231204145419-00519.warc.gz | 252,662,133 | 42,900 | # Determine whether bit sequence is hash?
I would like to know whether it is possible to determine whether a value of for example 256 bit length is a SHA-256 hash or a random, equally distributed value. Is there any research related to common hash functions? Can this property be derived from the avalanche effect?
I would like to know because I would like to include plain text hash values in a steganographic medium, where the stegosystem bases on white noise to be turned into sentences, with number of words per sentences, that have the same distribution of length as usual in this language. Encryption of the hash values is not possible, because at that point of the designed protocol, no key exchange has been performed, yet.
Thank you for all answers or questions related to this problem.
The point of a hash is that the slightest change in input has a cascading change on the resulting hash. With a hashing algorithm like SHA-256, it is designed to behave like a random oracle, which should provide a high amount of entropy, simliar to that of randomly generated numbers.
If you look at some of the applications of SHA256 today, they depend on the output values being randomly distributed.
A SHA-256 hash is, until broken by cryptanalysis, indistinguishable from 256 bits of random noise. The only way to defeat this is by enumerating inputs until you find a matching hash.
If there isn't much entropy in the input (e.g., it's an English word, or it's a value that repeats), it will be relatively simple for an attacker to distinguish it from random noise and possibly even determine the data that was originally hashed.
• Thank you for fast answer! Rated positive, but don't have enough reputations yet. Feb 26, 2017 at 23:07
• I have to point out that by enumerating inputs you are guarantee to find that hash, whatever the hash value is Feb 27, 2017 at 9:04
• @GianlucaGhettini I think it's important to note that it might take a while to enumerate all possible inputs. And that the value you find might not be the original value that was put in - at the very least, if you hash 2^256 values producing distinct outputs, the (2^256)+1th value will be a collision. Feb 27, 2017 at 12:41
• @GianlucaGhettini True but to add on to Matthew's comment on average it will take you on the order of 5 years of the sun's total energy output to succeed at a brute force attack on a random 256 bit hash. So unless you are part of at least a Kardashev type II civilization you probably don't want to get your hopes up.
– DRF
Feb 27, 2017 at 13:55
• @GianlucaGhettini I think it is not necessarily guaranteed that each 265-bit value actually has a preimage ... it could be that some are never hit. (Related: crypto.stackexchange.com/q/301/58) Feb 27, 2017 at 14:12 | 659 | 2,768 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2023-50 | latest | en | 0.940868 |
http://www.numbersaplenty.com/212304 | 1,590,467,564,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347390442.29/warc/CC-MAIN-20200526015239-20200526045239-00319.warc.gz | 177,572,413 | 3,635 | Search a number
212304 = 2434423
BaseRepresentation
bin110011110101010000
3101210020010
4303311100
523243204
64314520
71542651
oct636520
9353203
10212304
11135564
12a2a40
1375831
1457528
1542d89
hex33d50
212304 has 20 divisors (see below), whose sum is σ = 548576. Its totient is φ = 70752.
The previous prime is 212297. The next prime is 212353. The reversal of 212304 is 403212.
Adding to 212304 its reverse (403212), we get a palindrome (615516).
It can be divided in two parts, 21 and 2304, that multiplied together give a palindrome (48384).
212304 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.
It is a Harshad number since it is a multiple of its sum of digits (12).
It is a self number, because there is not a number n which added to its sum of digits gives 212304.
It is a congruent number.
It is an unprimeable number.
212304 is an untouchable number, because it is not equal to the sum of proper divisors of any number.
It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2164 + ... + 2259.
2212304 is an apocalyptic number.
212304 is a gapful number since it is divisible by the number (24) formed by its first and last digit.
It is an amenable number.
212304 is an abundant number, since it is smaller than the sum of its proper divisors (336272).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
212304 is a wasteful number, since it uses less digits than its factorization.
212304 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 4434 (or 4428 counting only the distinct ones).
The product of its (nonzero) digits is 48, while the sum is 12.
The square root of 212304 is about 460.7645819722. The cubic root of 212304 is about 59.6558070738.
The spelling of 212304 in words is "two hundred twelve thousand, three hundred four", and thus it is an iban number. | 560 | 2,005 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2020-24 | latest | en | 0.891993 |
https://forum.processing.org/two/discussion/22114/minimum-distance-step-movement-for-orbiting-circle | 1,624,485,664,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488540235.72/warc/CC-MAIN-20210623195636-20210623225636-00385.warc.gz | 255,639,627 | 13,439 | #### Howdy, Stranger!
We are about to switch to a new forum software. Until then we have removed the registration on this forum.
# Minimum distance step movement for orbiting circle
edited April 2017
I've partly borrowed some code that creates a 'clock' by splitting 360 degrees around the center of the screen into 12 steps. While the circle does 'jump' between steps, the 'jumping' behaviour doesn't work the way it is supposed to. The problem is that the circle will only jump forward by one step, if the angle of the mouse is >= the angle of the step, and it jumps backwards a step as soon as the mouse angle goes below the angle of the step.
I've through various different methods tried (and failed) to create an effective method to make the stepping circle jump to the step which angle is closest to the angle of the mouse, so that it would jump step 1 when the angle was greater than 15 degrees and less than 45.
Any ideas?
(Also: I am for some reason completely unable to format the code into the forum(???) so i've uploaded it to github): github.com/xtxte/RebelScum/blob/master/sketch_170325b.pde
Tagged:
• to format the code, edit your post, highlight the code, press ctrl-o.
i must've written those words 100000 times.
``````float rad; //radius of circle
PVector vCent, vMouse;
float angle1;
final float half=0.5;
int step;
float stepAngle;
final float twelve=12;
float cxubx;
float cyubx;
float ccx;
void setup() {
fullScreen();
fill(255);
vCent= new PVector(0, -height*half); //Straight upwards
ccx=half*width;
}
void draw() {
background(0);
translate(width/2, height/2);
vMouse= new PVector(mouseX-width/2, mouseY-height/2);
fill(#FFB803);
angle1=(mouseX<=ccx) ? 360-degrees(PVector.angleBetween(vCent, vMouse)) : degrees(PVector.angleBetween(vCent, vMouse));
step=int(map(angle1, 0, 360, 0, twelve)); //dividing 360 degrees into 12 steps
if (step==12) {
step=0;
}
stepAngle=((step / twelve) * TWO_PI);
fill(#2303FF);
fill(255);
textSize(34);
text("mouseangle;"+angle1, 100, 100);
text("step:"+step, 100, 150);
text("stepangle:"+degrees(stepAngle), 100, 200);
}
``````
• edited April 2017
I know exactly what you mean and have an idea for how to solve it that I know works as I'we done it years ago, but it wasn't in processing or even for mouse,
actually it was for a xbox 360 controller, and 8 steps rather than 12,
but the principle should be the same, you check the "change of rotation" in steps and add it to the clock, rather than direct the clock towards the mouse.
Something like this..
``````stepchange=step-pstep;
if(abs(stepchange)>=2){
clockstep+=stepchange+((stepchange>0)?-1:1);
previous_step=step;
}
``````
You need a special case for when it goes from 12 to 1 and vice versa
Also having 36 mouse steps and 12 clock steps would help
• solution to this was to use round() instead of int() when mapping the angles | 773 | 2,866 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2021-25 | longest | en | 0.794117 |
http://www.traditionaloven.com/tutorials/distance/convert-japan-ri-unit-to-nail-cloth-length-unit-measure.html | 1,529,956,527,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267868876.81/warc/CC-MAIN-20180625185510-20180625205510-00476.warc.gz | 493,461,968 | 11,709 | Convert 里 to nail | Japanese ri to cloth nails
# length conversion
## Amount: 1 Japanese ri (里) of length Equals: 68,718.68 cloth nails (nail) in length
Converting Japanese ri to cloth nails value in the length units scale.
TOGGLE : from cloth nails into Japanese ri in the other way around.
## length from Japanese ri to cloth nail Conversion Results:
### Enter a New Japanese ri Amount of length to Convert From
* Whole numbers, decimals or fractions (ie: 6, 5.33, 17 3/8)
* Precision is how many numbers after decimal point (1 - 9)
Enter Amount :
Decimal Precision :
CONVERT : between other length measuring units - complete list.
Conversion calculator for webmasters.
## Length, Distance, Height & Depth units
Distance in the metric sense from any two A to Z points (interchangeable with Z and A), also applies to physical lengths, depths, heights or simply farness. Tool with multiple distance, depth and length measurement units.
Convert length measuring units between Japanese ri (里) and cloth nails (nail) but in the other reverse direction from cloth nails into Japanese ri.
conversion result for length: From Symbol Equals Result To Symbol 1 Japanese ri 里 = 68,718.68 cloth nails nail
# Converter type: length units
This online length from 里 into nail converter is a handy tool not just for certified or experienced professionals.
First unit: Japanese ri (里) is used for measuring length.
Second: cloth nail (nail) is unit of length.
## 68,718.68 nail is converted to 1 of what?
The cloth nails unit number 68,718.68 nail converts to 1 里, one Japanese ri. It is the EQUAL length value of 1 Japanese ri but in the cloth nails length unit alternative.
How to convert 2 Japanese ri (里) into cloth nails (nail)? Is there a calculation formula?
First divide the two units variables. Then multiply the result by 2 - for example:
68718.6828919 * 2 (or divide it by / 0.5)
QUESTION:
1 里 = ? nail
1 里 = 68,718.68 nail
## Other applications for this length calculator ...
With the above mentioned two-units calculating service it provides, this length converter proved to be useful also as a teaching tool:
1. in practicing Japanese ri and cloth nails ( 里 vs. nail ) values exchange.
2. for conversion factors training exercises between unit pairs.
3. work with length's values and properties.
International unit symbols for these two length measurements are:
Abbreviation or prefix ( abbr. short brevis ), unit symbol, for Japanese ri is:
Abbreviation or prefix ( abbr. ) brevis - short unit symbol for cloth nail is:
nail
### One Japanese ri of length converted to cloth nail equals to 68,718.68 nail
How many cloth nails of length are in 1 Japanese ri? The answer is: The change of 1 里 ( Japanese ri ) unit of length measure equals = to 68,718.68 nail ( cloth nail ) as the equivalent measure for the same length type.
In principle with any measuring task, switched on professional people always ensure, and their success depends on, they get the most precise conversion results everywhere and every-time. Not only whenever possible, it's always so. Often having only a good idea ( or more ideas ) might not be perfect nor good enough solution. If there is an exact known measure in 里 - Japanese ri for length amount, the rule is that the Japanese ri number gets converted into nail - cloth nails or any other length unit absolutely exactly.
Conversion for how many cloth nails ( nail ) of length are contained in a Japanese ri ( 1 里 ). Or, how much in cloth nails of length is in 1 Japanese ri? To link to this length Japanese ri to cloth nails online converter simply cut and paste the following.
The link to this tool will appear as: length from Japanese ri (里) to cloth nails (nail) conversion.
I've done my best to build this site for you- Please send feedback to let me know how you enjoyed visiting. | 879 | 3,849 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2018-26 | latest | en | 0.850713 |
https://math.stackexchange.com/questions/2651744/axlers-ladr-algebraic-multiplicity-of-an-eigenvalue-is-the-number-of-times-it | 1,563,525,427,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526153.35/warc/CC-MAIN-20190719074137-20190719100137-00537.warc.gz | 465,033,068 | 35,665 | # Axler's LADR. Algebraic multiplicity of an eigenvalue is the number of times it appears on the diagonal of an upper triangular matrix?
This problem is from Sheldon Axler's Linear Algebra Done Right, Chapter 8. Let $T \in \mathcal{L}(V)$, where $V$ is a finite dimensional complex vector space. If the matrix of $T$ is upper triangular with respect to any basis of $V$, the number of times $\lambda$ appears on the diagonal of this matrix equals the (algebraic) multiplicity of $\lambda$ as an eigenvalue of $T$.
It suffices to show that $\dim \text{null } T^n = \dim G(0, T)$ equals the number of $0$'s on the diagonal, where $G(0, T)$ is the space of generalized eigenvectors of $T$ with respect to $0$.
I found this rather nice proof on this blog, which uses induction on the dimension of $V$.
I'm interested in finding alternative ways to prove this statement, which may provide a different way of looking at it.
• +1, this was the unique exercise in the whole book that I couldnt solve. I found the same proof using induction over the dimension of $V$. – Masacroso Feb 15 '18 at 14:27
• I am puzzled, if you take $\det(T-\lambda I_n)$, you will see the factor $(\lambda-\alpha)$ in the result exactly as many times $\alpha$ appears on the diagonal - simply because the determinant of a triangular matrix is the product of the entries on the diagonal. Where is the catch? In other words, why even talk about generalised eigenvectors? – user491874 Feb 15 '18 at 14:47
• @user8734617 Axler's book defines the multiplicity of $\lambda$ as the dimension of $G(\lambda, T)$ and the characteristic polynomial as $(z - \lambda_1)^{d_1}\cdots(z - \lambda_m)^{d_m}$ where $\lambda_1,\dots,\lambda_m$ are the distinct eigenvalues of $T$, and $d_1,\dots,d_m$ their corresponding multiplicities. It's only later in the book that he shows that the more familiar definition of the characteristic polynomial involving determinants is equivalent to this one. – Anu Feb 15 '18 at 14:51
• @Anu I see, thanks! – user491874 Feb 15 '18 at 15:14 | 544 | 2,033 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2019-30 | longest | en | 0.892885 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/chapter-11-11-7-probability-11-7-exercises-page-834/33 | 1,720,799,571,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514404.71/warc/CC-MAIN-20240712125648-20240712155648-00802.warc.gz | 579,091,187 | 12,653 | ## Algebra and Trigonometry 10th Edition
$\frac{2}{5}$
We know that $probability=\frac{\text{number of favourable outcomes}}{\text{number of all outcomes}}$ The total number of outcomes is $6\cdot5=30$ because we can select any of the marbles as the first one and then any of the marbles that we have not selected as the first one. The number of favourable outcomes is $4\cdot3=12$ because we can select any of the non-yellow marbles as the first one and then any of the non-yellow marbles that we have not selected as the first one. Hence the probability here is: $\frac{12}{30}=\frac{2}{5}$ | 156 | 593 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-30 | latest | en | 0.917772 |
https://web2.0calc.com/questions/trig-identities_10 | 1,606,602,974,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141195929.39/warc/CC-MAIN-20201128214643-20201129004643-00330.warc.gz | 554,249,762 | 5,504 | +0
# Trig Identities
0
141
1
+104
Angle α lies in quadrant II , and tanα=−12/5 . Angle β lies in quadrant IV , and cosβ=3/5 . What is the exact value of cos(α−β) ?
Apr 1, 2020
#1
+21957
+1
cos(a - b) = cos(a)·cos(b) + sin(a)·sin(b)
Since tan(a) = -12/5 and is in quadrant II, sin(a) = 12/13 and cos(a) = -5/13
(It's a 5-12-13 right triangle, with x-value negative and y-value positive.)
Since cos(b) = 3/5 and is in quadrant IV, sin(b) = -4/5.
(It's a 3-4-5 right triangle, with x-value positive and y-value negative.) | 212 | 539 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2020-50 | latest | en | 0.700902 |
https://www.piramalfinance.com/vidya/how-emi-calculator-plays-an-important-role-in-calculating-personal-loan-amount/ | 1,713,668,361,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817699.6/warc/CC-MAIN-20240421005612-20240421035612-00472.warc.gz | 857,182,202 | 11,773 | Personal Loan
# How EMI Calculator Plays An Important Role In Calculating Personal Loan Amount?
Borrow
08-11-2023
A personal loan EMI calculator is a tool that calculates the amount of money that you must pay to the bank each month on a certain loan. You can figure out how much you’ll have to pay monthly on loans from distinct banks and NBFCs. You may do this by putting the principal sum, interest rate, and loan period into the online tool. A personal loan EMI calculator will determine the sum you must repay the bank in monthly payments.
EMI calculators may also assist you in grasping the loan’s interest. You may use them to compute EMIs for all types of personal loans, like auto, house, and personal loans. It assists you in making wise financial decisions. Continue reading to learn about the perks of using a personal loan EMI calculator when planning to apply for a personal loan.
## How to Use an EMI Calculator?
A personal loan EMI calculator is easy to use. It has charts and gives quick results. Given below is the list to find loans using a personal loan EMI calculator:
• The principal amount (in Rupees).
• Term of Loan (in months or years).
• Interest Rate (percentage).
• Unpaid EMIs or Pre-paid EMIs (for car loans only).
You can adjust the values using a slider. If you want exact values, you can directly type them. A personal loan EMI calculator will find the amount of your EMI when you change the value.
For a better understanding, let’s take an example:
• Borrowed amount – Rs. 5 lakhs from a bank.
• Rate of interest -10.5% annually.
• Tenure of loan – 5 years (60 months).
Then, the EMI =
Rs. 5,00,000 x 0.00875 * (1 + 0.00875)120 / ((1 + 0.00875)60 – 1) = Rs. 10,869
This means that you will have to pay Rs. 10,869 every month for 60 months to repay the entire loan amount.
The total amount payable will be Rs. 10,869 x 60 = Rs. 6,52,140, which includes Rs. 1,52,140 as interest toward the loan.
## Features of a Personal Loan EMI Calculator
1. Helps Pick Offers in Terms of Cost
Choosing offers is one of the reasons to get help from a personal EMI loan calculator. You can compare offers easily because of how simple it is to use an EMI calculator. You may review the repayment details. There are many loan term options that may fit your needs.
1. Exact Outcomes
The quality of the findings is one of the major perks of using the personal loan EMI calculator. There is always the chance of wrong data when using a manual system to determine how much rate is due. You do not need to use a pencil and paper and risk miscalculating the rate due. Also, you do not need to sit down and manually test many rate pairings, desired loan rates, & loan tenures.
1. Saves Time
One of the main perks of using the Loan EMI system to calculate personal loan EMI is that it saves time by providing quick and precise answers. A personal loan EMI calculator is available online, saving time and effort to go to the bank and wait for your loan EMI to be computed.
1. Removes The Need For a Manual Sum
The EMI calculator’s user-friendly interface assists you in avoiding complex sums. To find the EMI amount, just input the desired loan balance, the loan rate, and the loan tenure. This saves you the time and effort of using the EMI formula manually. It should be noted that using the formula would need more work. It is also more time-consuming. You will need to convert data to fit the criteria of the equations in use.
1. Makes Loan Planning Easier
Personal loan EMI calculators are intended to assist you in figuring out how much interest and the total is due on a certain loan sum. Due to their ease of use, personal loan EMI calculators are now the main method of calculating EMIs. Also, a loan EMI calculator doesn’t merely show how much EMI is due. It also offers you a repayment schedule/table for the life of the personal loan. A repayment plan may seem formal, but it refers to a plan or table that shows a split of the loan sum you must repay throughout the term.
The repayment table displays the precise interest rate due each month until the loan is paid off. During the loan term, the sums in the repayment plan are equal. Having access to this table might help you plan out your loan instalments ahead of time and avoid late payments. It assists you in evaluating your lifestyle & financial demands and determining how you will put away the allotted EMIs for loan repayment. Paying off a loan on time might be hard if you don’t prepare.
## Process To Calculate Personal Loan EMI with an Online EMI Calculator
There are many steps to calculate the personal loan EMI. These are as follows:
• Step 1: Visit any reliable website.
• Step 2: Click on the calculator tab to access the EMI calculator.
• Step 3: Decide the type of loan needed. This may be a house loan, a personal loan, a vehicle loan, and so on.
• Step 4: You must now provide the proper details. This includes the loan amount, principle, rate, and loan time.
• Step 5: The EMI calculator will show the payable EMI amount after entering the details.
• Step 6: You may try other combinations to find the best fit EMI amount.
## Conclusion
Loans are now a vital part of many lives. They help in reaching specific life goals. EMI is the most vital term to keep in mind when it comes to loans. There are many personal loan EMI calculators that you can use to calculate loan EMI. This includes personal loan calculators, home loan calculators, and business loan calculators. They may be used to calculate the personal loan EMI of various loans.
When you enter the needed data into an EMI calculator, it makes calculations based on the EMI calculation formula. Then, it provides the EMI you must pay monthly in seconds. If you want to know more about personal loan EMI calculators, visit Piramal Finance. You may also explore their products and services.
Know More
Know More | 1,372 | 5,892 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2024-18 | latest | en | 0.918275 |
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Mar6 comment How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? good tricky and mnemonic way! Mar6 accepted How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? Mar4 comment How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? @Arturo: thanks for editing, english is not my main language! Mar4 comment How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? i didn't know exactly what are best tags for this post Mar4 asked How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? Feb9 accepted how many bits to write $\sqrt x$? Feb7 awarded Critic Feb7 awarded Teacher Feb7 answered how many bits to write $\sqrt x$? Feb7 comment how many bits to write $\sqrt x$? ohu yeah ross, i've got the point and i was writing last comment while you get me the solutions! thanks to all! Feb7 comment how many bits to write $\sqrt x$? mhmmm one moment.. no! $\sqrt x$ is long..$\sqrt x$! so the formula is $log_2 \sqrt x$ = $\frac{log x}{2}$ Feb7 comment how many bits to write $\sqrt x$? @Yuval: "how big can $\sqrt x$ be" is the point :-) sure more less that $\frac{x}{2}$.. i can't see a link with exponential.. the problem is that i don't manage to solve $log^{\frac{1}{2}}x$. Feb7 awarded Editor Feb7 revised how many bits to write $\sqrt x$? added 27 characters in body Feb7 asked how many bits to write $\sqrt x$? Feb7 accepted clarification on Chernoff's inequality Feb7 comment clarification on Chernoff's inequality thanks for your response, but i'm quite new in probability.. could you be a little more verbous? Feb5 asked clarification on Chernoff's inequality Feb3 awarded Commentator Feb3 comment RSA in plain English @yuval, you mistook me for a native speaker?? ohu, this is a compliment! ; ) | 488 | 1,995 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2015-18 | longest | en | 0.909371 |
https://www.aopa.org/news-and-media/all-news/2022/june/flight-training-magazine/character-counts-windsock | 1,656,167,339,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103035636.10/warc/CC-MAIN-20220625125944-20220625155944-00464.warc.gz | 718,787,454 | 22,569 | # Character counts
## The windsock tells you more than speed and direction
As Clint Eastwood (Harry Callahan in Dirty Harry) said, “A man’s got to know his limitations,” and that applies to pilots, too.
Every airplane has a placarded maximum demonstrated crosswind for landings, and the same is true of every pilot. Our individual wind skills are a function of training, experience, common sense, and confidence, and every pilot possesses a different combination of those factors. However, when training is combined with real-life, head-to-head wrestling with winds they would normally avoid, pilots can learn to handle far more wind than they think they can. Understanding what the windsock is telling you is one of the mental skills necessary to do that.
In addition to the speed and direction, the windsock tells you what skills will be needed and how hard you’re going to have to work to make the flight comfortable.
How do we read velocity in a windsock?
A standard FAA windsock won’t be picked up from hanging until it is seeing three knots or so. It will be fully extended at 15 knots, although there are some 20- and 25-knot socks out there. Generally, if the windsock has alternating white and orange bands around it, each band represents three knots of wind. The number of bands from the pole to the band where the sock bends down gives the speed in three-knot increments. However, most socks are a single color, usually orange for increased visibility. In that case, estimate how much of the length is straight out and how much is bent, and determine what percentage that is of 15 knots.
Wind seldom flows smoothly like the wide river people like to think it does. The wind-river almost always contains invisible eddies and swirls.If you see a sock so stiff that it looks as if it is made of sheet metal, that’s nature’s way of telling you to leave your bird in the barn.
Wind stability, gusts, and gusts
A windsock that points in one direction and pretty much stays there is one thing. One that is continually waving around is a different matter.
As the wind changes direction, the wind experienced on the nose of the airplane changes with it. If the changes are slow and smooth, they have an almost unnoticeable effect in the cockpit. If, however, the changes, right and left, are much faster and across a wider angle, then the airplane will continually require attention to keep the nose where you want it.
Illustration by Charles Floyd
These changes in wind direction are not to be confused with gusts. True gusts are a sudden change in wind speed that could be likened to an ocean wave rolling in. In front of the wave, there is no indication it’s coming. Then it rapidly peaks, hits us, then just as rapidly disappears. All gusts are built around that concept. However, the character of gusts can vary wildly, and these differences are clearly shown in the way the windsock reacts.
Gusts are numerically quantified on the ATIS, AWOS, or ASOS broadcast, but not all airports have automated weather reports. So, depend on the windsock for gust info. When the wind is whipping the sock from slack to stiff and back again, it’s next to impossible to categorize it with a specific number. However, you can develop an eye for the motions and mentally catalog them as being high or low, a threat or a nuisance. Do they look violent or just pesky? That’s a relative comparison that can only be made after spending some time studying the sock and comparing what you see to what you’ve seen in the past.
The wind may be reported as “10 gusting to 15” or a gust spread of five knots. How you view gust spread depends on what kind of airplane you’re flying. Depending on the airplane, five knots may not be worth worrying about. If, however, the reported spread is 10 knots, pilots of most general aviation aircraft need to pay more attention to it. The degree of worry attached then builds exponentially with further increases: the difference between a 10-knot gust spread and a 15-knot spread, in terms of how it will affect you, is much more than 50 percent. And the difference between a 10-knot spread and a 20-knot spread raises the question of whether you should be flying at all.
Gusts can become especially dangerous when they are not aligned with the main wind. The sock is stiffened and pointing in one direction, then it instantaneously whips in another direction at an obviously higher velocity. Most training aircraft are going to get bounced around.
A special wind situation, one to be avoided, is when the wind is 90 degrees to the runway, but violent, off-heading gusts are taking the wind behind the wing tip. When the wind suddenly jumps behind the wing, there may be a sudden loss of lift. Here the airspeed drops in a heartbeat and the airplane momentarily sinks. If this happens while the airplane is being flared for landing, it can smack the runway.
Windsock locations on the field are important
Many windsocks are located mid-runway, which is not where pilots need them. They really should be about where you’re going to be touching down, so you have a good indication of what to expect right before touchdown. That’s when you’re the most vulnerable.
It’s also worth noting that windsocks are often affected by nearby topographical features, buildings, or trees. Most airport operators try to locate socks out in the open where they are getting the same air that the runway is getting.
Regardless of where the windsock is located, it can’t tell you what to expect when you’re low on short final. If there’s any kind of vertical drop-off at the end of the runway, for instance, odds are that when the wind is really blowing there will be a downward curl just short of the threshold. Windsocks can’t tell you what’s happening off the runway, but they can at least give you a hint of what to expect.
What the windsock can’t tell us
There are two distinct bits of information windsocks can’t give: They can’t tell you how the wind slows down as you get closer to the ground (the velocity gradient) or the way the wind changes as you travel down the runway.
Wind speed is always zero in boundary layer right on the pavement. Then it increases up to about 15 feet, where the windsock is tethered and where sensors probably measure the wind speed. It is not a constant gradient. Every wind will be a little different and sometimes this difference can surprise you. Crosswinds that are still strong close to the ground demand much more dramatic corrections in the last few seconds of the landing.
A windsock gives lots of information, but only for the exact spot where it’s mounted. It can’t tell what the wind is doing 500 or 1,000 feet either direction down the runway. For that reason, the wind experienced on landing is almost never exactly what the sock predicts. And the wind you experience on landing may change several times. Wind seldom flows smoothly like the wide river people like to think it does. The wind-river almost always contains invisible eddies and swirls.
The western part of the country is especially known for winds that are often circular in nature. They are like small cyclones, so windsocks at opposite ends of the runway are sometimes pointing at each another. Those are wind conditions in which there is no “right” direction to take off or land. Every direction is downwind. Only if there are windsocks at opposite ends of the runway can a pilot know that.
The windsock gives lots of clues, but it can’t possibly tell the whole story. That being the case, revert to the basic rule of aviation: Fly the airplane. Deal with the situation as it develops—which pretty much summarizes what it means to be a pilot.
#### Budd Davisson
Budd Davisson is an aviation writer/photographer and magazine editor. A CFI since 1967, he teaches about 30 hours a month in his Pitts S–2A. | 1,686 | 7,843 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2022-27 | latest | en | 0.963252 |
http://megacode-ws.ru/weight/micrograms-milligrams | 1,524,788,965,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125948738.65/warc/CC-MAIN-20180427002118-20180427022118-00516.warc.gz | 219,399,998 | 10,249 | # Convert Micrograms to Milligrams
Finding it difficult to convert between micrograms and milligrams in your head? Use our weight converter calculator to make life easier! It’s imple to use.
## Conversion Micrograms - Milligrams
ug
The milligram and the microgram are both used to measure mass within the metric system. They are typically used to measure smaller quantities, for example in the case of medical information and pharmaceutics. Have a look at our other weight converters for more conversion options. Use this ug to mg calculator for any of your conversion needs.
## How to Convert from ug to mg?
In the box above, enter the quanitity of micrograms you wish to convert and press the ¨convert¨ button for your new quantity to appear in milligrams. Use our opposite weight converter to convert milligrams to micrograms. This microgram to milligram converter is accurate in its calculations.
## Formula to Calculate Micrograms – Milligrams
The microgram to milligram conversion formula is as follows, ug / 1000 = mg. This is the same calculation used by our online ug to mg converter. Some examples include 1ug = 0.001mg and 25ug = 0.025mg.
## Measurements in Micrograms
As a microgram is one-millionth of a gram, it is one of the smallest units of mass that is used. It is most commonly used in the food and drug industries due to the extremely precise measurements that are needed. Above you will find the ug – mg conversion tool to calculate between different units.
## Measurements in Milligrams
Milligrams are also a small unit of measure and can sometimes be confused with the microgram, although the microgram is a thousand times smaller. They too are used in the medical field for small doses and quantities. Our calculator ug to mg above will help with any calculation.
### How many is 1 Microgram in Milligrams?
1 Microgram equals 0 Milligrams `(1ug = 0mg)`
### How many are 2 Micrograms in Milligrams?
2 Micrograms equal 0 Milligrams `(2ug = 0mg)`
### How many are 3 Micrograms in Milligrams?
3 Micrograms equal 0 Milligrams `(3ug = 0mg)`
### How many are 4 Micrograms in Milligrams?
4 Micrograms equal 0 Milligrams `(4ug = 0mg)`
### How many are 5 Micrograms in Milligrams?
5 Micrograms equal 0.01 Milligrams `(5ug = 0.01mg)`
### How many are 10 Micrograms in Milligrams?
10 Micrograms equal 0.01 Milligrams `(10ug = 0.01mg)`
### How many are 15 Micrograms in Milligrams?
15 Micrograms equal 0.02 Milligrams `(15ug = 0.02mg)`
### How many are 20 Micrograms in Milligrams?
20 Micrograms equal 0.02 Milligrams `(20ug = 0.02mg)`
### How many are 25 Micrograms in Milligrams?
25 Micrograms equal 0.03 Milligrams `(25ug = 0.03mg)`
### How many are 30 Micrograms in Milligrams?
30 Micrograms equal 0.03 Milligrams `(30ug = 0.03mg)`
### How many are 50 Micrograms in Milligrams?
50 Micrograms equal 0.05 Milligrams `(50ug = 0.05mg)`
### How many are 100 Micrograms in Milligrams?
100 Micrograms equal 0.1 Milligrams `(100ug = 0.1mg)`
### How many are 200 Micrograms in Milligrams?
200 Micrograms equal 0.2 Milligrams `(200ug = 0.2mg)`
### How many are 500 Micrograms in Milligrams?
500 Micrograms equal 0.5 Milligrams `(500ug = 0.5mg)`
### How many are 1000 Micrograms in Milligrams?
1000 Micrograms equal 1 Milligrams `(1000ug = 1mg)`
Insert this converter to your website | 868 | 3,330 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2018-17 | latest | en | 0.88608 |
https://puzzlefry.com/puzzles/i-sit-between-you-and-a-star-riddle/?sort=oldest | 1,558,320,759,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255536.6/warc/CC-MAIN-20190520021654-20190520043654-00514.warc.gz | 595,974,807 | 31,364 | # I sit between you and a star riddle
I sit between you and a star,
but far below me is an empty space.
I can be infinite or finite depending on how you look at me.
What am I?
SherlockHolmes Expert Asked on 26th July 2017 in
“I sit between you and a star”: The number 8 sits between the letter U (you) and the asterisk (a star) on a standard keyboard.
“but far below me is an empty space”: far below the 8 key is the space bar
“I can be infinite or finite depending on how you look at me.”: If you look at an 8 sideways, it’s the symbol for infinity. If you look at it normally, it’s an 8, which is finite.
kjscola Curious Answered on 27th August 2017.
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What comes one time in today, three times in tomorrow and never in the future?Read More » | 872 | 3,521 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2019-22 | longest | en | 0.939818 |
http://betterlesson.com/lesson/resource/2948743/triangle-pairs-docx | 1,487,598,073,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170562.59/warc/CC-MAIN-20170219104610-00144-ip-10-171-10-108.ec2.internal.warc.gz | 30,246,578 | 19,035 | ## Triangle Pairs.docx - Section 1: Warm-Up
Triangle Pairs.docx
# Odd and Even Groups
Unit 4: Working With Numbers!
Lesson 8 of 8
## Big Idea: In this lesson students will classify, and recognize even and odd numbers in a variety ways.
Print Lesson
Standards:
Subject(s):
Math, explain
50 minutes
### Carol Redfield
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###### Odd or Even
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Environment: Urban | 259 | 1,084 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2017-09 | latest | en | 0.836946 |
https://www.cfd-online.com/Forums/main/16461-sod-shock-tube-problem.html | 1,718,944,323,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862036.35/warc/CC-MAIN-20240621031127-20240621061127-00053.warc.gz | 635,114,722 | 16,266 | # Sod Shock Tube problem
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March 13, 2009, 12:02 Sod Shock Tube problem #1 cfd Guest Posts: n/a Hi all, I'm trying to model the Sod Shock Tube Riemann Problem using a Riemann decomposition method. The theory is outlined in EF Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, section 3.1. The problem consists of an area of density, pressure of 1 and initial velocity of 0.75 on the left of a membrane, and an area with density of 0.125, and pressure of 0.1 with a speed of 0 on the right. At time zero the membrane is removed. I'm using a Riemann method to solve the problem, first for the Riemann variables, which is the matrix of right eigenvectors (of the Jacobian matrix of the flux) premultiplied by the variables (rho, rho.u, E)^T where the right eigenvectors are | 1 , 1 , 1 | | u-a , u , u+a | | H -ua , 0.5u^2 , H+ua | a = soundspeed, H = (E + p)/rho, p = pressure, E = total energy = rho.(0.5u^2 + specific internal energy). The eigenvalues of this system are (u-a, u, u+a). For the next timestep. If the eigenvalue is greater than zero, we take INITOUTPUT(i,k) = INITOUTPUT(i,k)*(1 - EIG(i,k)*(DT/DX)) + EIG(i,k)*(DT/DX)*(INITOUTPUT(i-1,k). If the eigenvalue is less than zero, we take INITOUTPUT(i,k) = INITOUTPUT(i,k)*(1 + (DT/DX)*(EIG(i,k)) - EIG(i,k)*(DT/DX)*INITOUTPUT(i+1,k). Where INITOUTPUT(i,k) are the Riemann variables, i is the x variable. Then we use a newton solver to solve the non-linear relationship between the Riemann variables and the original variables, (rho, rho.u, E). Regardless of the timestep or grid spacing, I seem to get the density decreasing smoothly towards the discontinuity over time, then sharply reducing to much lower than the original 0.125 on the right hand side just after the discontinuity and only then going back to the original 0.125. The solution to this problem is well known and not this. I'm using reflective boundary conditions for the near wall rho(0) = rho(1), u(0) = -u(1), E(0)=E(1) and the same on the far wall. Can anyone help? I would really appreciate it.
March 13, 2009, 13:41 Re: Sod Shock Tube problem #2 Mr Bean Guest Posts: n/a I advise you to look at "soundtube" software: http://www.cerfacs.fr/cfd/softwares.php
March 13, 2009, 15:33 Re: Sod Shock Tube problem #3 cfd Guest Posts: n/a Thanks, but I want to generate my own code. This is part of a project for a PhD.
March 17, 2009, 07:45 Try without the initial velocity #4 New Member Join Date: Mar 2009 Posts: 4 Rep Power: 17 Hi Have you tried the test without the initial velocity? Try that first, and you should also have open boundary on both sides. Try ul=0. The star values are shown on pg 133. Looks like you get a rarefaction wave on the right side of the discont.
July 7, 2009, 13:24 #5 Member Nishant Kumar Join Date: Jun 2009 Posts: 32 Rep Power: 16 Hi, I am dealing with kind of the same problem. Were you able to figure it out? Reply me at babuu.nishu@gmail.com Thanks | 865 | 3,008 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2024-26 | latest | en | 0.837908 |
https://ebin.pub/ordinary-differential-equations-d-4074054.html | 1,660,819,245,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00583.warc.gz | 227,980,205 | 11,648 | ##### Citation preview
9RDINARY DIFFERENTIAL EQUATIONS
Fritz John
1964- 1965 I
I
I
/
I Chapter 1:
Local Existence Theorems
1.1
General Rerna.rks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. l
1.2 1.- 3 1.4
Local Existence Proof by Picard Iteration......... First Order Systems . . . . . . . . • . . . . . . . . . . . . • . . . • . . . • . A Fixed Point Theorem ....................••.......
19 25
Chapter 2: 2.1 2. 2 2.3
9
Solutions in the Large
Global Solutions .•.•••••••.••.••..•.......••....•.. Euler Polygon Method • . • . . • • • • • . . • • • . . . . . . • • . . • . .. • . Continuous Dependence on Parameters ........•••.••.
Notes by
Michael Balch and Martin Braun
.--_.
courant Institute of Mathematical Sciences New York University
33 38
43
l
Chapter 1 Local Existence Theorem
·1.1:
General Remarks An ordinary differential equation is a functional relation
between an ·unknown function of one independent variable and its derivatives.
( In contrast to partial differentia:l e.quations
which involve derivatives with respect to several independent variables).
Thus F(x,y(x),y
(1)
(x), ••• ,y
(n)
(x)) = 0
shall denot·e the general differential equation of order n (where n we write y(n)(x) on occasion for d n y(x) ) . We shall often dx
want to pµt F = 0 into .. standard form; that is we should like to solve for the highest order derivative, thus
Y(n) = f ( X,Y,¥ (1) , ... ,y (n-1)) • How to achieve this is a question of application of the implicit function theorem.
The equation is called linear if it has the
given functions of x • In addition to single equations for one unknown function, we shall deal with systems of equations · for several unknown functions.
Thus i=l,.:.,n
2
is a sys~em of n first order equations inn unknown functions ui, i=l, ... , n. We remark that a single equation
of nth order in one
unknown function can be brought into system form, as follows. cl V -1 . . . Define = OX V -1 y ( X) j V = l, .•• , . n. Then
goes over into the 1st order system .s!_u
dx
.£.._ u
dx
1
n
=
f ( X, u , • • • , U ) 2 n .
for then-tuple of unknowns
(u 1 , ... ,un).
This special first
order system is equivalent to the corresponding nth order equation, and the advantage here is that the theory developed for the one goes over into the other. Our point of departure for the general theory will be the study.of the single equation of first order,
F(x,y, ~~)
=
O.
This is the simplest to deal with, and provides a prototype for the study of fi~st order systems.
3
No general statements can be made about the equation in the form F
= o.
We put it into standard form by the implicit function
theorem of calculus, =
We ·supp~·se f to exist ( be. defined as a real function of its arguments) in som~ domain D of the xy plane.
The equation now
defines a direction field at every point (x,y) of D. we can find a function
y = y(x)
That is, if
defined in some x interval I,
that when substituted for yin y' = f(x,y) makes the equation an identity in x for x
~
I, the slope y' (x) a~ (x,y(x)) for x € I
must be given by f(x,y(x)).
Thus the direction field prescribes
the slope at each point of D for any·conceivable solution passing through ·that point.
We a~e led to expect that at-every point P
of D, we can find at least one such function y = y(x) satisfying these requirements, and passing through P.
stipulation of continuity for fin D, this will turn out to be the case.
These last remarks implicitly suggest that in order to
attach a label to. functions y £ C(I) satisfying y' = f(x,y) for x € I, we append to the differential equation a side condition of the ~orm y(x 0
)
= y 0 • Even so, we shall see that uniqueness is
not guaranteed without a further condition on f. We turn now to specific examples which highlight our introductory remarks, and hint at other cons.iderations of importance. We note that it will occasionally happen (as in our first few examples to follow) that we can solve an equation explicitly in terms of the given data.
In contrast to elementary courses in
4
t he subject, which deal amply with such special situations, our emphasis will be placed in developing other aspects of the general theory, whose study will often be sufficient for the purposes at hand.
The reader interested.in this very special and
often difficult question of explicit integration of a differential equation is referred to Ritt, Integration in Finite Terms, and to work of Liouville. We remind the reader that the general linear equation of first order,
~ = a(x)y + b(x) , where a and b.are given functions of x, say defined and continuous in
I= {xla ~ x ~ ~}, is an example of an equation that
can be solved expl~citly.
The function
y(x) = e
satisfies the equation in [a,~], and is that function for which X
0
€..
Thus the initial value problem
(a)
y' = a(x)y + b(x)
( b)
y(xo) = y 0
has an answer in every case.
X {; X
0
E
I I
If a and ~-are not. finite, we see
that solutions exist for all x.
This explicit solution is
Another example of solution.by quadrature is given by the non-linear equation describing the motion of a simple pendulum, d 2y . : fl. + "'r"' dx2 .LJ
sin y = O
Again,
the solution by quadrature of the non-linear equation
_gives the Weierstrassj_-function as the inverse map of an elliptic integral function. For the non-linear Ricatti equation
l
= · A(x)y
2 + B(x)y + C(x) ,
where the coefficients depend on x, solution by quadrature is no longer possible in general.
An interesting result for this equa-·
tion is its equivalence with the general linear equation of second order. fined by
Thus, in terms of a new dependent variable z de-
y =
z' - -Az
, the equation goes over into z
Exercise 1.1.1 kinematics.
11
. A'
-
(
B + r ) z 1 + CAz = 0.
The Ric·atti equation is related to a proble_m in
The first order·system
6 dt
dx
=
& dt
= rx .. az
dz dt
=
PZ - ")'y
A. ay - ..,x
for the tri~le of unknown functions {x,y,z) in terms of a given triple of functions (a(t),~(t),r{t)), can be expressed by the single vector equation d dt £
where r
= (x, y, z) and
CD
=
CD )(
£ ,
= (a, t3, -y )°.
If r is the position vector -
•r
-----....
of a point Pin a rigid body rotating with angular velocity~ about a fixed origin, then the system above is just the familiar kinematical result for the instantaneous velocity of P. If .r, = .r,(t) is a solution, then 1~1 2 = c 2 = constant. Show that the new dependent variable A= A(t) defined by . ). = X
+ iy
C -
Z
,
which is a stereographic projection from the sphere of radius c onto the complex A-plane, satisfies a complex Ricat~i equation. (For a more complete discussion of the Ricatti equation, see Darboux, Theorie
~
Surfaces, Vol. I.).
The following examples illustrate what is to be expected for the manifold of solutions of a differential equation. · The non-linear equation (y 1 ) 2 + y 2 = - l is an example of a real . equation with no real solutions (the direction field defined by this equation is everywhere imaginary), regardless of side conditions imposed.
7
On the other hand, the equation (y 1 ) 2 + y 2 real direction fielo. only for
Iy I ~ . i,
= 1 detines a
and we can expect real .
solutions only for side conditions .of the form y(x0
IY0 1
~ 1.
y0
) =
,
The direction field
predict s at least 2 soluti ons pass ing through each point (x 0 ,y0 - co< x 0 < oo,
IY0 1
< l.
We see that functions yc(x)
),
= cos(x+c~.
'
where c is a constant, and z 1 : 1, z_ 1 = -~the envelopes Or ye.) satisfy the equation. But so does any continu,ously differentiable
combination
~(x) of the form (in say a~ x
cos(x-cr
a ~-
C
n,
m integers,
for ~(x) =
- 1Tn
Q
V
for
~
~
=
is similarly defined for x t f3 and x
+
~ C
X
X ~ C
1 = r+ l- 1 C
V
~
~! p),
m
+
1Tm ~
>
n
~
f3 0
- 1Tn if n even if n odd
M1T < X ~
t
f3 if m even if m odd
~ a •
Thus there exist
+1 - 1
infinitely many continuously differentiable solutions to the initial value problem ~
dx
(b)
=
8
that exist for all x, but which, when restricted to a small enough neighborhood of x 0 , | 2,319 | 8,182 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2022-33 | latest | en | 0.778019 |
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# Potential difference between two points in an electric field is:(A) A scalar quantity(B) A vector quantity(C) A tensor quantity(D) None of these
Last updated date: 20th Jun 2024
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Hint: For distinguishing between a vector and a scalar quantity, we check whether it follows rules of vector addition. If it follows the rules of vector addition, then it is a vector quantity, otherwise it is a scalar quantity.
Complete step-by-step solution
We know that the vectors are the quantities which are associated with the magnitude and the direction. So it can change by the change either of the magnitude or the direction.
But scalars are associated only with the magnitude. No direction is defined for the scalar quantities. So it cannot change with the direction. Therefore its magnitude is independent of the direction.
We know that the resultant electric field at a particular point, in a region where there are multiple fields present, is obtained by the vector addition of all the electric field vectors. So the electric field is a vector quantity.
But we know that the potential difference between two points in an electric field is independent of the path chosen for traversing from one point to the other. It only depends on the end points. Let us consider three points A, B, and C in an electric field. Let ${V_{AB}}$ be the potential difference between the points A and B, and ${V_{BC}}$ be the potential difference between the points B and C. For obtaining the potential difference between the points A and C, we algebraically add the potential differences ${V_{AB}}$ and ${V_{BC}}$. There is no vector addition involved.
So the potential difference between two points in an electric field is a scalar quantity.
Hence, the correct answer is option A.
Note
A tensor quantity is basically a multidimensional array. They are represented in the form of matrices. Both the scalars and vectors are the categories of the tensor. The scalar is a tensor having zero dimensions, while the vectors are the one dimensional tensors. | 462 | 2,161 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2024-26 | latest | en | 0.929688 |
https://domain.glass/search/?q=65.2%20kg%20to%20lbs | 1,659,990,690,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570871.10/warc/CC-MAIN-20220808183040-20220808213040-00301.warc.gz | 225,941,927 | 6,404 | ## "65.2 kg to lbs"
Request time (0.021 seconds) [cached] - Completion Score 150000
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### 65.2 Kilograms To Pounds Converter | 65.2 kg To lbs Converter
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### What is 65 kg in pounds? - Answers
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### 1.2 kg to lbs
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### How much pounds is 1 kg? - Answers
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### Rail profile - Wikipedia
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Rail profile - Wikipedia S Q OThe rail profile is the cross sectional shape of a railway rail, perpendicular to Early rails were made of wood, cast iron or wrought iron. All modern rails are hot rolled steel with a cross section approximate to M K I an I-beam, but asymmetric about a horizontal axis. The head is profiled to resist wear and to - give a good ride, and the foot profiled to suit the fixing system.
en.m.wikipedia.org/wiki/Rail_profile en.wikipedia.org/wiki/Grooved_rail en.wikipedia.org/wiki/Bullhead_rail en.wikipedia.org/wiki/Flanged_T_rail en.wikipedia.org/wiki/Pound_(rail) en.wikipedia.org/wiki/Vignoles_rail en.wikipedia.org/wiki/Fishbelly_rail en.wikipedia.org/wiki/Flat-bottom_rail en.m.wikipedia.org/wiki/Grooved_rail Rail profile23.3 Track (rail transport)18.2 Rail transport6.5 Cross section (geometry)6.3 Pound (mass)5.1 Kilogram3.6 Cast iron3.6 Wrought iron3.1 Rolling (metalworking)3.1 I-beam2.8 Perpendicular2.7 Steel2.5 Wear1.7 American Society of Civil Engineers1.7 Metre1.6 Yard1.1 Iron1.1 Asymmetry0.8 Wind turbine0.8 Branch line0.8
##### Domains
kg-to-lbs.appspot.com | lbs-to-kg.appspot.com | www.answers.com | kilograms-to-pounds.com | en.wikipedia.org | en.m.wikipedia.org | | 1,503 | 4,873 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2022-33 | latest | en | 0.70636 |
https://metanumbers.com/214728 | 1,638,011,152,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358180.42/warc/CC-MAIN-20211127103444-20211127133444-00079.warc.gz | 466,632,958 | 7,516 | # 214728 (number)
214,728 (two hundred fourteen thousand seven hundred twenty-eight) is an even six-digits composite number following 214727 and preceding 214729. In scientific notation, it is written as 2.14728 × 105. The sum of its digits is 24. It has a total of 6 prime factors and 32 positive divisors. There are 68,288 positive integers (up to 214728) that are relatively prime to 214728.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 6
• Sum of Digits 24
• Digital Root 6
## Name
Short name 214 thousand 728 two hundred fourteen thousand seven hundred twenty-eight
## Notation
Scientific notation 2.14728 × 105 214.728 × 103
## Prime Factorization of 214728
Prime Factorization 23 × 3 × 23 × 389
Composite number
Distinct Factors Total Factors Radical ω(n) 4 Total number of distinct prime factors Ω(n) 6 Total number of prime factors rad(n) 53682 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 214,728 is 23 × 3 × 23 × 389. Since it has a total of 6 prime factors, 214,728 is a composite number.
## Divisors of 214728
32 divisors
Even divisors 24 8 4 4
Total Divisors Sum of Divisors Aliquot Sum τ(n) 32 Total number of the positive divisors of n σ(n) 561600 Sum of all the positive divisors of n s(n) 346872 Sum of the proper positive divisors of n A(n) 17550 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 463.388 Returns the nth root of the product of n divisors H(n) 12.2352 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 214,728 can be divided by 32 positive divisors (out of which 24 are even, and 8 are odd). The sum of these divisors (counting 214,728) is 561,600, the average is 17,550.
## Other Arithmetic Functions (n = 214728)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 68288 Total number of positive integers not greater than n that are coprime to n λ(n) 4268 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 19134 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 68,288 positive integers (less than 214,728) that are coprime with 214,728. And there are approximately 19,134 prime numbers less than or equal to 214,728.
## Divisibility of 214728
m n mod m 2 3 4 5 6 7 8 9 0 0 0 3 0 3 0 6
The number 214,728 is divisible by 2, 3, 4, 6 and 8.
• Arithmetic
• Abundant
• Polite
• Practical
## Base conversion (214728)
Base System Value
2 Binary 110100011011001000
3 Ternary 101220112220
4 Quaternary 310123020
5 Quinary 23332403
6 Senary 4334040
8 Octal 643310
10 Decimal 214728
12 Duodecimal a4320
20 Vigesimal 16gg8
36 Base36 4loo
## Basic calculations (n = 214728)
### Multiplication
n×y
n×2 429456 644184 858912 1073640
### Division
n÷y
n÷2 107364 71576 53682 42945.6
### Exponentiation
ny
n2 46108113984 9900703099556352 2125958175161536352256 456502747036086377847226368
### Nth Root
y√n
2√n 463.388 59.882 21.5264 11.6514
## 214728 as geometric shapes
### Circle
Diameter 429456 1.34918e+06 1.44853e+11
### Sphere
Volume 4.1472e+16 5.79412e+11 1.34918e+06
### Square
Length = n
Perimeter 858912 4.61081e+10 303671
### Cube
Length = n
Surface area 2.76649e+11 9.9007e+15 371920
### Equilateral Triangle
Length = n
Perimeter 644184 1.99654e+10 185960
### Triangular Pyramid
Length = n
Surface area 7.98616e+10 1.16681e+15 175325
## Cryptographic Hash Functions
md5 f5ccb7fa2446fe0b02da98efebc01755 1fc84ee9b79fe643ddacce4bd5cfba105d2cfbbb 15cb686449e6e0662bd998b4efced07f8992d38a731ae0b5c583522d4521c8c3 967f282e3ba6dbcd394381e38ecc9c5ce71da5826178303e31af88062af2c4acd93c03f8a69b4236e045a57d6af0b768bccac34e15c5360498def70d289cc62a 438e71d7b36ba69f3ff25248bb37449fb94d27d0 | 1,440 | 4,159 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2021-49 | latest | en | 0.806961 |
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Perfect octave Play
All Cs possible on a piano (except C8, available on grand) Play.
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position."[1] Thus, using scientific pitch notation, the pitch class "C" is the set
{Cn : n is an integer} = {..., C-2, C-1, C0, C1, C2, C3 ...};
although there is no formal limit to this sequence on either end, only a limited number of these pitches will actually be audible to the human ear. Pitch class is important because human pitch-perception is periodic: pitches belonging to the same pitch class are perceived as having a similar "quality" or "color", a property called octave equivalence.
Psychologists refer to the quality of a pitch as its "chroma". A "chroma" is an attribute of pitches, just like hue is an attribute of color. A "pitch class" is a set of all pitches sharing the same chroma, just like "the set of all white things" is the collection of all white objects.[citation needed]
Note that in standard Western equal temperament, distinct spellings can refer to the same sounding object: B3, C4, and D4 all refer to the same pitch, hence share the same chroma, and therefore belong to the same pitch class; a phenomenon called enharmonic equivalence.
## Integer notation
To avoid the problem of enharmonic spellings, theorists typically represent pitch classes using numbers beginning from zero, with each successively larger integer representing a pitch class a semitone higher than the preceding one. Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. This cyclical system is referred to as modular arithmetic and, in the usual case of chromatic twelve-tone scales, pitch-class numbering is regarded as "mod 12"—that is, the twelfth member is identical to the first. One can map a pitch's fundamental frequency $f$ (measured in hertz) to a real number $p$ using the equation
$p = 69 + 12\log_2 {(f/440)}$
This creates a linear pitch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C is assigned the number 60. Indeed, the mapping from pitch to real numbers defined in this manner forms the basis of the MIDI Tuning Standard, which uses the real numbers from 0 to 127 to represent the pitches C-1 to G9. To represent pitch classes, we need to identify or "glue together" all pitches belonging to the same pitch class—i.e. all numbers p and p + 12. The result is a circular quotient space that musicians call pitch class space and mathematicians call R/12Z. Points in this space can be labelled using real numbers in the range 0 ≤ x < 12. These numbers provide numerical alternatives to the letter names of elementary music theory:
0 = C, 1 = C/D, 2 = D, 2.5 = "D quarter tone sharp", 3 = D/E,
and so on. In this system, pitch classes represented by integers are classes of twelve-tone equal temperament (assuming standard concert A).
To avoid confusing 10 with 1 and 0, some theorists assign pitch classes 10 and 11 the letters "t" (after "ten") and "e" (after "eleven"), respectively (or A and B, as in the writings of Allen Forte and Robert Morris).
Integer notation.
In music, integer notation is the translation of pitch classes and/or interval classes into whole numbers.[2] Thus C=0, C#=1 ... A#=10, B=11, with "10" and "11" substituted by "t" and "e" in some sources.[2] This allows the most economical presentation of information regarding post-tonal materials.[2]
In the integer model of pitch, all pitch classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to notate music for performance, but is a common analytical and compositional tool when working with chromatic music, including twelve tone, serial, or otherwise atonal music.
Pitch classes can be notated in this way by assigning the number 0 to some note—C natural by convention[citation needed]—and assigning consecutive integers to consecutive semitones; so if 0 is C natural, 1 is C sharp, 2 is D natural and so on up to 11, which is B natural. The C above this is not 12, but 0 again (12-12=0). Thus arithmetic modulo 12 is used to represent octave equivalence. One advantage of this system is that it ignores the "spelling" of notes (B sharp, C natural and D double-flat are all 0) according to their diatonic functionality.
There are a few disadvantages with integer notation. First, theorists have traditionally used the same integers to indicate elements of different tuning systems. Thus, the numbers 0, 1, 2, ... 5, are used to notate pitch classes in 6-tone equal temperament. This means that the meaning of a given integer changes with the underlying tuning system: "1" can refer to C♯ in 12-tone equal temperament, but D in 6-tone equal temperament.
Also, the same numbers are used to represent both pitches and intervals. For example, the number 4 serves both as a label for the pitch class E (if C=0) and as a label for the distance between the pitch classes D and F. (In much the same way, the term "10 degrees" can function as a label both for a temperature, and for the distance between two temperatures.) Only one of these labelings is sensitive to the (arbitrary) choice of pitch class 0. For example, if one makes a different choice about which pitch class is labeled 0, then the pitch class E will no longer be labelled "4." However, the distance between D and F will still be assigned the number 4. The late music theorist David Lewin was particularly sensitive to the confusions that this can cause[example needed], and both this and the above may be viewed as disadvantages.
## Other ways to label pitch classes
Pitch class
Pitch
class
Tonal counterparts
0 C (also B, D)
1 C, D (also B)
2 D (also C, E)
3 D, E (also F)
4 E (also D, F)
5 F (also E, G)
6 F, G (also E)
7 G (also F, A)
8 G, A
9 A (also G, B)
10, t or A A, B (also C)
11, e or B B (also A, C)
The system described above is flexible enough to describe any pitch class in any tuning system: for example, one can use the numbers {0, 2.4, 4.8, 7.2, 9.6} to refer to the five-tone scale that divides the octave evenly. However, in some contexts, it is convenient to use alternative labeling systems. For example, in just intonation, we may express pitches in terms of positive rational numbers p/q, expressed by reference to a 1 (often written "1/1"), which represents a fixed pitch. If a and b are two positive rational numbers, they belong to the same pitch class if and only if
$a/b = 2^n\,$
for some integer n. Therefore, we can represent pitch classes in this system using ratios p/q where neither p nor q is divisible by 2, that is, as ratios of odd integers. Alternatively, we can represent just intonation pitch classes by reducing to the octave, $1 \le p/q < 2$.
It is also very common to label pitch classes with reference to some scale. For example, one can label the pitch classes of n-tone equal temperament using the integers 0 to n-1. In much the same way, one could label the pitch classes of the C major scale, C-D-E-F-G-A-B using the numbers from 0 to 6. This system has two advantages over the continuous labeling system described above. First, it eliminates any suggestion that there is something natural about a 12-fold division of the octave. Second, it avoids pitch-class universes with unwieldy decimal expansions when considered relative to 12; for example, in the continuous system, the pitch-classes of 19-tet are labeled 0.63158..., 1.26316..., etc. Labeling these pitch classes {0, 1, 2, 3 ..., 18} simplifies the arithmetic used in pitch-class set manipulations.
The disadvantage of the scale-based system is that it assigns an infinite number of different names to chords that sound identical. For example, in twelve-tone equal-temperament the C major triad is notated {0, 4, 7}. In twenty-four-tone equal-temperament, this same triad is labeled {0, 8, 14}. Moreover, the scale-based system appears to suggest that different tuning systems use steps of the same size ("1") but have octaves of differing size ("12" in 12-tone equal-temperament, "19" in 19-tone equal temperament, and so on), whereas in fact the opposite is true: different tuning systems divide the same octave into different-sized steps.
In general, it is often more useful to use the traditional integer system when one is working within a single temperament; when one is comparing chords in different temperaments, the continuous system can be more useful.
## Sources
1. ^ Arnold Whitall, The Cambridge Introduction to Serialism (New York: Cambridge University Press, 2008): 276. ISBN 978-0-521-68200-8 (pbk).
2. ^ a b c Whittall (2008), p.273.
Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Pitch_class — Please support Wikipedia.
A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
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