Add files using upload-large-folder tool

pretraining/mathematica/geometry/solids/10505.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.2 & 0.939 & 0.838 \\
+ 0.593 & 0.795 & 0.827 \\
+ 0.449 & 0.613 & 0.497 \\
+ 0.985 & 0.754 & 0.428 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.41$ 
+Solid Angle: $0.14$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/12910.txt

@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{-4.042,-3.749,-0.511\}$ has radii $\{6.01,3.186,4.748\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Volume: $380.75$ 
+Surface Area: $268.59$

pretraining/mathematica/geometry/solids/1362.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.569 & 0.145 & 0.509 \\
+ 0.485 & 0.195 & 0.329 \\
+ 0.967 & 0.697 & 0.081 \\
+ 0.3 & 0.752 & 0.707 \\
+ 0.433 & 0.205 & 0.935 \\
+ 0.897 & 0.051 & 0.504 \\
+ 0.899 & 0.783 & 0.88 \\
+ 0.427 & 0.642 & 0.173 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.83$ 
+Volume: $0.17$ 
+Solid Angle: $5.64$

pretraining/mathematica/geometry/solids/14176.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.861 & 0.181 & 0.08 \\
+ 0.457 & 0.301 & 0.927 \\
+ 0.781 & 0.576 & 0.277 \\
+ 0.327 & 0.123 & 0.793 \\
+ 0.829 & 0.144 & 0.339 \\
+ 0.569 & 0.061 & 0.934 \\
+ 0.917 & 0.156 & 0.342 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.82$ 
+Volume: $0.03$ 
+Solid Angle: $0.59$

pretraining/mathematica/geometry/solids/17555.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.02 & 0.463 & 0.36 \\
+ 0.281 & 0.87 & 0.603 \\
+ 0.218 & 0.326 & 0.033 \\
+ 0.948 & 0.689 & 0.638 \\
+ 0.012 & 0.327 & 0.477 \\
+ 0.948 & 0.68 & 0.945 \\
+ 0.023 & 0.578 & 0.908 \\
+ 0.829 & 0.615 & 0.332 \\
+ 0.166 & 0.265 & 0.505 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $3.48$ 
+Surface Area: $1.7$ 
+Volume: $0.13$

pretraining/mathematica/geometry/solids/17953.txt

@@ -0,0 +1,32 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & -1.618 & 0. \\
+ 0. & 1.618 & 0. \\
+ -1.618 & 0. & -0.862 \\
+ 0.851 & 0. & 0.526 \\
+ 0.263 & -0.809 & 0.526 \\
+ 0.263 & 0.809 & 0.526 \\
+ 1.618 & 0. & -0.862 \\
+ -0.951 & -1.309 & 0. \\
+ -0.951 & 1.309 & 0. \\
+ 0.951 & -1.309 & 0. \\
+ 0.951 & 1.309 & 0. \\
+ -0.688 & -0.5 & 0.526 \\
+ -0.688 & 0.5 & 0.526 \\
+ -0.5 & -1.539 & -0.862 \\
+ -0.5 & 1.539 & -0.862 \\
+ 0.5 & -1.539 & -0.862 \\
+ 0.5 & 1.539 & -0.862 \\
+ -1.309 & -0.951 & -0.862 \\
+ -1.309 & 0.951 & -0.862 \\
+ 1.309 & -0.951 & -0.862 \\
+ 1.309 & 0.951 & -0.862 \\
+ -1.539 & -0.5 & 0. \\
+ -1.539 & 0.5 & 0. \\
+ 1.539 & -0.5 & 0. \\
+ 1.539 & 0.5 & 0. \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$55.$

pretraining/mathematica/geometry/solids/18470.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.92 & 0.009 & 0.246 \\
+ 0.832 & 0.77 & 0.679 \\
+ 0.908 & 0.775 & 0.491 \\
+ 0.626 & 0.89 & 0.851 \\
+ 0.012 & 0.908 & 0.638 \\
+ 0.799 & 0.306 & 0.786 \\
+ 0.312 & 0.503 & 0.178 \\
+ 0.539 & 0.83 & 0.859 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.42$ 
+Surface Area: $1.66$ 
+Volume: $0.11$

pretraining/mathematica/geometry/solids/19114.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.218 & 0.417 & 0.279 \\
+ 0.664 & 0.464 & 0.762 \\
+ 0.241 & 0.533 & 0.359 \\
+ 0.825 & 0.988 & 0.521 \\
+ 0.804 & 0.136 & 0.382 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.04$ 
+Solid Angle: $0.61$ 
+Surface Area: $0.82$

pretraining/mathematica/geometry/solids/21290.txt

@@ -0,0 +1,57 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & -\frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ -\frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ -\frac{1}{2} & \frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ -\frac{1}{2} & \frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ -\frac{1}{2} & -1-\frac{\sqrt{5}}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) & -\frac{1}{2} \\
+ 0 & \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(-5-\sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{2} & -\frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{2} & -1-\frac{\sqrt{5}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{4} \left(-5-\sqrt{5}\right) & 0 & \frac{1}{\sqrt{5}-3} \\
+ \frac{1}{4} \left(-5-\sqrt{5}\right) & 0 & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} \\
+ \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(1+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & -\frac{1}{2} & -\frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & -\frac{1}{2} & \frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} & -\frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(-5-\sqrt{5}\right) & 0 \\
+ \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(5+\sqrt{5}\right) & 0 \\
+ \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} \\
+ \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{\sqrt{5}-3} & \frac{1}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & -\frac{1}{2} & -\frac{1}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} & -\frac{1}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) & 0 \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) & 0 \\
+ \frac{1}{4} \left(5+\sqrt{5}\right) & 0 & \frac{1}{\sqrt{5}-3} \\
+ \frac{1}{4} \left(5+\sqrt{5}\right) & 0 & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$90$

pretraining/mathematica/geometry/solids/23154.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.299 & 0.581 & 0.913 \\
+ 0.752 & 0.307 & 0.572 \\
+ 0.024 & 0.483 & 0.987 \\
+ 0.543 & 0.039 & 0.555 \\
+ 0.276 & 0.597 & 0.138 \\
+ 0.936 & 0.097 & 0.23 \\
+ 0.922 & 0.573 & 0.333 \\
+ 0.148 & 0.033 & 0.024 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.94$ 
+Volume: $0.18$ 
+Solid Angle: $1.83$

pretraining/mathematica/geometry/solids/23609.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.081 & 0.964 & 0.488 \\
+ 0.353 & 0.22 & 0.973 \\
+ 0.133 & 0.108 & 0.056 \\
+ 0.835 & 0.768 & 0.222 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.54$ 
+Volume: $0.1$ 
+Solid Angle: $0.69$

pretraining/mathematica/geometry/solids/26187.txt

@@ -0,0 +1,21 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.619 & 0.489 & 0.198 \\
+ 0.818 & 0.109 & 0.397 \\
+ 0.942 & 0.189 & 0.887 \\
+ 0.271 & 0.547 & 0.856 \\
+ 0.357 & 0.05 & 0.805 \\
+ 0.024 & 0.448 & 0.435 \\
+ 0.496 & 0.434 & 0.937 \\
+ 0.457 & 0.932 & 0.484 \\
+ 0.917 & 0.052 & 0.606 \\
+ 0.134 & 0.275 & 0.629 \\
+ 0.451 & 0.764 & 0.148 \\
+ 0.272 & 0.863 & 0.715 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.29$ 
+Volume: $0.18$ 
+Surface Area: $1.89$

pretraining/mathematica/geometry/solids/26662.txt

@@ -0,0 +1,25 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -\frac{1}{\sqrt{2}} & 0 & 0 \\
+ -\frac{1}{2} & -\frac{1}{2} & 0 \\
+ -\frac{1}{2} & 0 & -\frac{1}{2} \\
+ -\frac{1}{2} & 0 & \frac{1}{2} \\
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ 0 & -\frac{1}{\sqrt{2}} & 0 \\
+ 0 & -\frac{1}{2} & -\frac{1}{2} \\
+ 0 & -\frac{1}{2} & \frac{1}{2} \\
+ 0 & 0 & -\frac{1}{\sqrt{2}} \\
+ 0 & 0 & \frac{1}{\sqrt{2}} \\
+ 0 & \frac{1}{2} & -\frac{1}{2} \\
+ 0 & \frac{1}{2} & \frac{1}{2} \\
+ 0 & \frac{1}{\sqrt{2}} & 0 \\
+ \frac{1}{2} & -\frac{1}{2} & 0 \\
+ \frac{1}{2} & 0 & -\frac{1}{2} \\
+ \frac{1}{2} & 0 & \frac{1}{2} \\
+ \frac{1}{2} & \frac{1}{2} & 0 \\
+ \frac{1}{\sqrt{2}} & 0 & 0 \\
+\end{array}
+\right)$. Determine the SurfaceArea.
+Answer:
+$8 \sqrt{3}$

pretraining/mathematica/geometry/solids/27307.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.949 & 0.586 & 0.097 \\
+ 0.779 & 0.47 & 0.942 \\
+ 0.388 & 0.525 & 0.892 \\
+ 0.442 & 0.523 & 0.046 \\
+ 0.141 & 0.616 & 0.114 \\
+ 0.529 & 0.398 & 0.62 \\
+ 0.971 & 0.161 & 0.242 \\
+ 0.466 & 0.592 & 0.057 \\
+ 0.683 & 0.354 & 0.954 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.08$ 
+Solid Angle: $1.21$ 
+Surface Area: $1.46$

pretraining/mathematica/geometry/solids/2751.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.208 & 0.34 & 0.158 \\
+ 0.244 & 0.574 & 0.367 \\
+ 0.733 & 0.261 & 0.115 \\
+ 0.765 & 0.918 & 0.609 \\
+ 0.627 & 0.88 & 0.136 \\
+ 0.931 & 0.704 & 0.596 \\
+ 0.54 & 0.931 & 0.541 \\
+ 0.184 & 0.858 & 0.253 \\
+ 0.163 & 0.944 & 0.021 \\
+ 0.36 & 0.975 & 0.157 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.1$ 
+Solid Angle: $1.18$ 
+Surface Area: $1.35$

pretraining/mathematica/geometry/solids/27869.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.041 & 0.836 & 0.281 \\
+ 0.768 & 0.921 & 0.742 \\
+ 0.851 & 0.959 & 0.205 \\
+ 0.154 & 0.062 & 0.119 \\
+ 0.033 & 0.965 & 0.217 \\
+ 0.978 & 0.241 & 0.673 \\
+ 0.935 & 0.311 & 0.865 \\
+ 0.673 & 0.234 & 0.333 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $2.19$ 
+Solid Angle: $3.51$ 
+Volume: $0.19$

pretraining/mathematica/geometry/solids/29498.txt

@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{-3.121,-2.864,-8.107\}$ has radii $\{1.465,9.586,4.16\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Surface Area: $287.5$ 
+Volume: $244.71$

pretraining/mathematica/geometry/solids/29682.txt

@@ -0,0 +1,99 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & 0. & -2.49 \\
+ 0. & 0. & 2.49 \\
+ 0. & -4.236 & -2.49 \\
+ 0. & -4.236 & 2.49 \\
+ 0. & 4.236 & -2.49 \\
+ 0. & 4.236 & 2.49 \\
+ -4.029 & -1.309 & -2.49 \\
+ -4.029 & -1.309 & 2.49 \\
+ -4.029 & 1.309 & -2.49 \\
+ -4.029 & 1.309 & 2.49 \\
+ 4.029 & -1.309 & -2.49 \\
+ 4.029 & -1.309 & 2.49 \\
+ 4.029 & 1.309 & -2.49 \\
+ 4.029 & 1.309 & 2.49 \\
+ -2.49 & -3.427 & -2.49 \\
+ -2.49 & -3.427 & 2.49 \\
+ -2.49 & 3.427 & -2.49 \\
+ -2.49 & 3.427 & 2.49 \\
+ 2.49 & -3.427 & -2.49 \\
+ 2.49 & -3.427 & 2.49 \\
+ 2.49 & 3.427 & -2.49 \\
+ 2.49 & 3.427 & 2.49 \\
+ -4.717 & -0.809 & -1.114 \\
+ -4.717 & 0.809 & -1.114 \\
+ 4.717 & -0.809 & 1.114 \\
+ 4.717 & 0.809 & 1.114 \\
+ -4.292 & -2.118 & 1.114 \\
+ -4.292 & 2.118 & 1.114 \\
+ 4.292 & -2.118 & -1.114 \\
+ 4.292 & 2.118 & -1.114 \\
+ -3.603 & 0. & -3.341 \\
+ 3.603 & 0. & 3.341 \\
+ -3.341 & -3.427 & 1.114 \\
+ -3.341 & 3.427 & 1.114 \\
+ 3.341 & -3.427 & -1.114 \\
+ 3.341 & 3.427 & -1.114 \\
+ -2.915 & -2.118 & 3.341 \\
+ -2.915 & 2.118 & 3.341 \\
+ 2.915 & -2.118 & -3.341 \\
+ 2.915 & 2.118 & -3.341 \\
+ -2.227 & 0. & -1.114 \\
+ -2.227 & -4.236 & -1.114 \\
+ -2.227 & 4.236 & -1.114 \\
+ 2.227 & 0. & 1.114 \\
+ 2.227 & -4.236 & 1.114 \\
+ 2.227 & 4.236 & 1.114 \\
+ -1.802 & -1.309 & 1.114 \\
+ -1.802 & 1.309 & 1.114 \\
+ 1.802 & -1.309 & -1.114 \\
+ 1.802 & 1.309 & -1.114 \\
+ -1.376 & 0. & -4.717 \\
+ -1.376 & 0. & 0.263 \\
+ 1.376 & 0. & 4.717 \\
+ 1.376 & 0. & -0.263 \\
+ -1.114 & -3.427 & -3.341 \\
+ -1.114 & -0.809 & 4.717 \\
+ -1.114 & -0.809 & -0.263 \\
+ -1.114 & 0.809 & 4.717 \\
+ -1.114 & 0.809 & -0.263 \\
+ -1.114 & 3.427 & -3.341 \\
+ 1.114 & -3.427 & 3.341 \\
+ 1.114 & -0.809 & -4.717 \\
+ 1.114 & -0.809 & 0.263 \\
+ 1.114 & 0.809 & -4.717 \\
+ 1.114 & 0.809 & 0.263 \\
+ 1.114 & 3.427 & 3.341 \\
+ -0.851 & 0. & 1.114 \\
+ 0.851 & 0. & -1.114 \\
+ -0.688 & -0.5 & -1.114 \\
+ -0.688 & 0.5 & -1.114 \\
+ -0.688 & -4.736 & -1.114 \\
+ -0.688 & -2.118 & -1.114 \\
+ -0.688 & 2.118 & -1.114 \\
+ -0.688 & 4.736 & -1.114 \\
+ 0.688 & -0.5 & 1.114 \\
+ 0.688 & 0.5 & 1.114 \\
+ 0.688 & -4.736 & 1.114 \\
+ 0.688 & -2.118 & 1.114 \\
+ 0.688 & 2.118 & 1.114 \\
+ 0.688 & 4.736 & 1.114 \\
+ -0.425 & -1.309 & -4.717 \\
+ -0.425 & -1.309 & 0.263 \\
+ -0.425 & 1.309 & -4.717 \\
+ -0.425 & 1.309 & 0.263 \\
+ -0.263 & -0.809 & 1.114 \\
+ -0.263 & 0.809 & 1.114 \\
+ 0.263 & -0.809 & -1.114 \\
+ 0.263 & 0.809 & -1.114 \\
+ 0.425 & -1.309 & 4.717 \\
+ 0.425 & -1.309 & -0.263 \\
+ 0.425 & 1.309 & 4.717 \\
+ 0.425 & 1.309 & -0.263 \\
+\end{array}
+\right)$. Determine the Centroid.
+Answer:
+$\{0.,0.,0.\}$

pretraining/mathematica/geometry/solids/3415.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.666 & 0.778 & 0.808 \\
+ 0.66 & 0.698 & 0.141 \\
+ 0.737 & 0.023 & 0.748 \\
+ 0.993 & 0.549 & 0.22 \\
+ 0.893 & 0.989 & 0.746 \\
+ 0.294 & 0.836 & 0.878 \\
+ 0.645 & 0.762 & 0.243 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.1$ 
+Surface Area: $1.4$ 
+Solid Angle: $5.86$

pretraining/mathematica/geometry/solids/34567.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.048 & 0.232 & 0.28 \\
+ 0.012 & 0.829 & 0.892 \\
+ 0.975 & 0.373 & 0.818 \\
+ 0.346 & 0.515 & 0.474 \\
+ 0.015 & 0.686 & 0.867 \\
+ 0.369 & 0.106 & 0.276 \\
+ 0.11 & 0.456 & 0.689 \\
+ 0.968 & 0.185 & 0.384 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.06$ 
+Surface Area: $1.47$ 
+Solid Angle: $0.63$

pretraining/mathematica/geometry/solids/3458.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.963 & 0.281 & 0.376 \\
+ 0.483 & 0.157 & 0.492 \\
+ 0.314 & 0.289 & 0.043 \\
+ 0.14 & 0.36 & 0.924 \\
+ 0.131 & 0.961 & 0.041 \\
+ 0.83 & 0.579 & 0.647 \\
+ 0.976 & 0.12 & 0.737 \\
+ 0.495 & 0.347 & 0.927 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.17$ 
+Surface Area: $1.97$ 
+Solid Angle: $1.92$

pretraining/mathematica/geometry/solids/35869.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.759 & 0.313 & 0.519 \\
+ 0.091 & 0.649 & 0.312 \\
+ 0.034 & 0.767 & 0.867 \\
+ 0.983 & 0.499 & 0.046 \\
+ 0.993 & 0.45 & 0.26 \\
+ 0.436 & 0.15 & 0.743 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.47$ 
+Surface Area: $1.27$ 
+Volume: $0.06$

pretraining/mathematica/geometry/solids/36132.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.769 & 0.267 & 0.051 \\
+ 0.473 & 0.68 & 0.076 \\
+ 0.704 & 0.921 & 0.558 \\
+ 0.532 & 0.229 & 0.346 \\
+ 0.652 & 0.057 & 0.297 \\
+ 0.081 & 0.395 & 0.337 \\
+ 0.355 & 0.034 & 0.12 \\
+ 0.859 & 0.652 & 0.307 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.2$ 
+Solid Angle: $1.98$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/36722.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.344 & 0.356 & 0.118 \\
+ 0.286 & 0.276 & 0.927 \\
+ 0.5 & 0.362 & 0.548 \\
+ 0.684 & 0.731 & 0.533 \\
+ 0.737 & 0.623 & 0.431 \\
+ 0.657 & 0.953 & 0.03 \\
+ 0.634 & 0.682 & 0.62 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.5$ 
+Volume: $0.03$ 
+Surface Area: $0.89$

pretraining/mathematica/geometry/solids/36924.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.902 & 0.539 & 0.42 \\
+ 0.153 & 0.802 & 0.341 \\
+ 0.135 & 0.47 & 0.603 \\
+ 0.45 & 0.364 & 0.279 \\
+ 0.859 & 0.483 & 0.849 \\
+ 0.724 & 0.019 & 0.775 \\
+ 0.331 & 0.228 & 0.634 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.18$ 
+Solid Angle: $1.38$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/38589.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.105 & 0.603 & 0.285 \\
+ 0.639 & 0.369 & 0.868 \\
+ 0.079 & 0.536 & 0.804 \\
+ 0.916 & 0.528 & 0.163 \\
+ 0.656 & 0.72 & 0.958 \\
+ 0.831 & 0.433 & 0.698 \\
+ 0.953 & 0.903 & 0.305 \\
+ 0.636 & 0.148 & 0.491 \\
+ 0.726 & 0.313 & 0.747 \\
+ 0.17 & 0.573 & 0.188 \\
+ 0.065 & 0.164 & 0.114 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $2.08$ 
+Solid Angle: $3.19$ 
+Volume: $0.21$

pretraining/mathematica/geometry/solids/40079.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.597 & 0.907 & 0.862 \\
+ 0.862 & 0.579 & 0.956 \\
+ 0.307 & 0.607 & 0.322 \\
+ 0.686 & 0.267 & 0.768 \\
+ 0.845 & 0.923 & 0. \\
+ 0.19 & 0.55 & 0.467 \\
+ 0.394 & 0.841 & 0.177 \\
+ 0.963 & 0.575 & 0.51 \\
+ 0.963 & 0.689 & 0.599 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.48$ 
+Solid Angle: $1.56$ 
+Volume: $0.11$

pretraining/mathematica/geometry/solids/40164.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.32 & 0.178 & 0.622 \\
+ 0.874 & 0.756 & 0.182 \\
+ 0.083 & 0.529 & 0.485 \\
+ 0.486 & 0.541 & 0.793 \\
+ 0.725 & 0.08 & 0.37 \\
+ 0.043 & 0.482 & 0.538 \\
+ 0.131 & 0.831 & 0.967 \\
+ 0.03 & 0.994 & 0.441 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.69$ 
+Volume: $0.12$ 
+Solid Angle: $2.01$

pretraining/mathematica/geometry/solids/41369.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.794 & 0.971 & 0.11 \\
+ 0.91 & 0.263 & 0.986 \\
+ 0.777 & 0.024 & 0.456 \\
+ 0.777 & 0.202 & 0.642 \\
+ 0.582 & 0.253 & 0.134 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.02$ 
+Solid Angle: $0.06$ 
+Surface Area: $0.9$

pretraining/mathematica/geometry/solids/42438.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.255 & 0.321 & 0.813 \\
+ 0.131 & 0.45 & 0.47 \\
+ 0.071 & 0.374 & 0.561 \\
+ 0.9 & 0.276 & 0.096 \\
+ 0.076 & 0.422 & 0.124 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.15$ 
+Volume: $0.01$ 
+Surface Area: $0.69$

pretraining/mathematica/geometry/solids/42442.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.062 & 0.759 & 0.722 \\
+ 0.138 & 0.358 & 0.462 \\
+ 0.556 & 0.553 & 0.007 \\
+ 0.234 & 0.141 & 0.674 \\
+ 0.919 & 0.9 & 0.525 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.07$ 
+Solid Angle: $0.75$ 
+Surface Area: $1.2$

pretraining/mathematica/geometry/solids/42692.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.2 & 0.879 & 0.912 \\
+ 0.427 & 0.419 & 0.212 \\
+ 0.193 & 0.582 & 0.177 \\
+ 0.091 & 0.966 & 0.148 \\
+ 0.349 & 0.68 & 0.128 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.09$ 
+Volume: $0.02$ 
+Surface Area: $0.59$

pretraining/mathematica/geometry/solids/42957.txt

@@ -0,0 +1,21 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.841 & 0.106 & 0.663 \\
+ 0.744 & 0.479 & 0.894 \\
+ 0.786 & 0.059 & 0.696 \\
+ 0.441 & 0.169 & 0.512 \\
+ 0.72 & 0.571 & 0.805 \\
+ 0.506 & 0.769 & 0.071 \\
+ 0.796 & 0.601 & 0.556 \\
+ 0.016 & 0.378 & 0.278 \\
+ 0.261 & 0.125 & 0.697 \\
+ 0.503 & 0.128 & 0.915 \\
+ 0.399 & 0.802 & 0.854 \\
+ 0.746 & 0.899 & 0.302 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.98$ 
+Surface Area: $1.85$ 
+Volume: $0.17$

pretraining/mathematica/geometry/solids/43233.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.691 & 0.484 & 0.81 \\
+ 0.582 & 0.289 & 0.346 \\
+ 0.423 & 0.588 & 0.404 \\
+ 0.708 & 0.516 & 0.116 \\
+ 0.1 & 0.759 & 0.941 \\
+ 0.655 & 0.642 & 0.936 \\
+ 0.618 & 0.909 & 0.798 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.05$ 
+Surface Area: $0.97$ 
+Solid Angle: $1.96$

pretraining/mathematica/geometry/solids/43956.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.176 & 0.513 & 0.693 \\
+ 0.188 & 0.907 & 0.207 \\
+ 0.907 & 0.799 & 0.043 \\
+ 0.068 & 0.92 & 0.709 \\
+ 0.41 & 0.113 & 0.718 \\
+ 0.75 & 0.414 & 0.276 \\
+ 0.062 & 0.029 & 0.015 \\
+ 0.129 & 0.288 & 0.593 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $5.44$ 
+Volume: $0.19$ 
+Surface Area: $2.03$

pretraining/mathematica/geometry/solids/46437.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.425 & 0.193 & 0.013 \\
+ 0.073 & 0.043 & 0.732 \\
+ 0.822 & 0.329 & 0.601 \\
+ 0.76 & 0.935 & 0.758 \\
+ 0.073 & 0.496 & 0.345 \\
+ 0.662 & 0.002 & 0.857 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.98$ 
+Surface Area: $1.72$ 
+Volume: $0.15$

pretraining/mathematica/geometry/solids/47203.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.798 & 0.164 & 0.45 \\
+ 0.039 & 0.705 & 0.127 \\
+ 0.616 & 0.369 & 0.876 \\
+ 0.155 & 0.723 & 0.959 \\
+ 0.174 & 0.958 & 0.826 \\
+ 0.099 & 0.851 & 0.558 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.19$ 
+Solid Angle: $0.14$ 
+Volume: $0.04$

pretraining/mathematica/geometry/solids/48457.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.77 & 0.096 & 0.623 \\
+ 0.96 & 0.415 & 0.284 \\
+ 0.883 & 0.975 & 0.664 \\
+ 0.33 & 0.382 & 0.817 \\
+ 0.522 & 0.593 & 0.19 \\
+ 0.972 & 0.856 & 0.35 \\
+ 0.62 & 0.328 & 0.323 \\
+ 0.12 & 0.477 & 0.815 \\
+ 0.175 & 0.945 & 0.955 \\
+ 0.251 & 0.879 & 0.34 \\
+ 0.216 & 0.746 & 0.152 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.11$ 
+Volume: $0.2$ 
+Surface Area: $2.08$

pretraining/mathematica/geometry/solids/49099.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.834 & 0.207 & 0.309 \\
+ 0.044 & 0.111 & 0.69 \\
+ 0.481 & 0.983 & 0.917 \\
+ 0.004 & 0.408 & 0.128 \\
+ 0.101 & 0.682 & 0.224 \\
+ 0.416 & 0.033 & 0.552 \\
+ 0.246 & 0.254 & 0.718 \\
+ 0.051 & 0.599 & 0.357 \\
+ 0.66 & 0.365 & 0.083 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.2$ 
+Volume: $0.16$ 
+Surface Area: $1.82$

pretraining/mathematica/geometry/solids/5166.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.129 & 0.697 & 0.997 \\
+ 0.884 & 0.596 & 0.445 \\
+ 0.924 & 0.666 & 0.123 \\
+ 0.279 & 0.112 & 0.192 \\
+ 0.018 & 0.284 & 0.187 \\
+ 0.582 & 0.992 & 0.387 \\
+ 0.959 & 0.052 & 0.743 \\
+ 0.656 & 0.29 & 0.867 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.74$ 
+Volume: $0.21$ 
+Surface Area: $2.28$

pretraining/mathematica/geometry/solids/52065.txt

@@ -0,0 +1,6 @@
+Problem:
+A cone with radius $6.524$ has its base centered at$\{9.44,2.481,8.669\}$ and its tip is at $\{1.458,4.574,4.535\}$. Estimate the cone's surface area, volume, and centroid.
+Answer:
+Centroid: $\{7.44,3.,7.64\}$ 
+Surface Area: $365.36$ 
+Volume: $411.37$

pretraining/mathematica/geometry/solids/54951.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.339 & 0.443 & 0.444 \\
+ 0.398 & 0.482 & 0.745 \\
+ 0.229 & 0.85 & 0.616 \\
+ 0.298 & 0.749 & 0.116 \\
+ 0.035 & 0.512 & 0.665 \\
+ 0.717 & 0.961 & 0.179 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.63$ 
+Volume: $0.04$ 
+Surface Area: $0.78$

pretraining/mathematica/geometry/solids/55553.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.497 & 0.045 & 0.193 \\
+ 0.139 & 0.165 & 0.357 \\
+ 0.546 & 0.506 & 0.63 \\
+ 0.429 & 0.284 & 0.691 \\
+ 0.564 & 0.569 & 0.833 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.01$ 
+Surface Area: $0.41$ 
+Solid Angle: $0.22$

pretraining/mathematica/geometry/solids/56213.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.022 & 0.546 & 0.861 \\
+ 0.246 & 0.644 & 0.526 \\
+ 0.949 & 0.823 & 0.237 \\
+ 0.757 & 0.203 & 0.719 \\
+ 0.172 & 0.024 & 0.927 \\
+ 0.447 & 0.266 & 0.016 \\
+ 0.333 & 0.734 & 0.508 \\
+ 0.485 & 0.892 & 0.551 \\
+ 0.373 & 0.68 & 0.997 \\
+ 0.999 & 0.173 & 0.556 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.87$ 
+Volume: $0.24$ 
+Surface Area: $2.27$

pretraining/mathematica/geometry/solids/56365.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.443 & 0.827 & 0.197 \\
+ 0.085 & 0.627 & 0.37 \\
+ 0.15 & 0.971 & 0.005 \\
+ 0.597 & 0.788 & 0.462 \\
+ 0.12 & 0.67 & 0.998 \\
+ 0.282 & 0.701 & 0.249 \\
+ 0.342 & 0.08 & 0.89 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.31$ 
+Surface Area: $1.19$ 
+Volume: $0.07$

pretraining/mathematica/geometry/solids/59186.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.798 & 0.459 & 0.559 \\
+ 0.65 & 0.713 & 0.146 \\
+ 0.686 & 0.207 & 0.654 \\
+ 0.122 & 0.351 & 0.06 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.$ 
+Surface Area: $0.57$ 
+Solid Angle: $0.18$

pretraining/mathematica/geometry/solids/60120.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.766 & 0.922 & 0.691 \\
+ 0.477 & 0.847 & 0.265 \\
+ 0.145 & 0.058 & 0.466 \\
+ 0.236 & 0.61 & 0.031 \\
+ 0.923 & 0.793 & 0.941 \\
+ 0.195 & 0.966 & 0.734 \\
+ 0.938 & 0.84 & 0.063 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $2.01$ 
+Volume: $0.17$ 
+Solid Angle: $4.57$

pretraining/mathematica/geometry/solids/63457.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.244 & 0.024 & 0.179 \\
+ 0.154 & 0.971 & 0.48 \\
+ 0.914 & 0.459 & 0.433 \\
+ 0.533 & 0.759 & 0.385 \\
+ 0.049 & 0.289 & 0.31 \\
+ 0.545 & 0.739 & 0.88 \\
+ 0.429 & 0.892 & 0.487 \\
+ 0.869 & 0.529 & 0.639 \\
+ 0.417 & 0.298 & 0.917 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.14$ 
+Solid Angle: $0.77$ 
+Surface Area: $1.65$

pretraining/mathematica/geometry/solids/66359.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.853 & 0.573 & 0.992 \\
+ 0.84 & 0.667 & 0.46 \\
+ 0.22 & 0.549 & 0.333 \\
+ 0.69 & 0.113 & 0.231 \\
+ 0.621 & 0.796 & 0.29 \\
+ 0.822 & 0.308 & 0.797 \\
+ 0.025 & 0.382 & 0.172 \\
+ 0.475 & 0.93 & 0.285 \\
+ 0.692 & 0.141 & 0.579 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.61$ 
+Surface Area: $1.48$ 
+Volume: $0.11$

pretraining/mathematica/geometry/solids/6798.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.172 & 0.87 & 0.806 \\
+ 0.347 & 0.472 & 0.458 \\
+ 0.603 & 0.753 & 0.051 \\
+ 0.245 & 0.511 & 0.288 \\
+ 0.456 & 0.657 & 0.092 \\
+ 0.13 & 0.851 & 0.976 \\
+ 0.094 & 0.862 & 0.053 \\
+ 0.533 & 0.495 & 0.764 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.06$ 
+Solid Angle: $4.18$ 
+Volume: $0.06$