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pretraining/mathematica/geometry/solids/10338.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.979 & 0.479 & 0.188 \\
+ 0.125 & 0.889 & 0.639 \\
+ 0.431 & 0.444 & 0.167 \\
+ 0.916 & 0.1 & 0.141 \\
+ 0.694 & 0.88 & 0.085 \\
+\end{array}
+\right)$. 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: $1.26$ 
+Volume: $0.04$ 
+Surface Area: $0.94$

pretraining/mathematica/geometry/solids/10833.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.616 & 0.962 & 0.625 \\
+ 0.801 & 0.453 & 0.174 \\
+ 0.105 & 0.516 & 0.487 \\
+ 0.109 & 0.634 & 0.963 \\
+ 0.502 & 0.207 & 0.936 \\
+ 0.33 & 0.03 & 0.742 \\
+ 0.587 & 0.09 & 0.448 \\
+ 0.951 & 0.832 & 0.562 \\
+\end{array}
+\right)$. 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: $1.63$ 
+Volume: $0.15$ 
+Surface Area: $1.74$

pretraining/mathematica/geometry/solids/11865.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.248 & 0.55 & 0.191 \\
+ 0.245 & 0.587 & 0.215 \\
+ 0.478 & 0.152 & 0.798 \\
+ 0.57 & 0.109 & 0.983 \\
+ 0.405 & 0.458 & 0.241 \\
+ 0.657 & 0.456 & 0.542 \\
+ 0.413 & 0.805 & 0.749 \\
+ 0.108 & 0.53 & 0.654 \\
+ 0.284 & 0.861 & 0.954 \\
+ 0.448 & 0.066 & 0.052 \\
+\end{array}
+\right)$. 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: $2.04$ 
+Surface Area: $1.44$ 
+Volume: $0.1$

pretraining/mathematica/geometry/solids/12635.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.498 & 0.193 & 0.21 \\
+ 0.006 & 0.845 & 0.669 \\
+ 0.348 & 0.677 & 0.739 \\
+ 0.564 & 0.274 & 0.986 \\
+ 0.758 & 0.549 & 0.423 \\
+\end{array}
+\right)$. 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: $0.05$ 
+Solid Angle: $0.54$

pretraining/mathematica/geometry/solids/13732.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.645 & 0.254 & 0.561 \\
+ 0.085 & 0.696 & 0.569 \\
+ 0.005 & 0.457 & 0.298 \\
+ 0.377 & 0.253 & 0.239 \\
+ 0.36 & 0.092 & 0.275 \\
+ 0.979 & 0.888 & 0.125 \\
+ 0.819 & 0.259 & 0.979 \\
+\end{array}
+\right)$. 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:
+Surface Area: $1.68$ 
+Solid Angle: $5.96$ 
+Volume: $0.12$

pretraining/mathematica/geometry/solids/14934.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.576 & 0.576 & 0.474 \\
+ 0.857 & 0.418 & 0.274 \\
+ 0.305 & 0.207 & 0.78 \\
+ 0.926 & 0.658 & 0.929 \\
+\end{array}
+\right)$. 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: $1.93$ 
+Volume: $0.02$

pretraining/mathematica/geometry/solids/15513.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.253 & 0.66 & 0.75 \\
+ 0.758 & 0.344 & 0.062 \\
+ 0.42 & 0.186 & 0.852 \\
+ 0.709 & 0.032 & 0.847 \\
+ 0.423 & 0.409 & 0.859 \\
+ 0.697 & 0.629 & 0.555 \\
+ 0.267 & 0.742 & 0.508 \\
+\end{array}
+\right)$. 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: $1.17$ 
+Volume: $0.06$

pretraining/mathematica/geometry/solids/16335.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.601 & 0.478 & 0.333 \\
+ 0.982 & 0.158 & 0.98 \\
+ 0.373 & 0.07 & 0.771 \\
+ 0.542 & 0.839 & 0.832 \\
+\end{array}
+\right)$. 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: $0.87$ 
+Solid Angle: $0.64$

pretraining/mathematica/geometry/solids/17045.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.617 & 0.975 & 0.794 \\
+ 0.978 & 0.983 & 0.712 \\
+ 0.354 & 0.035 & 0.574 \\
+ 0.685 & 0.284 & 0.648 \\
+ 0.545 & 0.334 & 0.894 \\
+ 0.164 & 0.829 & 0.463 \\
+ 0.788 & 0.566 & 0.196 \\
+ 0.883 & 0.174 & 0.162 \\
+\end{array}
+\right)$. 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: $2.06$ 
+Surface Area: $1.81$ 
+Volume: $0.16$

pretraining/mathematica/geometry/solids/18477.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.64 & 0.85 & 0.139 \\
+ 0.47 & 0.361 & 0.03 \\
+ 0.858 & 0.944 & 0.105 \\
+ 0.662 & 0.12 & 0.321 \\
+ 0.95 & 0.359 & 0.43 \\
+ 0.204 & 0.352 & 0.382 \\
+\end{array}
+\right)$. 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: $0.04$ 
+Surface Area: $0.91$ 
+Solid Angle: $1.61$

pretraining/mathematica/geometry/solids/21602.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.118 & 0.697 & 0.956 \\
+ 0.067 & 0.891 & 0.729 \\
+ 0.667 & 0.89 & 0.244 \\
+ 0.006 & 0.756 & 0.26 \\
+ 0.153 & 0.931 & 0.743 \\
+ 0.885 & 0.771 & 0.865 \\
+ 0.078 & 0.383 & 0.404 \\
+ 0.612 & 0.311 & 0.387 \\
+ 0.96 & 0.205 & 0.879 \\
+\end{array}
+\right)$. 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: $1.85$ 
+Volume: $0.21$ 
+Surface Area: $2.05$

pretraining/mathematica/geometry/solids/2239.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.369 & 0.153 & 0.917 \\
+ 0.846 & 0.291 & 0.69 \\
+ 0.698 & 0.07 & 0.717 \\
+ 0.103 & 0.324 & 0.24 \\
+ 0.989 & 0.996 & 0.46 \\
+ 0.174 & 0.11 & 0.66 \\
+ 0.076 & 0.508 & 0.683 \\
+ 0.896 & 0.586 & 0.245 \\
+ 0.38 & 0.548 & 0.253 \\
+ 0.932 & 0.241 & 0.633 \\
+\end{array}
+\right)$. 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: $1.8$ 
+Volume: $0.16$ 
+Solid Angle: $1.89$

pretraining/mathematica/geometry/solids/24177.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.557 & 0.097 & 0.213 \\
+ 0.998 & 0.306 & 0.295 \\
+ 0.86 & 0.118 & 0.616 \\
+ 0.635 & 0.089 & 0.716 \\
+ 0.904 & 0.729 & 0.557 \\
+ 0.248 & 0.253 & 0.637 \\
+ 0.668 & 0.514 & 0.246 \\
+ 0.22 & 0.194 & 0.309 \\
+ 0.136 & 0.219 & 0.555 \\
+\end{array}
+\right)$. 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: $2.13$ 
+Volume: $0.09$ 
+Surface Area: $1.16$

pretraining/mathematica/geometry/solids/24562.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.475 & 0.839 & 0.686 \\
+ 0.324 & 0.915 & 0.803 \\
+ 0.104 & 0.003 & 0.401 \\
+ 0.329 & 0.593 & 0.147 \\
+ 0.004 & 0.394 & 0.228 \\
+ 0.276 & 0.499 & 0.948 \\
+ 0.356 & 0.066 & 0.816 \\
+ 0.005 & 0.254 & 0.103 \\
+ 0.211 & 0.595 & 0.692 \\
+ 0.341 & 0.124 & 0.125 \\
+ 0.799 & 0.35 & 0.412 \\
+\end{array}
+\right)$. 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: $0.16$ 
+Surface Area: $1.76$ 
+Solid Angle: $2.57$

pretraining/mathematica/geometry/solids/25230.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.916 & 0.439 & 0.734 \\
+ 0.048 & 0.078 & 0.251 \\
+ 0.941 & 0.338 & 0.207 \\
+ 0.699 & 0.278 & 0.124 \\
+ 0.741 & 0.421 & 0.891 \\
+ 0.69 & 0.691 & 0.128 \\
+ 0.468 & 0.346 & 0.138 \\
+ 0.645 & 0.904 & 0.839 \\
+\end{array}
+\right)$. 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: $1.55$ 
+Solid Angle: $2.1$ 
+Volume: $0.12$

pretraining/mathematica/geometry/solids/29440.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.232 & 0.214 & 0.172 \\
+ 0.143 & 0.682 & 0.546 \\
+ 0.035 & 0.875 & 0.807 \\
+ 0.224 & 0.671 & 0.977 \\
+ 0.935 & 0.783 & 0.227 \\
+ 0.649 & 0.719 & 0.226 \\
+ 0.05 & 0.329 & 0.926 \\
+ 0.695 & 0.361 & 0.829 \\
+ 0.179 & 0.06 & 0.872 \\
+ 0.764 & 0.024 & 0.508 \\
+\end{array}
+\right)$. 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: $1.67$ 
+Surface Area: $2.2$ 
+Volume: $0.24$

pretraining/mathematica/geometry/solids/30070.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.838 & 0.118 & 0.86 \\
+ 0.332 & 0.853 & 0.276 \\
+ 0.353 & 0.728 & 0.964 \\
+ 0.941 & 0.419 & 0.269 \\
+ 0.103 & 0.113 & 0.687 \\
+ 0.255 & 0.032 & 0.127 \\
+ 0.851 & 0.74 & 0.072 \\
+ 0.43 & 0.935 & 0.458 \\
+ 0.904 & 0.965 & 0.543 \\
+ 0.205 & 0.602 & 0.097 \\
+ 0.153 & 0.069 & 0.608 \\
+\end{array}
+\right)$. 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: $2.66$ 
+Solid Angle: $1.5$ 
+Volume: $0.33$

pretraining/mathematica/geometry/solids/30343.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.295 & 0.242 & 0.632 \\
+ 0.962 & 0.425 & 0.208 \\
+ 0.735 & 0.511 & 0.984 \\
+ 0.664 & 0.99 & 0.526 \\
+ 0.295 & 0.421 & 0.632 \\
+ 0.479 & 0.991 & 0.199 \\
+ 0.913 & 0.449 & 0.175 \\
+ 0.878 & 0.677 & 0.299 \\
+ 0.034 & 0.528 & 0.186 \\
+\end{array}
+\right)$. 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: $1.66$ 
+Solid Angle: $1.64$ 
+Volume: $0.14$

pretraining/mathematica/geometry/solids/30823.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.925 & 0.684 & 0.908 \\
+ 0.38 & 0.545 & 0.25 \\
+ 0.088 & 0.302 & 0.102 \\
+ 0.376 & 0.013 & 0.92 \\
+ 0.395 & 0.711 & 0.69 \\
+ 0.927 & 0.138 & 0.858 \\
+ 0.076 & 0.029 & 0.287 \\
+\end{array}
+\right)$. 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: $0.12$ 
+Solid Angle: $0.7$ 
+Surface Area: $1.7$

pretraining/mathematica/geometry/solids/32233.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.871 & 0.881 & 0.024 \\
+ 0.773 & 0.827 & 0.328 \\
+ 0.105 & 0.908 & 0.145 \\
+ 0.221 & 0.114 & 0.482 \\
+ 0.991 & 0.415 & 0.427 \\
+ 0.456 & 0.213 & 0.84 \\
+ 0.697 & 0.002 & 0.419 \\
+ 0.609 & 0.894 & 0.271 \\
+\end{array}
+\right)$. 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: $1.8$ 
+Solid Angle: $0.92$ 
+Volume: $0.14$

pretraining/mathematica/geometry/solids/33277.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.137 & 0.626 & 0.948 \\
+ 0.381 & 0.827 & 0.88 \\
+ 0.669 & 0.153 & 0.538 \\
+ 0.066 & 0.514 & 0.494 \\
+ 0.207 & 0.549 & 0.905 \\
+ 0.777 & 0.19 & 0.616 \\
+ 0.23 & 0.166 & 0.223 \\
+ 0.423 & 0.377 & 0.131 \\
+ 0.674 & 0.674 & 0.073 \\
+\end{array}
+\right)$. 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: $1.13$ 
+Volume: $0.11$ 
+Surface Area: $1.45$

pretraining/mathematica/geometry/solids/34079.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.564 & 0.826 & 0.759 \\
+ 0.203 & 0.564 & 0.621 \\
+ 0.931 & 0.792 & 0.448 \\
+ 0.241 & 0.738 & 0.256 \\
+ 0.514 & 0.256 & 0.973 \\
+ 0.959 & 0.972 & 0.898 \\
+ 0.451 & 0.107 & 0.581 \\
+\end{array}
+\right)$. 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: $1.43$ 
+Solid Angle: $4.11$ 
+Volume: $0.1$

pretraining/mathematica/geometry/solids/34115.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.508 & 0.76 & 0.376 \\
+ 0.21 & 0.83 & 0.119 \\
+ 0.011 & 0.139 & 0.726 \\
+ 0.519 & 0.603 & 0.957 \\
+ 0.835 & 0.122 & 0.966 \\
+\end{array}
+\right)$. 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: $1.29$ 
+Volume: $0.06$ 
+Solid Angle: $1.67$

pretraining/mathematica/geometry/solids/34272.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.81 & 0.185 & 0.741 \\
+ 0.8 & 0.052 & 0.858 \\
+ 0.308 & 0.153 & 0.752 \\
+ 0.951 & 0.753 & 0.497 \\
+ 0.355 & 0.96 & 0.955 \\
+ 0.018 & 0.591 & 0.336 \\
+ 0.445 & 0.066 & 0.602 \\
+ 0.814 & 0.922 & 0.497 \\
+ 0.144 & 0.278 & 0.237 \\
+\end{array}
+\right)$. 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: $0.18$ 
+Surface Area: $1.94$ 
+Solid Angle: $4.94$

pretraining/mathematica/geometry/solids/36666.txt

@@ -0,0 +1,31 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & 0.577 & 0.289 \\
+ -0.577 & 0. & -0.289 \\
+ 0. & -0.577 & 0.289 \\
+ 0.577 & 0. & -0.289 \\
+ -0.577 & 0. & 0.289 \\
+ 0. & -0.577 & -0.289 \\
+ 0.577 & 0. & 0.289 \\
+ 0. & 0.577 & -0.289 \\
+ 0.289 & 0. & 0.577 \\
+ -0.289 & -0.577 & 0. \\
+ 0.289 & 0. & -0.577 \\
+ -0.289 & 0.577 & 0. \\
+ 0.289 & -0.577 & 0. \\
+ -0.289 & 0. & -0.577 \\
+ 0.289 & 0.577 & 0. \\
+ -0.289 & 0. & 0.577 \\
+ 0.577 & 0.289 & 0. \\
+ 0. & -0.289 & -0.577 \\
+ -0.577 & 0.289 & 0. \\
+ 0. & -0.289 & 0.577 \\
+ 0. & 0.289 & -0.577 \\
+ -0.577 & -0.289 & 0. \\
+ 0. & 0.289 & 0.577 \\
+ 0.577 & -0.289 & 0. \\
+\end{array}
+\right)$. Determine the FaceCount.
+Answer:
+$24.$

pretraining/mathematica/geometry/solids/37742.txt

@@ -0,0 +1,5 @@
+Problem:
+A sphere centered at $\{-9.588,-9.491,1.119\}$ has radius $5.273$. Estimate the sphere's surface area and volume.
+Answer:
+Volume: $614.02$ 
+Surface Area: $349.36$

pretraining/mathematica/geometry/solids/38557.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.39 & 0.94 & 0.556 \\
+ 0.759 & 0.97 & 0.401 \\
+ 0.739 & 0.386 & 0.546 \\
+ 0.194 & 0.008 & 0.796 \\
+ 0.074 & 0.611 & 0.832 \\
+ 0.189 & 0.068 & 0.374 \\
+ 0.819 & 0.301 & 0.017 \\
+ 0.28 & 0.173 & 0.755 \\
+\end{array}
+\right)$. 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: $1.23$ 
+Surface Area: $1.77$ 
+Volume: $0.12$

pretraining/mathematica/geometry/solids/38962.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.233 & 0.157 & 0.595 \\
+ 0.463 & 0.883 & 0. \\
+ 0.439 & 0.004 & 0.436 \\
+ 0.328 & 0.46 & 0.779 \\
+ 0.993 & 0.909 & 0.337 \\
+ 0.023 & 0.246 & 0.625 \\
+ 0.563 & 0.907 & 0.651 \\
+ 0.944 & 0.33 & 0.339 \\
+ 0.077 & 0.843 & 0.957 \\
+\end{array}
+\right)$. 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: $4.66$ 
+Volume: $0.19$ 
+Surface Area: $2.17$

pretraining/mathematica/geometry/solids/41665.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.168 & 0.963 & 0.072 \\
+ 0.579 & 0.736 & 0.664 \\
+ 0.255 & 0.657 & 0.865 \\
+ 0.91 & 0.019 & 0.627 \\
+ 0.416 & 0.827 & 0.251 \\
+\end{array}
+\right)$. 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: $1.$ 
+Volume: $0.04$ 
+Solid Angle: $0.2$

pretraining/mathematica/geometry/solids/45631.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.902 & 0.241 & 0.287 \\
+ 0.378 & 0.791 & 0.554 \\
+ 0.053 & 0.496 & 0.759 \\
+ 0.651 & 0.621 & 0.059 \\
+ 0.957 & 0.258 & 0.235 \\
+ 0.835 & 0.051 & 0.015 \\
+\end{array}
+\right)$. 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:
+Surface Area: $1.02$ 
+Volume: $0.05$ 
+Solid Angle: $3.31$

pretraining/mathematica/geometry/solids/47464.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.046 & 0.968 & 0.312 \\
+ 0.066 & 0.912 & 0.036 \\
+ 0.632 & 0.581 & 0.466 \\
+ 0.917 & 0.871 & 0.724 \\
+\end{array}
+\right)$. 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: $0.56$ 
+Solid Angle: $0.49$

pretraining/mathematica/geometry/solids/48536.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.496 & 0.116 & 0.931 \\
+ 0.809 & 0.596 & 0.042 \\
+ 0.544 & 0.117 & 0.715 \\
+ 0.304 & 0.925 & 0.93 \\
+ 0.458 & 0.04 & 0.879 \\
+ 0.964 & 0.972 & 0.481 \\
+ 0.108 & 0.622 & 0.496 \\
+ 0.387 & 0.249 & 0.143 \\
+ 0.29 & 0.43 & 0.736 \\
+\end{array}
+\right)$. 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: $2.$ 
+Solid Angle: $1.91$

pretraining/mathematica/geometry/solids/49187.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.243 & 0.283 & 0.363 \\
+ 0.987 & 0.256 & 0.943 \\
+ 0.781 & 0.241 & 0.545 \\
+ 0.892 & 0.256 & 0.876 \\
+ 0.944 & 0.908 & 0.855 \\
+\end{array}
+\right)$. 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: $0.75$ 
+Volume: $0.02$ 
+Solid Angle: $0.12$

pretraining/mathematica/geometry/solids/4942.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.818 & 0.352 & 0.245 \\
+ 0.496 & 0.373 & 0.865 \\
+ 0.475 & 0.352 & 0.513 \\
+ 0.657 & 0.004 & 0.037 \\
+ 0.18 & 0.944 & 0.585 \\
+ 0.842 & 0.707 & 0.479 \\
+ 0.781 & 0.224 & 0.518 \\
+ 0.767 & 0.797 & 0.019 \\
+ 0.036 & 0.979 & 0.122 \\
+\end{array}
+\right)$. 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:
+Surface Area: $1.99$ 
+Solid Angle: $4.85$ 
+Volume: $0.18$

pretraining/mathematica/geometry/solids/50923.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.31 & 0.649 & 0.091 \\
+ 0.964 & 0.358 & 0.54 \\
+ 0.644 & 0.538 & 0.284 \\
+ 0.218 & 0.115 & 0.417 \\
+ 0.41 & 0.988 & 0.332 \\
+ 0.933 & 0.605 & 0.649 \\
+ 0.332 & 0.713 & 0.116 \\
+ 0.745 & 0.161 & 0.676 \\
+\end{array}
+\right)$. 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: $0.06$ 
+Surface Area: $1.2$

pretraining/mathematica/geometry/solids/51378.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ \frac{1}{4} \left(-2-\sqrt{2 \left(1+\sqrt{5}\right)}\right) & \frac{1}{2} \sqrt{1+\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)}} & -\frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \\
+ \frac{1}{4} \left(-3-\sqrt{5}+2 \sqrt{2+\sqrt{5}}\right) & \frac{1}{2} \sqrt{\frac{1}{2} \left(-10-4 \sqrt{5}+\sqrt{2 \left(89+41 \sqrt{5}\right)}\right)} & \frac{1}{4} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(\sqrt{5}-3\right) & -\frac{1}{2} \sqrt{1+\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)}} & \frac{1}{4} \left(1-\sqrt{5}-2 \sqrt{\sqrt{5}-2}\right) \\
+ \frac{1}{4} \left(3-\sqrt{5}\right) & -\frac{1}{2} \sqrt{1+\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)}} & \frac{1}{4} \left(-1+\sqrt{5}+2 \sqrt{\sqrt{5}-2}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}-2 \sqrt{2+\sqrt{5}}\right) & \frac{1}{2} \sqrt{\frac{1}{2} \left(-10-4 \sqrt{5}+\sqrt{2 \left(89+41 \sqrt{5}\right)}\right)} & \frac{1}{4} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(2+\sqrt{2 \left(1+\sqrt{5}\right)}\right) & \frac{1}{2} \sqrt{1+\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)}} & \frac{1}{2} \sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \\
+\end{array}
+\right)$. Determine the SurfaceArea.
+Answer:
+$\sqrt{\text{Root}\left[\text{$\#$1}^{16}-144 \text{$\#$1}^{15}+8000 \text{$\#$1}^{14}-238336 \text{$\#$1}^{13}+4471808 \text{$\#$1}^{12}-59056128 \text{$\#$1}^{11}+582574080 \text{$\#$1}^{10}-4450287616 \text{$\#$1}^9+27899592704 \text{$\#$1}^8-131002793984 \text{$\#$1}^7+465349640192 \text{$\#$1}^6-1506711437312 \text{$\#$1}^5+3103331975168 \text{$\#$1}^4-2996008124416 \text{$\#$1}^3+1021665345536 \text{$\#$1}^2-98784247808 \text{$\#$1}+4294967296\&,4\right]}$

pretraining/mathematica/geometry/solids/5329.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.579 & 0.81 & 0.78 \\
+ 0.933 & 0.45 & 0.715 \\
+ 1. & 0.717 & 0.78 \\
+ 0.489 & 0.969 & 0.454 \\
+ 0.277 & 0.802 & 0.697 \\
+ 0.677 & 0.687 & 0.95 \\
+ 0.697 & 0.538 & 0.187 \\
+\end{array}
+\right)$. 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: $0.89$ 
+Solid Angle: $5.14$

pretraining/mathematica/geometry/solids/53734.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.136 & 0.768 & 0.426 \\
+ 0.362 & 0.794 & 0.671 \\
+ 0.176 & 0.028 & 0.624 \\
+ 0.885 & 0.711 & 0.145 \\
+ 0.033 & 0.409 & 0.605 \\
+ 0.195 & 0.42 & 0.243 \\
+ 0.285 & 0.174 & 0.708 \\
+ 0.898 & 0.137 & 0.575 \\
+ 0.569 & 0.216 & 0.703 \\
+\end{array}
+\right)$. 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: $2.04$ 
+Surface Area: $1.59$ 
+Volume: $0.13$

pretraining/mathematica/geometry/solids/55402.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.581 & 0.633 & 0.854 \\
+ 0.268 & 0.266 & 0.328 \\
+ 0.831 & 0.687 & 0.833 \\
+ 0.987 & 0.034 & 0.195 \\
+\end{array}
+\right)$. 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: $0.78$ 
+Solid Angle: $0.36$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/57959.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.832 & 0.085 & 0.02 \\
+ 0.989 & 0.263 & 0.875 \\
+ 0.97 & 0.948 & 0.951 \\
+ 0.16 & 0.345 & 0.548 \\
+ 0.246 & 0.267 & 0.065 \\
+ 0.621 & 0.589 & 0.34 \\
+\end{array}
+\right)$. 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: $0.67$ 
+Surface Area: $1.78$ 
+Volume: $0.12$

pretraining/mathematica/geometry/solids/58418.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.16 & 0.413 & 0.784 \\
+ 0.386 & 0.795 & 0.019 \\
+ 0.621 & 0.401 & 0.159 \\
+ 0.642 & 0.741 & 0.202 \\
+ 0.34 & 0.422 & 0.465 \\
+ 0.654 & 0.738 & 0.411 \\
+ 0.337 & 0.62 & 0.712 \\
+ 0.555 & 0.208 & 0.424 \\
+ 0.912 & 0.618 & 0.845 \\
+\end{array}
+\right)$. 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: $1.19$ 
+Volume: $0.08$ 
+Solid Angle: $0.87$

pretraining/mathematica/geometry/solids/59476.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.095 & 0.826 & 0.946 \\
+ 0.482 & 0.592 & 0.424 \\
+ 0.355 & 0.592 & 0.451 \\
+ 0.402 & 0.738 & 0.634 \\
+\end{array}
+\right)$. 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:
+Volume: $0.$ 
+Solid Angle: $0.01$ 
+Surface Area: $0.12$

pretraining/mathematica/geometry/solids/60186.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.28 & 0.566 & 0.305 \\
+ 0.125 & 0.623 & 0.983 \\
+ 0.473 & 0.224 & 0.959 \\
+ 0.051 & 0.365 & 0.827 \\
+\end{array}
+\right)$. 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: $0.16$ 
+Surface Area: $0.48$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/61795.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.147 & 0.331 & 0.475 \\
+ 0.006 & 0.044 & 0.216 \\
+ 0.39 & 0.425 & 0.936 \\
+ 0.924 & 0.669 & 0.052 \\
+ 0.653 & 0.281 & 0.286 \\
+\end{array}
+\right)$. 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: $3.25$ 
+Volume: $0.05$ 
+Surface Area: $1.05$

pretraining/mathematica/geometry/solids/61921.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.778 & 0.716 & 0.375 \\
+ 0.309 & 0.367 & 0.823 \\
+ 0.355 & 0.905 & 0.549 \\
+ 0.72 & 0.737 & 0.598 \\
+ 0.547 & 0.452 & 0.043 \\
+ 0.422 & 0.093 & 0.283 \\
+ 0.406 & 0.527 & 0.313 \\
+\end{array}
+\right)$. 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: $1.$ 
+Volume: $0.05$ 
+Solid Angle: $1.6$

pretraining/mathematica/geometry/solids/62841.txt

@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{-5.144,-6.244,-9.122\}$ has radii $\{1.97,5.484,8.629\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Surface Area: $349.63$ 
+Volume: $390.47$

pretraining/mathematica/geometry/solids/63406.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.645 & 0.527 & 0.912 \\
+ 0.144 & 0.392 & 0.041 \\
+ 0.042 & 0.084 & 0.077 \\
+ 0.556 & 0.124 & 0.229 \\
+ 0.736 & 0.563 & 0.11 \\
+ 0.12 & 0.249 & 0.843 \\
+ 0.815 & 0.654 & 0.293 \\
+\end{array}
+\right)$. 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: $1.54$ 
+Solid Angle: $0.51$ 
+Volume: $0.09$

pretraining/mathematica/geometry/solids/64780.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.409 & 0.277 & 0.961 \\
+ 0.637 & 0.187 & 0.979 \\
+ 0.1 & 0.194 & 0.426 \\
+ 0.256 & 0.066 & 0.634 \\
+ 0.344 & 0.878 & 0.403 \\
+ 0.31 & 0.596 & 0.796 \\
+ 0.437 & 0.937 & 0.034 \\
+ 0.016 & 0.219 & 0.585 \\
+ 0.241 & 0.731 & 0.547 \\
+ 0.254 & 0.046 & 0.837 \\
+\end{array}
+\right)$. 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: $3.65$ 
+Surface Area: $1.3$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/65088.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.815 & 0.027 & 0.182 \\
+ 0.937 & 0.632 & 0.93 \\
+ 0.812 & 0.076 & 0.318 \\
+ 0.094 & 0.961 & 0.241 \\
+ 0.149 & 0.296 & 0.813 \\
+\end{array}
+\right)$. 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: $0.11$ 
+Solid Angle: $0.56$

pretraining/mathematica/geometry/solids/65891.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.817 & 0.404 & 0.993 \\
+ 0.709 & 0.31 & 0.717 \\
+ 0.448 & 0.71 & 0.386 \\
+ 0.835 & 0.067 & 0.795 \\
+ 0.755 & 0.679 & 0.376 \\
+ 0.854 & 0.481 & 0.969 \\
+ 0.594 & 0.684 & 0.199 \\
+ 0.633 & 0.7 & 0.43 \\
+\end{array}
+\right)$. 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: $1.49$ 
+Surface Area: $0.65$ 
+Volume: $0.02$