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pretraining/mathematica/geometry/solids/10071.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.65 & 0.954 & 0.355 \\
+ 0.652 & 0.262 & 0.397 \\
+ 0.026 & 0.268 & 0.031 \\
+ 0.007 & 0.579 & 0.199 \\
+ 0.763 & 0.067 & 0.143 \\
+ 0.329 & 0.008 & 0.582 \\
+ 0.474 & 0.509 & 0.776 \\
+ 0.22 & 0.326 & 0.721 \\
+\end{array}
+\right)$. 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: $1.68$ 
+Volume: $0.14$ 
+Solid Angle: $0.68$

pretraining/mathematica/geometry/solids/10303.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.372 & 0.017 & 0.222 \\
+ 0.484 & 0.321 & 0.313 \\
+ 0.019 & 0.964 & 0.045 \\
+ 0.992 & 0.17 & 0.195 \\
+\end{array}
+\right)$. 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: $0.72$ 
+Volume: $0.02$ 
+Solid Angle: $0.41$

pretraining/mathematica/geometry/solids/11241.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.841 & 0.266 & 0.238 \\
+ 0.943 & 0.769 & 0.083 \\
+ 0.323 & 0.053 & 0.636 \\
+ 0.252 & 0.2 & 0.558 \\
+ 0.766 & 0.822 & 0.122 \\
+\end{array}
+\right)$. 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: $0.29$ 
+Volume: $0.01$ 
+Surface Area: $0.61$

pretraining/mathematica/geometry/solids/13099.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.592 & 0.528 & 0.068 \\
+ 0.49 & 0.672 & 0.131 \\
+ 0.489 & 0.025 & 0.941 \\
+ 0.919 & 0.888 & 0.953 \\
+ 0.068 & 0.376 & 0.653 \\
+\end{array}
+\right)$. 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: $1.46$ 
+Solid Angle: $1.06$ 
+Volume: $0.09$

pretraining/mathematica/geometry/solids/13557.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.754 & 0.406 & 0.769 \\
+ 0.879 & 0.843 & 0.196 \\
+ 0.453 & 0.48 & 0.019 \\
+ 0.327 & 0.208 & 0.486 \\
+ 0.085 & 0.981 & 0.504 \\
+ 0.572 & 0.22 & 0.081 \\
+ 0.452 & 0.956 & 0.119 \\
+ 0.768 & 0.546 & 0.239 \\
+ 0.894 & 0.92 & 0.732 \\
+\end{array}
+\right)$. 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: $1.86$ 
+Volume: $0.18$ 
+Solid Angle: $1.56$

pretraining/mathematica/geometry/solids/14430.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.132 & 0.668 & 0.78 \\
+ 0.716 & 0.233 & 0.03 \\
+ 0.615 & 0.88 & 0.263 \\
+ 0.039 & 0.143 & 0.119 \\
+ 0.964 & 0.793 & 0.081 \\
+ 0.871 & 0.276 & 0.558 \\
+ 0.281 & 0.768 & 0.761 \\
+\end{array}
+\right)$. 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: $1.82$ 
+Solid Angle: $0.96$ 
+Volume: $0.15$

pretraining/mathematica/geometry/solids/15923.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -0.483 & -0.129 & 0.354 \\
+ -0.483 & 0.129 & -0.354 \\
+ -0.354 & -0.354 & -0.354 \\
+ -0.354 & 0.354 & 0.354 \\
+ -0.129 & -0.483 & 0.354 \\
+ -0.129 & 0.483 & -0.354 \\
+ 0.129 & -0.483 & -0.354 \\
+ 0.129 & 0.483 & 0.354 \\
+ 0.354 & -0.354 & 0.354 \\
+ 0.354 & 0.354 & -0.354 \\
+ 0.483 & -0.129 & -0.354 \\
+ 0.483 & 0.129 & 0.354 \\
+\end{array}
+\right)$. Determine the Circumdiameter.
+Answer:
+$1.22$

pretraining/mathematica/geometry/solids/16294.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.991 & 0.639 & 0.526 \\
+ 0.274 & 0.992 & 0.545 \\
+ 0.219 & 0.845 & 0.577 \\
+ 0.259 & 0.95 & 0.942 \\
+ 0.269 & 0.508 & 0.085 \\
+\end{array}
+\right)$. 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: $0.17$ 
+Volume: $0.03$ 
+Surface Area: $0.88$

pretraining/mathematica/geometry/solids/1694.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.547 & 0.967 & 0.245 \\
+ 0.863 & 0.035 & 0.468 \\
+ 0.83 & 0.708 & 0.277 \\
+ 0.35 & 0.049 & 0.719 \\
+ 0.249 & 0.014 & 0.745 \\
+ 0.324 & 0.996 & 0.829 \\
+ 0.263 & 0.233 & 0.222 \\
+\end{array}
+\right)$. 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:
+Volume: $0.14$ 
+Solid Angle: $1.29$ 
+Surface Area: $1.77$

pretraining/mathematica/geometry/solids/17347.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -1 & 0 & -\frac{1}{2} \\
+ -1 & 0 & \frac{1}{2} \\
+ -\frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ -\frac{1}{2} & \frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ \frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ \frac{1}{2} & \frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ 1 & 0 & -\frac{1}{2} \\
+ 1 & 0 & \frac{1}{2} \\
+ \frac{1}{4} \left(3+\sqrt{6}\right) & \frac{1}{4} \sqrt{5+2 \sqrt{6}} & 0 \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$22$

pretraining/mathematica/geometry/solids/18157.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.689 & 0.678 & 0.462 \\
+ 0.638 & 0.675 & 0.22 \\
+ 0.358 & 0.042 & 0.933 \\
+ 0.51 & 0.194 & 0.243 \\
+ 0.453 & 0.085 & 0.879 \\
+ 0.105 & 0.768 & 0.049 \\
+ 0.77 & 0.242 & 0.065 \\
+ 0.357 & 0.679 & 0.932 \\
+\end{array}
+\right)$. 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: $2.67$ 
+Volume: $0.13$ 
+Surface Area: $1.65$

pretraining/mathematica/geometry/solids/19434.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.053 & 0.512 & 0.358 \\
+ 0.331 & 0.772 & 0.492 \\
+ 0.966 & 0.476 & 0.281 \\
+ 0.448 & 0.385 & 0.725 \\
+\end{array}
+\right)$. 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: $0.39$ 
+Volume: $0.02$ 
+Surface Area: $0.58$

pretraining/mathematica/geometry/solids/25657.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.792 & 0.432 & 0.525 \\
+ 0.143 & 0.216 & 0.393 \\
+ 0.718 & 0.245 & 0.492 \\
+ 0.992 & 0.506 & 0.85 \\
+ 0.599 & 0.841 & 0.487 \\
+ 0.302 & 0.661 & 0.937 \\
+ 0.909 & 0.016 & 0.75 \\
+ 0.871 & 0.717 & 0.663 \\
+\end{array}
+\right)$. 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: $1.4$ 
+Solid Angle: $4.64$ 
+Volume: $0.1$

pretraining/mathematica/geometry/solids/27454.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.689 & 0.773 & 0.36 \\
+ 0.291 & 0.764 & 0.848 \\
+ 0.867 & 0.271 & 0.418 \\
+ 0.726 & 0.843 & 0.644 \\
+ 0.428 & 0.757 & 0.499 \\
+\end{array}
+\right)$. 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: $1.44$ 
+Surface Area: $0.53$ 
+Volume: $0.02$

pretraining/mathematica/geometry/solids/28778.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.038 & 0.867 & 0.418 \\
+ 0.388 & 0.557 & 0.052 \\
+ 0.895 & 0.773 & 0.471 \\
+ 0.48 & 0.596 & 0.895 \\
+ 0.209 & 0.53 & 0.5 \\
+\end{array}
+\right)$. 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: $0.04$ 
+Surface Area: $0.91$ 
+Solid Angle: $0.75$

pretraining/mathematica/geometry/solids/29583.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.757 & 0.874 & 0.347 \\
+ 0.089 & 0.811 & 0.246 \\
+ 0.407 & 0.631 & 0.937 \\
+ 0.031 & 0.353 & 0.276 \\
+ 0.575 & 0.322 & 0.207 \\
+ 0.499 & 0.188 & 0.538 \\
+ 0.059 & 0.807 & 0.001 \\
+ 0.96 & 0.272 & 0.533 \\
+ 0.957 & 0.394 & 0.885 \\
+ 0.808 & 0.367 & 0.096 \\
+\end{array}
+\right)$. 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: $2.11$ 
+Solid Angle: $2.17$ 
+Volume: $0.22$

pretraining/mathematica/geometry/solids/29826.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.385 & 0.83 & 0.593 \\
+ 0.256 & 0.898 & 0.508 \\
+ 0.949 & 0.714 & 0.009 \\
+ 0.947 & 0.651 & 0.037 \\
+\end{array}
+\right)$. 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: $0.$ 
+Solid Angle: $0.09$ 
+Surface Area: $0.19$

pretraining/mathematica/geometry/solids/29946.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.082 & 0.038 & 0.478 \\
+ 0.169 & 0.534 & 0.024 \\
+ 0.104 & 0.696 & 0.776 \\
+ 0.683 & 0.731 & 0.363 \\
+ 0.285 & 0.782 & 0.761 \\
+ 0.111 & 0.83 & 0.804 \\
+ 0.616 & 0.532 & 0.257 \\
+ 0.323 & 0.74 & 0.804 \\
+ 0.015 & 0.53 & 0.539 \\
+\end{array}
+\right)$. 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: $0.64$ 
+Surface Area: $1.2$

pretraining/mathematica/geometry/solids/32409.txt

@@ -0,0 +1,39 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & 0. & -1.504 \\
+ 0. & 0. & 1.504 \\
+ 0.416 & -1.279 & 0.672 \\
+ 0.416 & 1.279 & 0.672 \\
+ 1.088 & -0.791 & -0.672 \\
+ 1.088 & 0.791 & -0.672 \\
+ 1.575 & 0. & -0.301 \\
+ -1.088 & -0.791 & 0.672 \\
+ -1.088 & 0.791 & 0.672 \\
+ -0.787 & -0.572 & -1.274 \\
+ -0.787 & 0.572 & -1.274 \\
+ 0.787 & -0.572 & 1.274 \\
+ 0.787 & 0.572 & 1.274 \\
+ 0.301 & -0.926 & -1.274 \\
+ 0.301 & 0.926 & -1.274 \\
+ -0.301 & -0.926 & 1.274 \\
+ -0.301 & 0.926 & 1.274 \\
+ 1.345 & 0. & 0.672 \\
+ -0.973 & 0. & 1.274 \\
+ -0.487 & -1.498 & 0.301 \\
+ -0.487 & 1.498 & 0.301 \\
+ 0.487 & -1.498 & -0.301 \\
+ 0.487 & 1.498 & -0.301 \\
+ 0.973 & 0. & -1.274 \\
+ 1.274 & -0.926 & 0.301 \\
+ 1.274 & 0.926 & 0.301 \\
+ -1.345 & 0. & -0.672 \\
+ -0.416 & -1.279 & -0.672 \\
+ -0.416 & 1.279 & -0.672 \\
+ -1.575 & 0. & 0.301 \\
+ -1.274 & -0.926 & -0.301 \\
+ -1.274 & 0.926 & -0.301 \\
+\end{array}
+\right)$. Determine the SurfaceArea.
+Answer:
+$29.05$

pretraining/mathematica/geometry/solids/3425.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.094 & 0.521 & 0.434 \\
+ 0.368 & 0.905 & 0.911 \\
+ 0.153 & 0.649 & 0.472 \\
+ 0.107 & 0.092 & 0.135 \\
+ 0.282 & 0.475 & 0.78 \\
+ 0.658 & 0.887 & 0.653 \\
+\end{array}
+\right)$. 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: $0.79$ 
+Solid Angle: $2.93$ 
+Volume: $0.03$

pretraining/mathematica/geometry/solids/34420.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.221 & 0.371 & 0.67 \\
+ 0.609 & 0.909 & 0.221 \\
+ 0.37 & 0.072 & 0.531 \\
+ 0.658 & 0.927 & 0.572 \\
+ 0.594 & 0.731 & 0.491 \\
+ 0.194 & 0.473 & 0.19 \\
+\end{array}
+\right)$. 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: $0.8$ 
+Volume: $0.03$ 
+Solid Angle: $1.33$

pretraining/mathematica/geometry/solids/34670.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.211 & 0.294 & 0.86 \\
+ 0.477 & 0.15 & 0.034 \\
+ 0.577 & 0.84 & 0.091 \\
+ 0.135 & 0.108 & 0.139 \\
+ 0.97 & 0.3 & 0.935 \\
+ 0.964 & 0.618 & 0.538 \\
+ 0.798 & 0.951 & 0.524 \\
+ 0.02 & 0.39 & 0.303 \\
+ 0.606 & 0.83 & 0.682 \\
+ 0.936 & 0.991 & 0.455 \\
+ 0.334 & 0.727 & 0.141 \\
+\end{array}
+\right)$. 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: $2.34$ 
+Volume: $0.24$ 
+Solid Angle: $1.47$

pretraining/mathematica/geometry/solids/35310.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.055 & 0.632 & 0.062 \\
+ 0.988 & 0.179 & 0.65 \\
+ 0.799 & 0.106 & 0.7 \\
+ 0.792 & 0.826 & 0.698 \\
+ 0.811 & 0.234 & 0.107 \\
+ 0.054 & 0.759 & 0.627 \\
+ 0.995 & 0.825 & 0.918 \\
+\end{array}
+\right)$. 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: $1.96$ 
+Volume: $0.15$ 
+Solid Angle: $0.53$

pretraining/mathematica/geometry/solids/36045.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.237 & 0.72 & 0.872 \\
+ 0.896 & 0.561 & 0.989 \\
+ 0.016 & 0.857 & 0.329 \\
+ 0.703 & 0.256 & 0.911 \\
+ 0.391 & 0.189 & 0.583 \\
+ 0.188 & 0.214 & 0.574 \\
+ 0.207 & 0.588 & 0.808 \\
+ 0.918 & 0.55 & 0.521 \\
+\end{array}
+\right)$. 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: $1.92$ 
+Surface Area: $1.42$ 
+Volume: $0.1$

pretraining/mathematica/geometry/solids/37236.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.093 & 0.434 & 0.811 \\
+ 0.824 & 0.149 & 0.906 \\
+ 0.826 & 0.063 & 0.104 \\
+ 0.664 & 0.876 & 0.37 \\
+ 0.606 & 0.958 & 0.401 \\
+ 0.861 & 0.641 & 0.296 \\
+ 0.335 & 0.125 & 0.377 \\
+\end{array}
+\right)$. 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: $0.77$ 
+Surface Area: $1.67$ 
+Volume: $0.13$

pretraining/mathematica/geometry/solids/37371.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.933 & 0.483 & 0.026 \\
+ 0.077 & 0.161 & 0.892 \\
+ 0.923 & 0.964 & 0.725 \\
+ 0.415 & 0.261 & 0.272 \\
+ 0.839 & 0.357 & 0.199 \\
+ 0.077 & 0.301 & 0.703 \\
+ 0.19 & 0.524 & 0.07 \\
+ 0.398 & 0.848 & 0.042 \\
+\end{array}
+\right)$. 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: $1.32$ 
+Volume: $0.17$ 
+Surface Area: $1.96$

pretraining/mathematica/geometry/solids/37552.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.338 & 0.996 & 0.595 \\
+ 0.094 & 0.094 & 0.253 \\
+ 0.778 & 0.287 & 0.275 \\
+ 0.631 & 0.074 & 0.162 \\
+ 0.381 & 0.553 & 0.823 \\
+ 0.247 & 0.823 & 0.37 \\
+ 0.024 & 0.498 & 0.018 \\
+ 0.231 & 0.917 & 0.745 \\
+ 0.847 & 0.824 & 0.56 \\
+\end{array}
+\right)$. 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: $0.15$ 
+Surface Area: $1.8$ 
+Solid Angle: $2.43$

pretraining/mathematica/geometry/solids/37624.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.392 & 0.817 & 0.108 \\
+ 1. & 0.163 & 0.257 \\
+ 0.468 & 0.047 & 0.6 \\
+ 0.24 & 0.124 & 0.318 \\
+ 0.028 & 0.305 & 0.301 \\
+\end{array}
+\right)$. 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: $0.99$ 
+Solid Angle: $0.21$ 
+Volume: $0.03$

pretraining/mathematica/geometry/solids/38878.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.064 & 0.832 & 0.921 \\
+ 0.569 & 0.075 & 0.906 \\
+ 0.556 & 0.092 & 0.047 \\
+ 0.514 & 0.91 & 0.446 \\
+\end{array}
+\right)$. 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: $0.05$ 
+Solid Angle: $0.32$ 
+Surface Area: $1.33$

pretraining/mathematica/geometry/solids/3919.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.893 & 0.631 & 0.462 \\
+ 0.094 & 0.024 & 0.615 \\
+ 0.034 & 0.698 & 0.178 \\
+ 0.434 & 0.096 & 0.861 \\
+ 0.599 & 0.666 & 0.137 \\
+ 0.068 & 0.827 & 0.372 \\
+ 0.866 & 0.785 & 0.352 \\
+ 0.778 & 0.503 & 0.843 \\
+ 0.479 & 0.799 & 0.024 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $2.57$ 
+Volume: $0.13$ 
+Surface Area: $1.77$

pretraining/mathematica/geometry/solids/40055.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.526 & 0.361 & 0.198 \\
+ 0.967 & 0.722 & 0.095 \\
+ 0.408 & 0.721 & 0.014 \\
+ 0.895 & 0.043 & 0.952 \\
+ 0.543 & 0.927 & 0.559 \\
+ 0.336 & 0.138 & 0.743 \\
+ 0.356 & 0.943 & 0.786 \\
+ 0.506 & 0.911 & 0.637 \\
+ 0.344 & 0.105 & 0.914 \\
+ 0.034 & 0.337 & 0.159 \\
+\end{array}
+\right)$. 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: $4.52$ 
+Volume: $0.24$ 
+Surface Area: $2.38$

pretraining/mathematica/geometry/solids/40397.txt

@@ -0,0 +1,23 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\
+ -\frac{1}{2} & \frac{1}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{2} & \frac{1}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \\
+ 0 & -\frac{1}{\sqrt{2}} & -\frac{1}{2} \\
+ 0 & -\frac{1}{\sqrt{2}} & \frac{1}{2} \\
+ -\frac{1}{\sqrt{2}} & 0 & -\frac{1}{2} \\
+ -\frac{1}{\sqrt{2}} & 0 & \frac{1}{2} \\
+ \frac{1}{\sqrt{2}} & 0 & -\frac{1}{2} \\
+ \frac{1}{\sqrt{2}} & 0 & \frac{1}{2} \\
+ 0 & \frac{1}{\sqrt{2}} & -\frac{1}{2} \\
+ 0 & \frac{1}{\sqrt{2}} & \frac{1}{2} \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$24$

pretraining/mathematica/geometry/solids/40820.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.45 & 0.038 & 0.423 \\
+ 0.632 & 0.406 & 0.719 \\
+ 0.269 & 0.215 & 0.015 \\
+ 0.026 & 0.975 & 0.105 \\
+ 0.542 & 0.153 & 0.431 \\
+ 0.391 & 0.532 & 0.142 \\
+ 0.087 & 0.288 & 0.837 \\
+ 0.71 & 0.68 & 0.729 \\
+ 0.168 & 0.89 & 0.886 \\
+\end{array}
+\right)$. 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: $1.96$ 
+Volume: $0.18$ 
+Solid Angle: $2.02$

pretraining/mathematica/geometry/solids/4320.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.156 & 0.752 & 0.109 \\
+ 0.225 & 0.341 & 0.848 \\
+ 0.593 & 0.634 & 0.937 \\
+ 0.551 & 0.801 & 0.297 \\
+ 0.894 & 0.147 & 0.848 \\
+ 0.034 & 0.136 & 0.183 \\
+\end{array}
+\right)$. 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: $1.65$ 
+Solid Angle: $0.79$ 
+Volume: $0.12$

pretraining/mathematica/geometry/solids/45433.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.707 & 0.096 & 0.076 \\
+ 0.054 & 0.839 & 0.511 \\
+ 0.798 & 0.805 & 0.933 \\
+ 0.567 & 0.25 & 0.889 \\
+ 0.961 & 0.468 & 0.74 \\
+\end{array}
+\right)$. 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: $0.32$ 
+Surface Area: $1.45$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/48918.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.39 & 0.632 & 0.706 \\
+ 0.527 & 0.995 & 0.587 \\
+ 0.576 & 0.136 & 0.809 \\
+ 0.638 & 0.727 & 0.208 \\
+ 0.756 & 0.89 & 0.416 \\
+ 0.883 & 0.458 & 0.139 \\
+ 0.158 & 0.477 & 0.48 \\
+ 0.041 & 0.237 & 0.22 \\
+\end{array}
+\right)$. 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: $1.47$ 
+Volume: $0.12$ 
+Solid Angle: $3.62$

pretraining/mathematica/geometry/solids/49462.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.912 & 0.892 & 0.093 \\
+ 0.328 & 0.123 & 0.707 \\
+ 0.151 & 0.774 & 0.012 \\
+ 0.511 & 0.998 & 0.393 \\
+ 0.902 & 0.585 & 0.99 \\
+ 0.29 & 0.283 & 0.144 \\
+ 0.508 & 0.883 & 0.118 \\
+ 0.157 & 0.208 & 0.22 \\
+ 0.823 & 0.607 & 0.504 \\
+ 0.547 & 0.465 & 0.11 \\
+ 0.139 & 0.872 & 0.703 \\
+\end{array}
+\right)$. 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: $0.24$ 
+Surface Area: $2.32$

pretraining/mathematica/geometry/solids/50898.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.614 & 0.213 & 0.015 \\
+ 0.512 & 0.676 & 0.596 \\
+ 0.966 & 0.626 & 0.301 \\
+ 0.393 & 0.669 & 0.319 \\
+ 0.095 & 0.719 & 0.724 \\
+ 0.152 & 0.492 & 0.055 \\
+ 0.402 & 0.095 & 0.266 \\
+ 0.622 & 0.591 & 0.136 \\
+ 0.853 & 0.366 & 0.452 \\
+ 0.61 & 0.632 & 0.939 \\
+\end{array}
+\right)$. 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: $1.84$ 
+Surface Area: $1.63$

pretraining/mathematica/geometry/solids/54341.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.883 & 0.358 & 0.093 \\
+ 0.457 & 0.2 & 0.937 \\
+ 0.19 & 0.478 & 0.507 \\
+ 0.175 & 0.358 & 0.191 \\
+ 0.793 & 0.428 & 0.52 \\
+ 0.175 & 0.832 & 0.18 \\
+\end{array}
+\right)$. 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: $0.6$ 
+Surface Area: $1.18$

pretraining/mathematica/geometry/solids/5578.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.454 & 0.707 & 0.596 \\
+ 0.521 & 0.253 & 0.871 \\
+ 0.192 & 0.193 & 0.652 \\
+ 0.554 & 0.89 & 0.252 \\
+ 0.696 & 0.8 & 0.568 \\
+ 0.385 & 0.257 & 0.538 \\
+ 0.023 & 0.893 & 0.366 \\
+\end{array}
+\right)$. 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: $5.79$ 
+Surface Area: $1.01$ 
+Volume: $0.05$

pretraining/mathematica/geometry/solids/56318.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.439 & 0.917 & 0.327 \\
+ 0.869 & 0.225 & 0.393 \\
+ 0.678 & 0.755 & 0.946 \\
+ 0.239 & 0.134 & 0.686 \\
+ 0.065 & 0.877 & 0.557 \\
+ 0.095 & 0.331 & 0.29 \\
+ 0.613 & 0.608 & 0.276 \\
+ 0.974 & 0.364 & 0.869 \\
+ 0.644 & 0.19 & 0.924 \\
+\end{array}
+\right)$. 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: $0.19$ 
+Surface Area: $1.94$ 
+Solid Angle: $1.89$

pretraining/mathematica/geometry/solids/62884.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.814 & 0.406 & 0.236 \\
+ 0.267 & 0.059 & 0.443 \\
+ 0.391 & 0.877 & 0.461 \\
+ 0.482 & 0.998 & 0.547 \\
+ 0.396 & 0.053 & 0.663 \\
+\end{array}
+\right)$. 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: $0.03$ 
+Solid Angle: $0.45$ 
+Surface Area: $0.79$

pretraining/mathematica/geometry/solids/64690.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.285 & 0.379 & 0.364 \\
+ 0.563 & 0.081 & 0.027 \\
+ 0.843 & 0.827 & 0.672 \\
+ 0.146 & 0.117 & 0.263 \\
+ 0.682 & 0.038 & 0.602 \\
+\end{array}
+\right)$. 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: $0.95$ 
+Volume: $0.04$ 
+Solid Angle: $1.72$

pretraining/mathematica/geometry/solids/65382.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.714 & 0.753 & 0.075 \\
+ 0.153 & 0.814 & 0.187 \\
+ 0.463 & 0.707 & 0.954 \\
+ 0.342 & 0.367 & 0.662 \\
+ 0.015 & 0.117 & 0.226 \\
+ 0.725 & 0.303 & 0.016 \\
+ 0.502 & 0.929 & 0.298 \\
+ 0.767 & 0.332 & 0.475 \\
+\end{array}
+\right)$. 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: $1.76$ 
+Volume: $0.16$ 
+Solid Angle: $1.8$

pretraining/mathematica/geometry/solids/65720.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.142 & 0.797 & 0.163 \\
+ 0.652 & 0.305 & 0.939 \\
+ 0.8 & 0.281 & 0.738 \\
+ 0.304 & 0.353 & 0.199 \\
+ 0.651 & 0.981 & 0.242 \\
+ 0.457 & 0.443 & 0.931 \\
+ 0.18 & 0.709 & 0.045 \\
+ 0.929 & 0.737 & 0.992 \\
+ 0.373 & 0.154 & 0.663 \\
+\end{array}
+\right)$. 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: $1.74$ 
+Volume: $0.13$ 
+Solid Angle: $1.88$

pretraining/mathematica/geometry/solids/66246.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.503 & 0.116 & 0.636 \\
+ 0.42 & 0.519 & 0.876 \\
+ 0.417 & 0.06 & 0.772 \\
+ 0.084 & 0.958 & 0.683 \\
+ 0.157 & 0.567 & 0.338 \\
+ 0.119 & 0.941 & 0.03 \\
+ 0.639 & 0.583 & 0.046 \\
+ 0.322 & 0.772 & 0.979 \\
+\end{array}
+\right)$. 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: $1.56$ 
+Volume: $0.09$ 
+Surface Area: $1.59$

pretraining/mathematica/geometry/solids/66563.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.747 & 0.725 & 0.758 \\
+ 0.253 & 0.02 & 0.841 \\
+ 0.685 & 0.989 & 0.304 \\
+ 0.519 & 0.26 & 0.481 \\
+ 0.988 & 0.028 & 0.415 \\
+ 0.179 & 0.928 & 0.35 \\
+\end{array}
+\right)$. 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: $0.11$ 
+Solid Angle: $1.94$ 
+Surface Area: $1.66$

pretraining/mathematica/geometry/solids/66755.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.212 & 0.708 & 0.77 \\
+ 0.001 & 0.005 & 0.195 \\
+ 0.384 & 0.844 & 0.594 \\
+ 0.805 & 0.674 & 0.869 \\
+ 0.7 & 0.794 & 0.797 \\
+ 0.948 & 0.258 & 0.637 \\
+ 0.856 & 0.872 & 0.612 \\
+ 0.19 & 0.272 & 0.799 \\
+ 0.058 & 0.278 & 0.051 \\
+ 0.658 & 0.51 & 0.084 \\
+\end{array}
+\right)$. 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: $2.12$ 
+Solid Angle: $2.39$ 
+Volume: $0.22$

pretraining/mathematica/geometry/solids/66768.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.737 & 0.67 & 0.452 \\
+ 0.5 & 0.031 & 0.791 \\
+ 0.493 & 0.837 & 0.178 \\
+ 0.08 & 0.134 & 0.085 \\
+ 0.488 & 0.925 & 0.384 \\
+ 0.002 & 0.468 & 0.018 \\
+ 0.484 & 0.949 & 0.886 \\
+ 0.627 & 0.413 & 0.833 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $2.65$ 
+Volume: $0.12$ 
+Surface Area: $1.76$

pretraining/mathematica/geometry/solids/67228.txt

@@ -0,0 +1,127 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -1 & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) \\
+ -1 & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) \\
+ -1 & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) \\
+ -1 & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) \\
+ -\frac{1}{2} & -\frac{1}{2} & -\frac{3}{2}-\sqrt{5} \\
+ -\frac{1}{2} & -\frac{1}{2} & \frac{3}{2}+\sqrt{5} \\
+ -\frac{1}{2} & \frac{1}{2} & -\frac{3}{2}-\sqrt{5} \\
+ -\frac{1}{2} & \frac{1}{2} & \frac{3}{2}+\sqrt{5} \\
+ -\frac{1}{2} & -\frac{3}{2}-\sqrt{5} & -\frac{1}{2} \\
+ -\frac{1}{2} & -\frac{3}{2}-\sqrt{5} & \frac{1}{2} \\
+ -\frac{1}{2} & -1-\frac{\sqrt{5}}{2} & -2-\frac{\sqrt{5}}{2} \\
+ -\frac{1}{2} & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(4+\sqrt{5}\right) \\
+ -\frac{1}{2} & \frac{3}{2}+\sqrt{5} & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{3}{2}+\sqrt{5} & \frac{1}{2} \\
+ -\frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) & -2-\frac{\sqrt{5}}{2} \\
+ -\frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(4+\sqrt{5}\right) \\
+ \frac{1}{2} & -\frac{1}{2} & -\frac{3}{2}-\sqrt{5} \\
+ \frac{1}{2} & -\frac{1}{2} & \frac{3}{2}+\sqrt{5} \\
+ \frac{1}{2} & \frac{1}{2} & -\frac{3}{2}-\sqrt{5} \\
+ \frac{1}{2} & \frac{1}{2} & \frac{3}{2}+\sqrt{5} \\
+ \frac{1}{2} & -\frac{3}{2}-\sqrt{5} & -\frac{1}{2} \\
+ \frac{1}{2} & -\frac{3}{2}-\sqrt{5} & \frac{1}{2} \\
+ \frac{1}{2} & -1-\frac{\sqrt{5}}{2} & -2-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(4+\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{3}{2}+\sqrt{5} & -\frac{1}{2} \\
+ \frac{1}{2} & \frac{3}{2}+\sqrt{5} & \frac{1}{2} \\
+ \frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) & -2-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(4+\sqrt{5}\right) \\
+ 1 & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) \\
+ 1 & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) \\
+ 1 & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) \\
+ 1 & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(-7-3 \sqrt{5}\right) & -1 & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-7-3 \sqrt{5}\right) & -1 & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-7-3 \sqrt{5}\right) & 1 & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-7-3 \sqrt{5}\right) & 1 & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) & -1 \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) & 1 \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) & -1 \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) & 1 \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) \\
+ -\frac{3}{2}-\sqrt{5} & -\frac{1}{2} & -\frac{1}{2} \\
+ -\frac{3}{2}-\sqrt{5} & -\frac{1}{2} & \frac{1}{2} \\
+ -\frac{3}{2}-\sqrt{5} & \frac{1}{2} & -\frac{1}{2} \\
+ -\frac{3}{2}-\sqrt{5} & \frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) \\
+ -2-\frac{\sqrt{5}}{2} & -\frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ -2-\frac{\sqrt{5}}{2} & -\frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ -2-\frac{\sqrt{5}}{2} & \frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ -2-\frac{\sqrt{5}}{2} & \frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & -2-\frac{\sqrt{5}}{2} & -\frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & -2-\frac{\sqrt{5}}{2} & \frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(4+\sqrt{5}\right) & -\frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(4+\sqrt{5}\right) & \frac{1}{2} \\
+ -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) \\
+ \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{3}{2}+\sqrt{5} & -\frac{1}{2} & -\frac{1}{2} \\
+ \frac{3}{2}+\sqrt{5} & -\frac{1}{2} & \frac{1}{2} \\
+ \frac{3}{2}+\sqrt{5} & \frac{1}{2} & -\frac{1}{2} \\
+ \frac{3}{2}+\sqrt{5} & \frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & -2-\frac{\sqrt{5}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & -2-\frac{\sqrt{5}}{2} & \frac{1}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(4+\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(4+\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) & -1 \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-7-3 \sqrt{5}\right) & 1 \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) & -1 \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(7+3 \sqrt{5}\right) & 1 \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{3}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{3}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(4+\sqrt{5}\right) & -\frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} \left(4+\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{2} \left(4+\sqrt{5}\right) & \frac{1}{2} & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} \left(4+\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(-5-\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{4} \left(5+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(7+3 \sqrt{5}\right) & -1 & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(7+3 \sqrt{5}\right) & -1 & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(7+3 \sqrt{5}\right) & 1 & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(7+3 \sqrt{5}\right) & 1 & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+\end{array}
+\right)$. Determine the FaceCount.
+Answer:
+$62$