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pretraining/mathematica/geometry/solids/1050.txt

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+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.33 & 0.419 & 0.314 \\
+ 0.825 & 0.052 & 0.99 \\
+ 0.088 & 0.671 & 0.016 \\
+ 0.624 & 0.453 & 0.999 \\
+ 0.597 & 0.734 & 0.832 \\
+ 0.181 & 0.482 & 0.531 \\
+ 0.826 & 0.941 & 0.638 \\
+ 0.99 & 0.338 & 0.558 \\
+ 0.742 & 0.324 & 0.116 \\
+\end{array}
+\right)$. 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: $5.44$ 
+Surface Area: $1.94$ 
+Volume: $0.18$

pretraining/mathematica/geometry/solids/11576.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.53 & 0.187 & 0.395 \\
+ 0.542 & 0.972 & 0.899 \\
+ 0.152 & 0.789 & 0.959 \\
+ 0.749 & 0.769 & 0.153 \\
+ 0.296 & 0.396 & 0.916 \\
+ 0.345 & 0.486 & 0.352 \\
+\end{array}
+\right)$. 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: $1.2$ 
+Volume: $0.06$ 
+Solid Angle: $0.78$

pretraining/mathematica/geometry/solids/126.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.953 & 0.804 & 0.11 \\
+ 0.657 & 0.835 & 0.968 \\
+ 0.973 & 0.03 & 0.129 \\
+ 0.521 & 0.239 & 0.932 \\
+ 0.031 & 0.659 & 0.394 \\
+ 0.126 & 0.298 & 0.086 \\
+ 0.42 & 0.113 & 0.127 \\
+ 0.086 & 0.433 & 0.424 \\
+\end{array}
+\right)$. 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: $0.25$ 
+Solid Angle: $1.11$ 
+Surface Area: $2.43$

pretraining/mathematica/geometry/solids/14549.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.975 & 0.867 & 0.7 \\
+ 0.85 & 0.369 & 0.93 \\
+ 0.461 & 0.982 & 0.237 \\
+ 0.798 & 0.543 & 0.201 \\
+ 0.482 & 0.837 & 0.798 \\
+ 0.802 & 0.865 & 0.228 \\
+ 0.015 & 0.728 & 0.395 \\
+ 0.717 & 0.116 & 0.516 \\
+ 0.311 & 0.05 & 0.356 \\
+ 0.29 & 0.468 & 0.924 \\
+\end{array}
+\right)$. 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:
+Surface Area: $2.21$ 
+Volume: $0.24$ 
+Solid Angle: $1.61$

pretraining/mathematica/geometry/solids/1534.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.43 & 0.849 & 0.348 \\
+ 0.371 & 0.245 & 0.96 \\
+ 0.274 & 0.27 & 0.101 \\
+ 0.224 & 0.234 & 0.839 \\
+ 0.367 & 0.038 & 0.369 \\
+\end{array}
+\right)$. 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: $0.02$ 
+Surface Area: $0.8$ 
+Solid Angle: $0.18$

pretraining/mathematica/geometry/solids/16163.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.254 & 0.731 & 0.291 \\
+ 0.654 & 0.648 & 0.28 \\
+ 0.709 & 0.071 & 0.69 \\
+ 0.312 & 0.134 & 0.438 \\
+ 0.793 & 0.699 & 0.981 \\
+\end{array}
+\right)$. 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: $0.69$ 
+Surface Area: $1.05$ 
+Volume: $0.05$

pretraining/mathematica/geometry/solids/17715.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.408 & 0.604 & 0.289 \\
+ 0.997 & 0.783 & 0.571 \\
+ 0.181 & 0.017 & 0.861 \\
+ 0.88 & 0.482 & 0.239 \\
+ 0.244 & 0.872 & 0.494 \\
+ 0.02 & 0.212 & 0.876 \\
+ 0.11 & 0.468 & 0.295 \\
+ 0.668 & 0.004 & 0.201 \\
+\end{array}
+\right)$. 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: $1.92$ 
+Volume: $0.17$ 
+Solid Angle: $4.87$

pretraining/mathematica/geometry/solids/18910.txt

@@ -0,0 +1,29 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & 0. & 1.401 \\
+ 0. & 0. & -1.401 \\
+ 0.178 & -1.309 & 0.467 \\
+ 0.178 & 1.309 & 0.467 \\
+ 0.467 & -0.809 & -1.044 \\
+ 0.467 & 0.809 & -1.044 \\
+ 1.044 & -0.809 & 0.467 \\
+ 1.044 & 0.809 & 0.467 \\
+ -1.223 & -0.5 & 0.467 \\
+ -1.223 & 0.5 & 0.467 \\
+ 1.223 & -0.5 & -0.467 \\
+ 1.223 & 0.5 & -0.467 \\
+ -0.934 & 0. & -1.044 \\
+ -0.467 & -0.809 & 1.044 \\
+ -0.467 & 0.809 & 1.044 \\
+ 0.934 & 0. & 1.044 \\
+ -1.044 & -0.809 & -0.467 \\
+ -1.044 & 0.809 & -0.467 \\
+ -0.995 & 0. & 1.303 \\
+ -0.178 & -1.309 & -0.467 \\
+ -0.178 & 1.309 & -0.467 \\
+ 0.805 & -1.394 & -0.308 \\
+\end{array}
+\right)$. Determine the Volume.
+Answer:
+$8.27$

pretraining/mathematica/geometry/solids/19238.txt

@@ -0,0 +1,5 @@
+Problem:
+A sphere centered at $\{-6.57,2.079,5.098\}$ has radius $3.58$. Estimate the sphere's surface area and volume.
+Answer:
+Volume: $192.12$ 
+Surface Area: $161.02$

pretraining/mathematica/geometry/solids/1965.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.065 & 0.82 & 0.523 \\
+ 0.123 & 0.356 & 0.947 \\
+ 0.083 & 0.444 & 0.679 \\
+ 0.952 & 0.295 & 0.932 \\
+ 0.031 & 0.595 & 0.68 \\
+\end{array}
+\right)$. 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: $0.61$ 
+Solid Angle: $0.19$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/20647.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.957 & 0.783 & 0.172 \\
+ 0.76 & 0.888 & 0.999 \\
+ 0.881 & 0.344 & 0.635 \\
+ 0.233 & 0.93 & 0.444 \\
+ 0.75 & 0.236 & 0.861 \\
+ 0.576 & 0.587 & 0.902 \\
+ 0.607 & 0.95 & 0.872 \\
+ 0.693 & 0.971 & 0.891 \\
+\end{array}
+\right)$. 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: $1.29$ 
+Solid Angle: $0.55$ 
+Volume: $0.09$

pretraining/mathematica/geometry/solids/21259.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.867 & 0.008 & 0.813 \\
+ 0.276 & 0.913 & 0.138 \\
+ 0.696 & 0.475 & 0.174 \\
+ 0.226 & 0.857 & 0.019 \\
+ 0.147 & 0.843 & 0.117 \\
+ 0.933 & 0.538 & 0.526 \\
+ 0.986 & 0.919 & 0.973 \\
+\end{array}
+\right)$. 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: $0.09$ 
+Solid Angle: $0.38$ 
+Surface Area: $1.58$

pretraining/mathematica/geometry/solids/21372.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.015 & 0.624 & 0.275 \\
+ 0.18 & 0.761 & 0.695 \\
+ 0.029 & 0.414 & 0.165 \\
+ 0.883 & 0.6 & 0.952 \\
+ 0.641 & 0.488 & 0.189 \\
+\end{array}
+\right)$. 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: $0.03$ 
+Surface Area: $0.99$

pretraining/mathematica/geometry/solids/21957.txt

@@ -0,0 +1,21 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.326 & 0.863 & 0.275 \\
+ 0.463 & 0.049 & 0.36 \\
+ 0.602 & 0.01 & 0.436 \\
+ 0.82 & 0.154 & 0.218 \\
+ 0.31 & 0.802 & 0.048 \\
+ 0.006 & 0.392 & 0.221 \\
+ 0.791 & 0.031 & 0.522 \\
+ 0.342 & 0.31 & 0.052 \\
+ 0.596 & 0.639 & 0.122 \\
+ 0.62 & 0.046 & 0.063 \\
+ 0.002 & 0.267 & 0.89 \\
+ 0.374 & 0.747 & 0.953 \\
+\end{array}
+\right)$. 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: $2.18$ 
+Solid Angle: $2.47$ 
+Volume: $0.22$

pretraining/mathematica/geometry/solids/24731.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.853 & 0.306 & 0.698 \\
+ 0.34 & 0.609 & 0.125 \\
+ 0.49 & 0.767 & 0.159 \\
+ 0.918 & 0.771 & 0.534 \\
+ 0.522 & 0.972 & 0.835 \\
+ 0.468 & 0.863 & 0.456 \\
+ 0.018 & 0.506 & 0.682 \\
+ 0.123 & 0.03 & 0.246 \\
+ 0.302 & 0.141 & 0.178 \\
+\end{array}
+\right)$. 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: $1.81$ 
+Volume: $0.16$ 
+Solid Angle: $1.26$

pretraining/mathematica/geometry/solids/25817.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.05 & 0.558 & 0.991 \\
+ 0.667 & 0.102 & 0.926 \\
+ 0.509 & 0.206 & 0.063 \\
+ 0.439 & 0.841 & 0.152 \\
+ 0.952 & 0.558 & 0.302 \\
+ 0.303 & 0.292 & 0.547 \\
+ 0.787 & 0.857 & 0.737 \\
+ 0.23 & 0.634 & 0.452 \\
+\end{array}
+\right)$. 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: $0.2$ 
+Solid Angle: $0.83$

pretraining/mathematica/geometry/solids/26546.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.248 & 0.583 & 0.938 \\
+ 0.266 & 0.481 & 0.972 \\
+ 0.418 & 0.711 & 0.168 \\
+ 0.118 & 0.645 & 0.653 \\
+ 0.977 & 0.432 & 0.079 \\
+ 0.704 & 0.272 & 0.252 \\
+\end{array}
+\right)$. 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: $1.54$ 
+Surface Area: $0.91$ 
+Volume: $0.03$

pretraining/mathematica/geometry/solids/29389.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.561 & 0.571 & 0.41 \\
+ 0.109 & 0.471 & 0.216 \\
+ 0.67 & 0.012 & 0.673 \\
+ 0.462 & 0.341 & 0.804 \\
+ 0.623 & 0.808 & 0.722 \\
+ 0.088 & 0.706 & 0.629 \\
+\end{array}
+\right)$. 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: $0.97$ 
+Solid Angle: $2.85$ 
+Volume: $0.06$

pretraining/mathematica/geometry/solids/29601.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.869 & 0.661 & 0.889 \\
+ 0.006 & 0.528 & 0.679 \\
+ 0.043 & 0.359 & 0.279 \\
+ 0.589 & 0.47 & 0.352 \\
+ 0.089 & 0.883 & 0.393 \\
+ 0.011 & 0.573 & 0.324 \\
+ 0.948 & 0.746 & 0.107 \\
+ 0.579 & 0.303 & 0.793 \\
+ 0.162 & 0.34 & 0.146 \\
+\end{array}
+\right)$. 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: $0.91$ 
+Surface Area: $1.79$ 
+Volume: $0.15$

pretraining/mathematica/geometry/solids/31717.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.066 & 0.214 & 0.312 \\
+ 0.814 & 0.547 & 0.405 \\
+ 0.976 & 0.808 & 0.848 \\
+ 0.393 & 0.123 & 0.931 \\
+ 0.993 & 0.093 & 0.318 \\
+ 0.603 & 0.02 & 0.963 \\
+ 0.402 & 0.981 & 0.839 \\
+ 0.77 & 0.939 & 0.553 \\
+ 0.329 & 0.553 & 0.95 \\
+\end{array}
+\right)$. 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: $0.24$ 
+Solid Angle: $0.94$ 
+Surface Area: $2.27$

pretraining/mathematica/geometry/solids/3310.txt

@@ -0,0 +1,67 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -0.685 & 0. & -0.175 \\
+ -0.685 & 0. & 0.175 \\
+ -0.608 & -0.201 & -0.299 \\
+ -0.608 & -0.201 & 0.299 \\
+ -0.608 & 0.201 & -0.299 \\
+ -0.608 & 0.201 & 0.299 \\
+ -0.5 & -0.484 & -0.124 \\
+ -0.5 & -0.484 & 0.124 \\
+ -0.5 & 0.484 & -0.124 \\
+ -0.5 & 0.484 & 0.124 \\
+ -0.484 & -0.124 & -0.5 \\
+ -0.484 & -0.124 & 0.5 \\
+ -0.484 & 0.124 & -0.5 \\
+ -0.484 & 0.124 & 0.5 \\
+ -0.299 & -0.608 & -0.201 \\
+ -0.299 & -0.608 & 0.201 \\
+ -0.299 & 0.608 & -0.201 \\
+ -0.299 & 0.608 & 0.201 \\
+ -0.201 & -0.299 & -0.608 \\
+ -0.201 & -0.299 & 0.608 \\
+ -0.201 & 0.299 & -0.608 \\
+ -0.201 & 0.299 & 0.608 \\
+ -0.175 & -0.685 & 0. \\
+ -0.175 & 0.685 & 0. \\
+ -0.124 & -0.5 & -0.484 \\
+ -0.124 & -0.5 & 0.484 \\
+ -0.124 & 0.5 & -0.484 \\
+ -0.124 & 0.5 & 0.484 \\
+ 0. & -0.175 & -0.685 \\
+ 0. & -0.175 & 0.685 \\
+ 0. & 0.175 & -0.685 \\
+ 0. & 0.175 & 0.685 \\
+ 0.124 & -0.5 & -0.484 \\
+ 0.124 & -0.5 & 0.484 \\
+ 0.124 & 0.5 & -0.484 \\
+ 0.124 & 0.5 & 0.484 \\
+ 0.175 & -0.685 & 0. \\
+ 0.175 & 0.685 & 0. \\
+ 0.201 & -0.299 & -0.608 \\
+ 0.201 & -0.299 & 0.608 \\
+ 0.201 & 0.299 & -0.608 \\
+ 0.201 & 0.299 & 0.608 \\
+ 0.299 & -0.608 & -0.201 \\
+ 0.299 & -0.608 & 0.201 \\
+ 0.299 & 0.608 & -0.201 \\
+ 0.299 & 0.608 & 0.201 \\
+ 0.484 & -0.124 & -0.5 \\
+ 0.484 & -0.124 & 0.5 \\
+ 0.484 & 0.124 & -0.5 \\
+ 0.484 & 0.124 & 0.5 \\
+ 0.5 & -0.484 & -0.124 \\
+ 0.5 & -0.484 & 0.124 \\
+ 0.5 & 0.484 & -0.124 \\
+ 0.5 & 0.484 & 0.124 \\
+ 0.608 & -0.201 & -0.299 \\
+ 0.608 & -0.201 & 0.299 \\
+ 0.608 & 0.201 & -0.299 \\
+ 0.608 & 0.201 & 0.299 \\
+ 0.685 & 0. & -0.175 \\
+ 0.685 & 0. & 0.175 \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$120.$

pretraining/mathematica/geometry/solids/38854.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.557 & 0.249 & 0.096 \\
+ 0.361 & 0.762 & 0.016 \\
+ 0.201 & 0.174 & 0.985 \\
+ 0.988 & 0.083 & 0.682 \\
+ 0.752 & 0.136 & 0.882 \\
+ 0.189 & 0.662 & 0.879 \\
+ 0.868 & 0.832 & 0.292 \\
+ 0.639 & 0.436 & 0.117 \\
+ 0.398 & 0.8 & 0.015 \\
+\end{array}
+\right)$. 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: $1.91$ 
+Volume: $0.19$ 
+Surface Area: $2.09$

pretraining/mathematica/geometry/solids/41787.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.902 & 0.689 & 0.142 \\
+ 0.466 & 0.664 & 0.466 \\
+ 0.806 & 0.762 & 0.177 \\
+ 0.941 & 0.572 & 0.763 \\
+ 0.581 & 0.714 & 0.358 \\
+ 0.83 & 0.058 & 0.71 \\
+ 0.463 & 0.065 & 0.096 \\
+ 0.835 & 0.812 & 0.38 \\
+\end{array}
+\right)$. 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: $1.86$ 
+Surface Area: $1.22$

pretraining/mathematica/geometry/solids/42244.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.761 & 0.437 & 0.577 \\
+ 0.266 & 0.673 & 0.982 \\
+ 0.77 & 0.94 & 0.025 \\
+ 0.146 & 0.838 & 0.064 \\
+ 0.933 & 0.89 & 0.379 \\
+ 0.533 & 0.128 & 0.16 \\
+ 0.648 & 0.981 & 0.196 \\
+\end{array}
+\right)$. 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: $2.73$

pretraining/mathematica/geometry/solids/42739.txt

@@ -0,0 +1,33 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0 & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ 0 & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ 0 & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ 0 & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 \\
+ \frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ -\frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 \\
+ \frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ \frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ -\frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ \frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ -\frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ -\frac{7}{\sqrt{60-6 \sqrt{2}}} & -\frac{7}{\sqrt{60-6 \sqrt{2}}} & \frac{7}{\sqrt{60-6 \sqrt{2}}} \\
+ \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 \\
+ -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} \\
+ -\frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & \frac{1}{2} \sqrt{3+\frac{3}{\sqrt{2}}} & 0 \\
+ -\frac{1}{14} \sqrt{366+213 \sqrt{2}} & 0 & 0 \\
+ 0 & -\frac{1}{14} \sqrt{366+213 \sqrt{2}} & 0 \\
+ 0 & 0 & -\frac{1}{14} \sqrt{366+213 \sqrt{2}} \\
+ \frac{1}{14} \sqrt{366+213 \sqrt{2}} & 0 & 0 \\
+ 0 & \frac{1}{14} \sqrt{366+213 \sqrt{2}} & 0 \\
+ 0 & 0 & \frac{1}{14} \sqrt{366+213 \sqrt{2}} \\
+\end{array}
+\right)$. Determine the Inradius.
+Answer:
+$\frac{1}{2} \sqrt{\frac{3}{97} \left(166+95 \sqrt{2}\right)}$

pretraining/mathematica/geometry/solids/43260.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.638 & 0.876 & 0.418 \\
+ 0.245 & 0.385 & 0.139 \\
+ 0.288 & 0.203 & 0.98 \\
+ 0.488 & 0.059 & 0.066 \\
+\end{array}
+\right)$. 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: $0.97$ 
+Solid Angle: $0.27$ 
+Volume: $0.04$

pretraining/mathematica/geometry/solids/44291.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.217 & 0.067 & 0.12 \\
+ 0.462 & 0.742 & 0.64 \\
+ 0.373 & 0.944 & 0.201 \\
+ 0.967 & 0.412 & 0.421 \\
+ 0.397 & 0.017 & 0.015 \\
+ 0.583 & 0.168 & 0.799 \\
+ 0.625 & 0.335 & 0.874 \\
+\end{array}
+\right)$. 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: $1.5$ 
+Surface Area: $1.55$ 
+Volume: $0.12$

pretraining/mathematica/geometry/solids/48354.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.061 & 0.721 & 0.586 \\
+ 0.316 & 0.565 & 0.99 \\
+ 0.486 & 0.386 & 0.725 \\
+ 0.742 & 0.186 & 0.208 \\
+ 0.62 & 0.389 & 0.357 \\
+ 0.927 & 0.086 & 0.27 \\
+\end{array}
+\right)$. 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: $0.7$ 
+Solid Angle: $0.12$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/49598.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.143 & 0.608 & 0.286 \\
+ 0.519 & 0.871 & 0.994 \\
+ 0.856 & 0.055 & 0.229 \\
+ 0.114 & 0.218 & 0.747 \\
+ 0.777 & 0.103 & 0.22 \\
+ 0.911 & 0.571 & 0.491 \\
+ 0.429 & 0.055 & 0.796 \\
+ 0.444 & 0.372 & 0.201 \\
+\end{array}
+\right)$. 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: $1.25$ 
+Surface Area: $1.73$ 
+Volume: $0.14$

pretraining/mathematica/geometry/solids/4982.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.85 & 0.246 & 0.922 \\
+ 0.428 & 0.955 & 0.481 \\
+ 0.477 & 0.343 & 0.869 \\
+ 0.48 & 0.7 & 0.767 \\
+\end{array}
+\right)$. 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: $0.07$ 
+Surface Area: $0.32$

pretraining/mathematica/geometry/solids/50657.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.985 & 0.555 & 0.132 \\
+ 0.344 & 0.892 & 0.941 \\
+ 0.888 & 0.203 & 0.299 \\
+ 0.488 & 0.565 & 0.106 \\
+ 0.701 & 0.832 & 0.111 \\
+\end{array}
+\right)$. 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: $1.16$ 
+Volume: $0.05$ 
+Surface Area: $0.97$

pretraining/mathematica/geometry/solids/5155.txt

@@ -0,0 +1,39 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & 0. & 1.401 \\
+ 0. & 0. & -1.401 \\
+ 0.178 & -1.309 & 0.467 \\
+ 0.178 & 1.309 & 0.467 \\
+ 0.467 & -0.5 & 1.223 \\
+ 0.467 & 0.5 & 1.223 \\
+ 0.467 & -1.309 & -0.178 \\
+ 0.467 & -0.809 & -1.044 \\
+ 0.467 & 0.809 & -1.044 \\
+ 0.467 & 1.309 & -0.178 \\
+ 1.044 & 0. & -0.934 \\
+ 1.044 & -0.809 & 0.467 \\
+ 1.044 & 0.809 & 0.467 \\
+ -1.223 & -0.5 & 0.467 \\
+ -1.223 & 0.5 & 0.467 \\
+ 1.223 & -0.5 & -0.467 \\
+ 1.223 & 0.5 & -0.467 \\
+ 1.401 & 0. & 0. \\
+ -0.934 & 0. & -1.044 \\
+ -0.467 & -0.5 & -1.223 \\
+ -0.467 & 0.5 & -1.223 \\
+ -0.467 & -1.309 & 0.178 \\
+ -0.467 & -0.809 & 1.044 \\
+ -0.467 & 0.809 & 1.044 \\
+ -0.467 & 1.309 & 0.178 \\
+ 0.934 & 0. & 1.044 \\
+ -1.044 & 0. & 0.934 \\
+ -1.044 & -0.809 & -0.467 \\
+ -1.044 & 0.809 & -0.467 \\
+ -1.401 & 0. & 0. \\
+ -0.178 & -1.309 & -0.467 \\
+ -0.178 & 1.309 & -0.467 \\
+\end{array}
+\right)$. Determine the SurfaceArea.
+Answer:
+$41.29$

pretraining/mathematica/geometry/solids/522.txt

@@ -0,0 +1,5 @@
+Problem:
+A sphere centered at $\{-4.226,7.201,1.064\}$ has radius $4.835$. Estimate the sphere's surface area and volume.
+Answer:
+Surface Area: $293.77$ 
+Volume: $473.46$

pretraining/mathematica/geometry/solids/54818.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.35 & 0.492 & 0.079 \\
+ 0.213 & 0.261 & 0.146 \\
+ 0.913 & 0.717 & 0.358 \\
+ 0.829 & 0.818 & 0.754 \\
+ 0.005 & 0.942 & 0.531 \\
+ 0.788 & 0.8 & 0.232 \\
+\end{array}
+\right)$. 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: $0.07$ 
+Surface Area: $1.19$ 
+Solid Angle: $2.57$

pretraining/mathematica/geometry/solids/56848.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.109 & 0.576 & 0.748 \\
+ 0.381 & 0.164 & 0.283 \\
+ 0.823 & 0.586 & 0.763 \\
+ 0.865 & 0.606 & 0.143 \\
+ 0.241 & 0.076 & 0.006 \\
+ 0.288 & 0.818 & 0.058 \\
+ 0.226 & 0.065 & 0.127 \\
+ 0.725 & 0.912 & 0.242 \\
+ 0.419 & 0.669 & 0.743 \\
+\end{array}
+\right)$. 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:
+Volume: $0.15$ 
+Solid Angle: $1.07$ 
+Surface Area: $1.75$

pretraining/mathematica/geometry/solids/57938.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.614 & 0.018 & 0.252 \\
+ 0.043 & 0.267 & 0.857 \\
+ 0.453 & 0.977 & 0.837 \\
+ 0.513 & 0.023 & 0.164 \\
+ 0.886 & 0.978 & 0.646 \\
+ 0.188 & 0.793 & 0.155 \\
+\end{array}
+\right)$. 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: $1.88$ 
+Volume: $0.15$ 
+Solid Angle: $1.41$

pretraining/mathematica/geometry/solids/58362.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.462 & 0.186 & 0.489 \\
+ 0.997 & 0.612 & 0.611 \\
+ 0.198 & 0.422 & 0.683 \\
+ 0.114 & 0.584 & 0.891 \\
+ 0.719 & 0.743 & 0.27 \\
+ 0.62 & 0.604 & 0.211 \\
+ 0.639 & 0.953 & 0.666 \\
+ 0.351 & 0.804 & 0.702 \\
+\end{array}
+\right)$. 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: $1.04$ 
+Surface Area: $1.13$ 
+Volume: $0.07$

pretraining/mathematica/geometry/solids/60676.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.328 & 0.711 & 0.172 \\
+ 0.588 & 0.83 & 0.036 \\
+ 0.431 & 0.14 & 0.537 \\
+ 0.066 & 0.651 & 0.735 \\
+\end{array}
+\right)$. 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: $0.01$ 
+Solid Angle: $2.13$ 
+Surface Area: $0.61$

pretraining/mathematica/geometry/solids/63728.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.624 & 0.955 & 0.14 \\
+ 0.905 & 0.663 & 0.871 \\
+ 0.146 & 0.867 & 0.699 \\
+ 0.653 & 0.641 & 0.172 \\
+ 0.165 & 0.285 & 0.374 \\
+ 0.201 & 0.462 & 0.714 \\
+ 0.949 & 0.311 & 0.571 \\
+ 0.406 & 0.101 & 0.738 \\
+ 0.209 & 0.292 & 0.327 \\
+\end{array}
+\right)$. 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: $1.06$ 
+Volume: $0.17$ 
+Surface Area: $1.79$

pretraining/mathematica/geometry/solids/64249.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.126 & 0.545 & 0.389 \\
+ 0.01 & 0.925 & 0.87 \\
+ 0.851 & 0.782 & 0.995 \\
+ 0.032 & 0.186 & 0.066 \\
+ 0.274 & 0.271 & 0.858 \\
+ 0.962 & 0.787 & 0.117 \\
+ 0.692 & 0.022 & 0.374 \\
+ 0.719 & 0.445 & 0.051 \\
+\end{array}
+\right)$. 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: $2.72$ 
+Solid Angle: $6.26$ 
+Volume: $0.31$

pretraining/mathematica/geometry/solids/64670.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.955 & 0.757 & 0.445 \\
+ 0.525 & 0.541 & 0.625 \\
+ 0.535 & 0.626 & 0.599 \\
+ 0.016 & 0.134 & 0.311 \\
+ 0.382 & 0.024 & 0.367 \\
+ 0.171 & 0.932 & 0.547 \\
+ 0.937 & 0.079 & 0.065 \\
+ 0.268 & 0.512 & 0.31 \\
+\end{array}
+\right)$. 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: $1.63$ 
+Solid Angle: $0.56$ 
+Volume: $0.09$

pretraining/mathematica/geometry/solids/64815.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.047 & 0.671 & 0.108 \\
+ 0.829 & 0.933 & 0.662 \\
+ 0.442 & 0.869 & 0.054 \\
+ 0.357 & 0.89 & 0.33 \\
+ 0.957 & 0.813 & 0.627 \\
+ 0.884 & 0.881 & 0.921 \\
+ 0.347 & 0.093 & 0.781 \\
+ 0.361 & 0.708 & 0.009 \\
+ 0.155 & 0.458 & 0.831 \\
+\end{array}
+\right)$. 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: $1.79$ 
+Solid Angle: $1.17$

pretraining/mathematica/geometry/solids/65960.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.356 & 0.648 & 0.124 \\
+ 0.928 & 0.861 & 0.56 \\
+ 0.463 & 0.79 & 0.718 \\
+ 0.709 & 0.049 & 0.535 \\
+ 0.092 & 0.193 & 0.004 \\
+ 0.036 & 0.785 & 0.569 \\
+ 0.614 & 0.527 & 0.13 \\
+\end{array}
+\right)$. 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: $3.45$ 
+Surface Area: $1.69$

pretraining/mathematica/geometry/solids/66.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.23 & 0.277 & 0.297 \\
+ 0.719 & 0.476 & 0.626 \\
+ 0.093 & 0.516 & 0.859 \\
+ 0.767 & 0.908 & 0.414 \\
+ 0.453 & 0.522 & 0.98 \\
+ 0.189 & 0.055 & 0.167 \\
+ 0.966 & 0.904 & 0.71 \\
+\end{array}
+\right)$. 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: $1.36$ 
+Solid Angle: $4.98$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/66188.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.884 & 0.116 & 0.372 \\
+ 0.141 & 0.019 & 0.152 \\
+ 0.631 & 0.003 & 0.672 \\
+ 0.026 & 0.999 & 0.189 \\
+ 0.85 & 0.722 & 0.236 \\
+ 0.107 & 0.55 & 0.325 \\
+ 0.873 & 0.184 & 0.913 \\
+ 0.152 & 0.228 & 0.104 \\
+ 0.459 & 0.211 & 0.112 \\
+\end{array}
+\right)$. 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: $2.47$ 
+Volume: $0.18$ 
+Surface Area: $2.05$

pretraining/mathematica/geometry/solids/67198.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.101 & 0.282 & 0.029 \\
+ 0.634 & 0.838 & 0.079 \\
+ 0.641 & 0.97 & 0.287 \\
+ 0.666 & 0.07 & 0.785 \\
+ 0.109 & 0.799 & 0.941 \\
+ 0.688 & 0.701 & 0.776 \\
+ 0.433 & 0.937 & 0.197 \\
+ 0.195 & 0.171 & 0.128 \\
+\end{array}
+\right)$. 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:
+Surface Area: $2.01$ 
+Volume: $0.19$ 
+Solid Angle: $1.16$

pretraining/mathematica/geometry/solids/68660.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.911 & 0.177 & 0.516 \\
+ 0.395 & 0.18 & 0.696 \\
+ 0.334 & 0.788 & 0.963 \\
+ 0.931 & 0.314 & 0.817 \\
+ 0.16 & 0.951 & 0.085 \\
+ 0.248 & 0.487 & 0.154 \\
+\end{array}
+\right)$. 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: $1.56$ 
+Solid Angle: $1.08$

pretraining/mathematica/geometry/solids/70221.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.019 & 0.346 & 0.168 \\
+ 0.423 & 0.555 & 0.136 \\
+ 0.258 & 0.05 & 0.045 \\
+ 0.788 & 0.722 & 0.394 \\
+\end{array}
+\right)$. 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: $0.01$ 
+Solid Angle: $0.27$ 
+Surface Area: $0.43$

pretraining/mathematica/geometry/solids/71761.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.82 & 0.935 & 0.928 \\
+ 0.283 & 0.72 & 0.492 \\
+ 0.522 & 0.805 & 0.946 \\
+ 0.353 & 0.399 & 0.957 \\
+ 0.872 & 0.923 & 0.957 \\
+ 0.31 & 0.761 & 0.024 \\
+ 0.567 & 0.466 & 0.326 \\
+\end{array}
+\right)$. 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: $1.06$ 
+Solid Angle: $3.14$

pretraining/mathematica/geometry/solids/7302.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.3 & 0.036 & 0.208 \\
+ 0.172 & 0.667 & 0.373 \\
+ 0.062 & 0.959 & 0.686 \\
+ 0.822 & 0.549 & 0.172 \\
+ 0.069 & 0.319 & 0.894 \\
+\end{array}
+\right)$. 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: $0.54$ 
+Volume: $0.06$ 
+Surface Area: $1.29$