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h11 int64 1 491 | h12 int64 1 491 | ks_id int64 0 2.19M | fav_N bool 2
classes | fav_M bool 2
classes | trilayer bool 2
classes | n_rigids int64 0 492 | n_1faces int64 10 42 | n_2faces int64 10 60 | n_3faces int64 5 30 | max_2face int64 3 344 | vertices listlengths 5 13 | n_pts_1faces listlengths 10 42 | n_int_pts_1faces listlengths 10 42 | n_pts_2faces listlengths 10 60 | n_int_pts_2faces listlengths 10 60 | n_pts_3faces listlengths 5 30 | n_int_pts_3faces listlengths 5 30 | n_int_pts_dual_1faces listlengths 10 60 | n_int_pts_dual_2faces listlengths 10 42 | n_int_pts_dual_3faces listlengths 5 13 | __index_level_0__ int64 0 100k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 21 | 0 | true | true | false | 5 | 10 | 10 | 5 | 3 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
1,
2,
3,
5
],
[
-2,
-3,
-4,
-5
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
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0,
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0,
0,
0,
0,
0,
0,
0
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3,
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3,
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3
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0,
0,
0,
0
] | [
4,
4,
4,
4,
4
] | [
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
0,
0,
0
] | 0 |
21 | 1 | 0 | true | true | false | 25 | 10 | 10 | 5 | 5 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
2,
4,
5,
0
],
[
3,
3,
0,
5
],
[
-6,
-8,
-5,
-5
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
5,
5,
5,
5,
5,
5,
5,
5,
5,
5
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
12,
12,
12,
12,
12
] | [
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0
] | 1 |
1 | 101 | 1 | true | true | false | 0 | 10 | 10 | 5 | 3 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
0,
0,
0,
1
],
[
-1,
-1,
-1,
-1
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
3,
3,
3,
3,
3,
3,
3,
3,
3,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
4,
4,
4,
4,
4
] | [
0,
0,
0,
0,
0
] | [
4,
4,
4,
4,
4,
4,
4,
4,
4,
4
] | [
6,
6,
6,
6,
6,
6,
6,
6,
6,
6
] | [
4,
4,
4,
4,
4
] | 2 |
101 | 1 | 0 | true | true | false | 105 | 10 | 10 | 5 | 21 | [
[
1,
0,
0,
0
],
[
1,
5,
0,
0
],
[
1,
0,
5,
0
],
[
1,
0,
0,
5
],
[
-4,
-5,
-5,
-5
]
] | [
6,
6,
6,
6,
6,
6,
6,
6,
6,
6
] | [
4,
4,
4,
4,
4,
4,
4,
4,
4,
4
] | [
21,
21,
21,
21,
21,
21,
21,
21,
21,
21
] | [
6,
6,
6,
6,
6,
6,
6,
6,
6,
6
] | [
56,
56,
56,
56,
56
] | [
4,
4,
4,
4,
4
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0
] | 3 |
1 | 103 | 2 | true | true | false | 0 | 10 | 10 | 5 | 3 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
0,
0,
0,
1
],
[
-2,
-1,
-1,
-1
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
3,
3,
3,
3,
3,
3,
3,
3,
3,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
4,
4,
4,
4,
4
] | [
0,
0,
0,
0,
0
] | [
2,
2,
5,
2,
5,
5,
2,
5,
5,
5
] | [
4,
4,
4,
10,
4,
4,
10,
4,
10,
10
] | [
3,
3,
3,
3,
10
] | 4 |
103 | 1 | 0 | true | true | false | 107 | 10 | 10 | 5 | 28 | [
[
1,
0,
0,
0
],
[
1,
3,
0,
0
],
[
1,
3,
6,
0
],
[
1,
3,
0,
6
],
[
-5,
-9,
-6,
-6
]
] | [
4,
7,
7,
7,
4,
4,
4,
7,
7,
7
] | [
2,
5,
5,
5,
2,
2,
2,
5,
5,
5
] | [
16,
16,
16,
28,
28,
28,
16,
16,
16,
28
] | [
4,
4,
4,
10,
10,
10,
4,
4,
4,
10
] | [
50,
50,
50,
84,
50
] | [
3,
3,
3,
10,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0
] | 5 |
1 | 145 | 3 | true | true | true | 0 | 10 | 10 | 5 | 3 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
0,
0,
0,
1
],
[
-5,
-2,
-1,
-1
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
3,
3,
3,
3,
3,
3,
3,
3,
3,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
5,
4,
4,
4,
4
] | [
1,
0,
0,
0,
0
] | [
0,
1,
4,
1,
4,
9,
1,
4,
9,
9
] | [
2,
2,
4,
16,
2,
4,
16,
4,
16,
36
] | [
2,
2,
2,
6,
34
] | 6 |
145 | 1 | 0 | true | true | true | 148 | 10 | 10 | 5 | 66 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
5,
6,
10,
0
],
[
5,
6,
0,
10
],
[
-15,
-14,
-10,
-10
]
] | [
6,
3,
11,
11,
2,
6,
6,
3,
3,
11
] | [
4,
1,
9,
9,
0,
4,
4,
1,
1,
9
] | [
10,
36,
36,
18,
18,
66,
10,
10,
36,
18
] | [
2,
16,
16,
4,
4,
36,
2,
2,
16,
4
] | [
49,
49,
161,
88,
49
] | [
2,
2,
34,
6,
2
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
1,
0,
0
] | 7 |
1 | 149 | 4 | true | true | true | 0 | 10 | 10 | 5 | 3 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
0,
0,
0,
1
],
[
-4,
-1,
-1,
-1
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
3,
3,
3,
3,
3,
3,
3,
3,
3,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
5,
4,
4,
4,
4
] | [
1,
0,
0,
0,
0
] | [
1,
1,
7,
1,
7,
7,
1,
7,
7,
7
] | [
3,
3,
3,
21,
3,
3,
21,
3,
21,
21
] | [
3,
3,
3,
3,
35
] | 8 |
149 | 1 | 0 | true | true | true | 152 | 10 | 10 | 5 | 45 | [
[
1,
0,
0,
0
],
[
1,
2,
0,
0
],
[
1,
2,
8,
0
],
[
1,
2,
0,
8
],
[
-7,
-6,
-8,
-8
]
] | [
3,
9,
9,
9,
3,
3,
3,
9,
9,
9
] | [
1,
7,
7,
7,
1,
1,
1,
7,
7,
7
] | [
15,
15,
15,
45,
45,
45,
15,
15,
15,
45
] | [
3,
3,
3,
21,
21,
21,
3,
3,
3,
21
] | [
61,
61,
61,
165,
61
] | [
3,
3,
3,
35,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
1,
0,
0,
0
] | 9 |
2 | 38 | 0 | true | true | false | 4 | 10 | 10 | 5 | 4 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
1,
2,
1,
3
],
[
-4,
-5,
-2,
-3
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
3,
3,
4,
3,
3,
3,
3,
3,
3,
3
] | [
0,
0,
1,
0,
0,
0,
0,
0,
0,
0
] | [
4,
5,
5,
4,
4
] | [
0,
0,
0,
0,
0
] | [
0,
0,
0,
2,
0,
0,
2,
0,
0,
2
] | [
1,
3,
3,
1,
3,
3,
1,
10,
3,
3
] | [
0,
0,
3,
3,
0
] | 10 |
38 | 2 | 0 | true | true | false | 42 | 10 | 10 | 5 | 19 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
2,
2,
3,
0
],
[
5,
8,
3,
9
],
[
-10,
-13,
-6,
-9
]
] | [
2,
2,
4,
4,
2,
2,
2,
2,
2,
4
] | [
0,
0,
2,
2,
0,
0,
0,
0,
0,
2
] | [
4,
8,
8,
8,
8,
19,
4,
4,
8,
8
] | [
1,
3,
3,
3,
3,
10,
1,
1,
3,
3
] | [
14,
14,
32,
32,
14
] | [
0,
0,
3,
3,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
1,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0
] | 11 |
2 | 74 | 1 | true | false | false | 1 | 10 | 10 | 5 | 4 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
0,
0,
0,
1
],
[
-4,
-3,
-2,
-2
]
] | [
2,
2,
3,
2,
2,
2,
2,
2,
2,
2
] | [
0,
0,
1,
0,
0,
0,
0,
0,
0,
0
] | [
3,
4,
3,
4,
3,
4,
3,
3,
3,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
5,
4,
5,
5,
4
] | [
0,
0,
0,
0,
0
] | [
0,
2,
1,
2,
1,
5,
2,
3,
5,
5
] | [
1,
1,
4,
2,
3,
4,
7,
4,
7,
10
] | [
0,
2,
2,
3,
7
] | 12 |
74 | 2 | 0 | false | true | false | 70 | 10 | 10 | 5 | 28 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
4,
3,
6,
0
],
[
4,
3,
0,
6
],
[
-20,
-15,
-12,
-12
]
] | [
5,
4,
7,
7,
2,
3,
3,
4,
4,
7
] | [
3,
2,
5,
5,
0,
1,
1,
2,
2,
5
] | [
11,
19,
19,
16,
16,
28,
7,
7,
12,
16
] | [
3,
7,
7,
4,
4,
10,
1,
1,
2,
4
] | [
34,
34,
57,
50,
23
] | [
2,
2,
7,
3,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0
] | 13 |
2 | 86 | 2 | true | false | false | 0 | 10 | 10 | 5 | 4 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
0,
0,
0,
1
],
[
-2,
-2,
-2,
-1
]
] | [
3,
2,
2,
2,
2,
2,
2,
2,
2,
2
] | [
1,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
4,
4,
4,
3,
3,
3,
3,
3,
3,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
5,
5,
5,
4,
4
] | [
0,
0,
0,
0,
0
] | [
3,
3,
3,
3,
3,
3,
3,
3,
3,
7
] | [
3,
3,
3,
3,
3,
3,
3,
9,
9,
9
] | [
1,
1,
5,
5,
5
] | 14 |
86 | 2 | 0 | false | true | false | 84 | 10 | 10 | 5 | 25 | [
[
1,
0,
0,
0
],
[
1,
4,
0,
0
],
[
1,
0,
4,
0
],
[
1,
0,
0,
4
],
[
-7,
-8,
-8,
-4
]
] | [
5,
9,
5,
5,
5,
5,
5,
5,
5,
5
] | [
3,
7,
3,
3,
3,
3,
3,
3,
3,
3
] | [
25,
15,
15,
25,
25,
15,
15,
15,
15,
15
] | [
9,
3,
3,
9,
9,
3,
3,
3,
3,
3
] | [
55,
55,
35,
55,
35
] | [
5,
5,
1,
5,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
1,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0
] | 15 |
2 | 106 | 3 | true | false | true | 1 | 10 | 10 | 5 | 4 | [
[
1,
0,
0,
0
],
[
0,
1,
0,
0
],
[
0,
0,
1,
0
],
[
1,
0,
0,
2
],
[
-5,
-1,
-1,
-2
]
] | [
2,
2,
2,
2,
2,
2,
2,
2,
2,
3
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
1
] | [
3,
3,
3,
3,
3,
4,
3,
3,
4,
4
] | [
0,
0,
0,
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272 | 2 | 0 | true | true | true | 274 | 10 | 10 | 5 | 190 | [
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63 | 3 | 0 | false | true | false | 51 | 10 | 10 | 5 | 16 | [
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69 | 3 | 0 | false | true | false | 64 | 10 | 10 | 5 | 19 | [
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75 | 3 | 0 | false | true | false | 60 | 10 | 10 | 5 | 21 | [
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75 | 3 | 1 | false | true | true | 76 | 10 | 10 | 5 | 41 | [
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83 | 3 | 0 | false | true | true | 74 | 10 | 10 | 5 | 25 | [
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99 | 3 | 0 | false | true | true | 96 | 10 | 10 | 5 | 37 | [
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3 | 99 | 8 | true | false | true | 1 | 10 | 10 | 5 | 4 | [
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99 | 3 | 1 | false | true | true | 66 | 10 | 10 | 5 | 36 | [
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3 | 105 | 9 | true | false | true | 2 | 10 | 10 | 5 | 4 | [
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16,
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105 | 3 | 0 | false | true | true | 78 | 10 | 10 | 5 | 49 | [
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3 | 165 | 10 | false | true | true | 0 | 10 | 10 | 5 | 4 | [
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165 | 3 | 0 | true | false | true | 167 | 10 | 10 | 5 | 91 | [
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3 | 165 | 11 | true | false | true | 2 | 10 | 10 | 5 | 4 | [
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55
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2,
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10,
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165 | 3 | 1 | false | true | true | 57 | 10 | 10 | 5 | 91 | [
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[
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[
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3 | 243 | 12 | true | false | true | 1 | 10 | 10 | 5 | 5 | [
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[
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[
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22,
121
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1,
1,
3,
25,
58
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243 | 3 | 0 | false | true | true | 243 | 10 | 10 | 5 | 169 | [
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[
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4 | 52 | 0 | true | false | false | 2 | 10 | 10 | 5 | 6 | [
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112 | 4 | 1 | false | false | true | 58 | 10 | 10 | 5 | 55 | [
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112 | 4 | 2 | false | true | false | 30 | 10 | 10 | 5 | 55 | [
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148 | 4 | 0 | false | false | true | 148 | 10 | 10 | 5 | 81 | [
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53 | 5 | 0 | false | true | false | 34 | 10 | 10 | 5 | 16 | [
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53 | 5 | 1 | false | false | false | 44 | 10 | 10 | 5 | 19 | [
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65 | 5 | 0 | false | true | false | 53 | 10 | 10 | 5 | 16 | [
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5 | 69 | 5 | true | false | true | 3 | 10 | 10 | 5 | 6 | [
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69 | 5 | 1 | false | true | true | 32 | 10 | 10 | 5 | 25 | [
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0,
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5 | 101 | 7 | false | false | false | 0 | 10 | 10 | 5 | 5 | [
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25
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101 | 5 | 1 | false | false | false | 101 | 10 | 10 | 5 | 49 | [
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5 | 101 | 8 | false | false | true | 1 | 10 | 10 | 5 | 5 | [
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101 | 5 | 2 | false | false | true | 51 | 10 | 10 | 5 | 49 | [
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5 | 101 | 9 | true | false | true | 4 | 10 | 10 | 5 | 6 | [
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[
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0,
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] | [
0,
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101 | 5 | 3 | false | true | true | 68 | 10 | 10 | 5 | 45 | [
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101 | 5 | 4 | false | true | false | 26 | 10 | 10 | 5 | 49 | [
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5 | 101 | 10 | true | false | false | 3 | 10 | 10 | 5 | 5 | [
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25
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5 | 161 | 11 | true | false | true | 3 | 10 | 10 | 5 | 6 | [
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64
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161 | 5 | 0 | false | true | true | 129 | 10 | 10 | 5 | 100 | [
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5 | 185 | 12 | true | false | true | 2 | 10 | 10 | 5 | 7 | [
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10,
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91
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0,
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19,
44
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185 | 5 | 0 | false | true | true | 182 | 10 | 10 | 5 | 127 | [
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40,
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21,
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7,
7,
16,
12
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55,
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208,
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0
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0,
1,
0,
0,
0,
0,
0
] | [
0,
1,
2,
0,
0
] | 97 |
5 | 251 | 13 | false | true | true | 2 | 10 | 10 | 5 | 5 | [
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[
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[
-15,
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-1
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3,
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3,
3,
3,
3
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1,
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0,
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9,
7,
5,
4,
4
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2,
1,
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0,
1,
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1,
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9,
1,
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29
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9,
1,
4,
9,
14,
28,
126
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1,
1,
4,
26,
60
] | 98 |
251 | 5 | 0 | true | false | true | 252 | 10 | 10 | 5 | 176 | [
[
1,
0,
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0
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[
0,
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[
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[
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4,
7,
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14,
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32,
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287,
228,
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1,
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60,
26,
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0,
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End of preview. Expand in Data Studio
This dataset is based on the Kreuzer–Skarke database, which classifies all 473,800,776 reflexive lattice polytopes in four dimensions as enumerated by Maximilian Kreuzer and Harald Skarke. It contains additional geometric and combinatorial information about these polytopes that is particularly relevant for string theory compactifications and model building.
The dataset was primarily developed to interface with CYTools, a software package for the analysis of Calabi–Yau hypersurfaces in toric varieties, created by the group of Prof. Liam McAllister at Cornell University.
For questions, please contact as3475@cornell.edu or the developers of CYTools.
Dataset Details
This dataset is licensed under the CC BY-SA 4.0 license.
Data Fields
h11: The Hodge number h^{1,1} of the associated Calabi–Yau threefold hypersurface.h12: The Hodge number h^{2,1} of the associated Calabi–Yau threefold hypersurface.ks_id: Identifier of the polytope corresponding to the ordering for fixed ( h^{1,1} ) in the original Kreuzer–Skarke database.fav_N: Boolean flag indicating whether the polytope is favourable in the (N)-lattice.fav_M: Boolean flag indicating whether the dual polytope is favourable in the (M)-lattice.trilayer: Boolean flag indicating whether the polytope is trilayer.n_rigids: #rigid prime toric divisors associated with the polytope.n_1faces: #1-dimensional faces (1-faces, edges) of the polytope.n_2faces: #2-dimensional faces (2-faces) of the polytope.n_3faces: #3-dimensional faces (3-faces, facets) of the polytope.max_2face: Maximum number of lattice points contained in any 2-dimensional face.vertices: List of lattice vertices defining the four-dimensional reflexive polytope.n_pts_1faces: #points of each 1-face.n_int_pts_1faces: #interior points in each 1-face.n_pts_2faces: #points of each 2-face.n_int_pts_2faces: #interior points in each 2-face.n_pts_3faces: #points of each 3-face.n_int_pts_3faces: #interior points in each 3-face.n_int_pts_dual_1faces: #interior points in each dual 1-face.n_int_pts_dual_2faces: #interior points in each dual 2-face.n_int_pts_dual_3faces: #interior points in each dual 3-face.
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