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pretraining/mathematica/geometry/solids/10431.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.776 & 0.672 & 0.092 \\
+ 0.59 & 0.492 & 0.78 \\
+ 0.518 & 0.855 & 0.84 \\
+ 0.356 & 0.504 & 0.499 \\
+ 0.443 & 0.433 & 0.956 \\
+ 0.54 & 0.336 & 0.821 \\
+ 0.14 & 0.386 & 0.732 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $0.18$ 
+Surface Area: $0.8$ 
+Volume: $0.04$

pretraining/mathematica/geometry/solids/10873.txt

@@ -0,0 +1,6 @@
+Problem:
+A cylinder with radius $3.096$ is around the line from $\{3.698,5.556,4.246\}$ to $\{4.557,-4.42,-2.349\}$. Estimate the cylinder's surface area, volume, and centroid.
+Answer:
+Volume: $361.06$ 
+Centroid: $\{4.13,0.57,0.95\}$ 
+Surface Area: $293.46$

pretraining/mathematica/geometry/solids/1336.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.382 & 0.247 & 0.435 \\
+ 0.773 & 0.052 & 0.582 \\
+ 0.085 & 0.294 & 0.017 \\
+ 0.096 & 0.849 & 0.889 \\
+ 0.343 & 0.516 & 0.291 \\
+ 0.158 & 0.633 & 0.085 \\
+\end{array}
+\right)$. 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:
+Volume: $0.05$ 
+Surface Area: $1.14$ 
+Solid Angle: $5.49$

pretraining/mathematica/geometry/solids/136.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.433 & 0.289 & 0.375 \\
+ 0.725 & 0.511 & 0.143 \\
+ 0.628 & 0.173 & 0.823 \\
+ 0.399 & 0.395 & 0.245 \\
+ 0.858 & 0.294 & 0.855 \\
+ 0.841 & 0.732 & 0.732 \\
+ 0.151 & 0.642 & 0.288 \\
+ 0.858 & 0.288 & 0.041 \\
+ 0.841 & 0.178 & 0.764 \\
+ 0.588 & 0.159 & 0.779 \\
+ 0.972 & 0.492 & 0.752 \\
+\end{array}
+\right)$. 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: $1.35$ 
+Volume: $0.11$ 
+Solid Angle: $4.25$

pretraining/mathematica/geometry/solids/14058.txt

@@ -0,0 +1,57 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -1.633 & -0.816 & -0.577 \\
+ -1.633 & -0.816 & 0.577 \\
+ -1.633 & 0. & 0. \\
+ -1.633 & 0.816 & -0.577 \\
+ -1.633 & 0.816 & 0.577 \\
+ -0.816 & -1.633 & -0.577 \\
+ -0.816 & -1.633 & 0.577 \\
+ -0.816 & -0.816 & -1.155 \\
+ -0.816 & -0.816 & 0. \\
+ -0.816 & -0.816 & 1.155 \\
+ -0.816 & 0. & -1.732 \\
+ -0.816 & 0. & -0.577 \\
+ -0.816 & 0. & 0.577 \\
+ -0.816 & 0. & 1.732 \\
+ -0.816 & 0.816 & -1.155 \\
+ -0.816 & 0.816 & 0. \\
+ -0.816 & 0.816 & 1.155 \\
+ -0.816 & 1.633 & -0.577 \\
+ -0.816 & 1.633 & 0.577 \\
+ 0. & -1.633 & 0. \\
+ 0. & -0.816 & -1.732 \\
+ 0. & -0.816 & -0.577 \\
+ 0. & -0.816 & 0.577 \\
+ 0. & -0.816 & 1.732 \\
+ 0. & 0. & -1.155 \\
+ 0. & 0. & 1.155 \\
+ 0. & 0.816 & -1.732 \\
+ 0. & 0.816 & -0.577 \\
+ 0. & 0.816 & 0.577 \\
+ 0. & 0.816 & 1.732 \\
+ 0. & 1.633 & 0. \\
+ 0.816 & -1.633 & -0.577 \\
+ 0.816 & -1.633 & 0.577 \\
+ 0.816 & -0.816 & -1.155 \\
+ 0.816 & -0.816 & 0. \\
+ 0.816 & -0.816 & 1.155 \\
+ 0.816 & 0. & -1.732 \\
+ 0.816 & 0. & -0.577 \\
+ 0.816 & 0. & 0.577 \\
+ 0.816 & 0. & 1.732 \\
+ 0.816 & 0.816 & -1.155 \\
+ 0.816 & 0.816 & 0. \\
+ 0.816 & 0.816 & 1.155 \\
+ 0.816 & 1.633 & -0.577 \\
+ 0.816 & 1.633 & 0.577 \\
+ 1.633 & -0.816 & -0.577 \\
+ 1.633 & -0.816 & 0.577 \\
+ 1.633 & 0. & 0. \\
+ 1.633 & 0.816 & -0.577 \\
+ 1.633 & 0.816 & 0.577 \\
+\end{array}
+\right)$. Determine the Inradius.
+Answer:
+$0.82$

pretraining/mathematica/geometry/solids/14866.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.692 & 0.083 & 0.963 \\
+ 0.943 & 0.618 & 0.773 \\
+ 0.884 & 0.233 & 0.574 \\
+ 0.805 & 0.682 & 0.429 \\
+ 0.461 & 0.794 & 0.512 \\
+ 0.671 & 0.903 & 0.997 \\
+ 0.962 & 0.111 & 0.692 \\
+ 0.229 & 0.466 & 0.281 \\
+\end{array}
+\right)$. 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: $1.05$ 
+Volume: $0.11$ 
+Surface Area: $1.41$

pretraining/mathematica/geometry/solids/1495.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.861 & 0.556 & 0.932 \\
+ 0.01 & 0.365 & 0.037 \\
+ 0.128 & 0.551 & 0.769 \\
+ 0.265 & 0.098 & 0.097 \\
+ 0.732 & 0.563 & 0.267 \\
+ 0.016 & 0.329 & 0.595 \\
+ 0.724 & 0.318 & 0.848 \\
+ 0.041 & 0.598 & 0.709 \\
+ 0.787 & 0.865 & 0.761 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $1.32$ 
+Surface Area: $1.79$ 
+Volume: $0.16$

pretraining/mathematica/geometry/solids/15123.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.457 & 0.14 & 0.563 \\
+ 0.585 & 0.231 & 0.848 \\
+ 0.386 & 0.506 & 0.151 \\
+ 0.272 & 0.313 & 0.033 \\
+ 0.345 & 0.874 & 0.702 \\
+\end{array}
+\right)$. 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: $0.64$ 
+Surface Area: $0.75$ 
+Volume: $0.02$

pretraining/mathematica/geometry/solids/15126.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.153 & 0.487 & 0.977 \\
+ 0.733 & 0.399 & 0.509 \\
+ 0.672 & 0.496 & 0.889 \\
+ 0.992 & 0.353 & 0.668 \\
+\end{array}
+\right)$. 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: $0.03$ 
+Volume: $0.$ 
+Surface Area: $0.32$

pretraining/mathematica/geometry/solids/17756.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.138 & 0.38 & 0.62 \\
+ 0.172 & 0.72 & 0.796 \\
+ 0.599 & 0.337 & 0.153 \\
+ 0.19 & 0.164 & 0.374 \\
+ 0.016 & 0.547 & 0.581 \\
+ 0.167 & 0.959 & 0.035 \\
+ 0.868 & 0.152 & 0.69 \\
+\end{array}
+\right)$. 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: $0.11$ 
+Surface Area: $1.5$ 
+Solid Angle: $4.21$

pretraining/mathematica/geometry/solids/17928.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.802 & 0.876 & 0.043 \\
+ 0.112 & 0.902 & 0.991 \\
+ 0.543 & 0.594 & 0.84 \\
+ 0.729 & 0.184 & 0.358 \\
+\end{array}
+\right)$. 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: $0.14$ 
+Surface Area: $1.01$ 
+Volume: $0.03$

pretraining/mathematica/geometry/solids/19305.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.708 & 0.93 & 0.12 \\
+ 0.306 & 0.37 & 0.075 \\
+ 0.009 & 0.344 & 0.897 \\
+ 0.578 & 0.587 & 0.926 \\
+ 0.704 & 0.675 & 0.006 \\
+ 0.131 & 0.854 & 0.501 \\
+ 0.702 & 0.201 & 0.468 \\
+\end{array}
+\right)$. 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: $1.07$ 
+Volume: $0.16$ 
+Surface Area: $1.78$

pretraining/mathematica/geometry/solids/20660.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.347 & 0.508 & 0.138 \\
+ 0.159 & 0.021 & 0.028 \\
+ 0.151 & 0.135 & 0.829 \\
+ 0.162 & 0.068 & 0.46 \\
+ 0.088 & 0.715 & 0.601 \\
+ 0.752 & 0.149 & 0.933 \\
+ 0.618 & 0.597 & 0.863 \\
+ 0.064 & 0.182 & 0.23 \\
+ 0.002 & 0.929 & 0.363 \\
+\end{array}
+\right)$. 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: $0.16$ 
+Solid Angle: $2.71$ 
+Surface Area: $1.84$

pretraining/mathematica/geometry/solids/2069.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.16 & 0.744 & 0.757 \\
+ 0.648 & 0.155 & 0.341 \\
+ 0.144 & 0.937 & 0.395 \\
+ 0.034 & 0.594 & 0.936 \\
+ 0.365 & 0.492 & 0.128 \\
+ 0.147 & 0.616 & 0.064 \\
+ 0.752 & 0.663 & 0.488 \\
+ 0.425 & 0.078 & 0.497 \\
+ 0.033 & 0.064 & 0.615 \\
+ 0.97 & 0.94 & 0.281 \\
+\end{array}
+\right)$. 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: $2.04$ 
+Solid Angle: $4.75$ 
+Volume: $0.19$

pretraining/mathematica/geometry/solids/21070.txt

@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{1.773,3.471,1.594\}$ has radii $\{8.67,3.369,9.914\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Surface Area: $668.68$ 
+Volume: $1213.01$

pretraining/mathematica/geometry/solids/22055.txt

@@ -0,0 +1,42 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & -1.618 & -0.5 \\
+ 0. & -1.618 & 0.5 \\
+ 0. & 1.618 & -0.5 \\
+ 0. & 1.618 & 0.5 \\
+ 0.425 & -1.309 & 1.351 \\
+ 0.425 & 1.309 & 1.351 \\
+ 0.688 & -0.5 & -1.026 \\
+ 0.688 & -0.5 & 1.876 \\
+ 0.688 & 0.5 & -1.026 \\
+ 0.688 & 0.5 & 1.876 \\
+ -0.851 & 0. & -1.026 \\
+ -0.851 & 0. & 1.876 \\
+ -1.114 & -0.809 & 1.351 \\
+ -1.114 & 0.809 & 1.351 \\
+ -0.263 & -0.809 & -1.026 \\
+ -0.263 & -0.809 & 1.876 \\
+ -0.263 & 0.809 & -1.026 \\
+ -0.263 & 0.809 & 1.876 \\
+ -0.951 & -1.309 & -0.5 \\
+ -0.951 & -1.309 & 0.5 \\
+ -0.951 & 1.309 & -0.5 \\
+ -0.951 & 1.309 & 0.5 \\
+ 0.951 & -1.309 & -0.5 \\
+ 0.951 & -1.309 & 0.5 \\
+ 0.951 & 1.309 & -0.5 \\
+ 0.951 & 1.309 & 0.5 \\
+ -1.539 & -0.5 & -0.5 \\
+ -1.539 & -0.5 & 0.5 \\
+ -1.539 & 0.5 & -0.5 \\
+ -1.539 & 0.5 & 0.5 \\
+ 1.539 & -0.5 & -0.5 \\
+ 1.539 & -0.5 & 0.5 \\
+ 1.539 & 0.5 & -0.5 \\
+ 1.539 & 0.5 & 0.5 \\
+ 1.376 & 0. & 1.351 \\
+\end{array}
+\right)$. Determine the Centroid.
+Answer:
+$\{0.,0.,0.34\}$

pretraining/mathematica/geometry/solids/2211.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.851 & 0.253 & 0.167 \\
+ 0.219 & 0.938 & 0.517 \\
+ 0.259 & 0.935 & 0.46 \\
+ 0.078 & 0.818 & 0.433 \\
+ 0.797 & 0.838 & 0.381 \\
+ 0.57 & 0.497 & 0.772 \\
+ 0.646 & 0.319 & 0.007 \\
+ 0.154 & 0.268 & 0.602 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $1.27$ 
+Surface Area: $1.41$ 
+Volume: $0.11$

pretraining/mathematica/geometry/solids/23021.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.758 & 0.786 & 0.089 \\
+ 0.964 & 0.107 & 0.824 \\
+ 0.096 & 0.927 & 0.061 \\
+ 0.377 & 0.027 & 0.365 \\
+ 0.641 & 0.78 & 0.045 \\
+ 0.91 & 0.308 & 0.505 \\
+ 0.023 & 0.996 & 0.133 \\
+ 0.859 & 0.853 & 0.458 \\
+\end{array}
+\right)$. 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: $1.77$ 
+Volume: $0.12$ 
+Solid Angle: $2.24$

pretraining/mathematica/geometry/solids/23511.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.218 & 0.795 & 0.568 \\
+ 0.632 & 0.78 & 0.436 \\
+ 0.153 & 0.173 & 0.13 \\
+ 0.449 & 0.913 & 0.039 \\
+ 0.558 & 0.404 & 0.663 \\
+ 0.999 & 0.42 & 0.66 \\
+ 0.082 & 0.697 & 0.837 \\
+\end{array}
+\right)$. 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:
+Volume: $0.11$ 
+Surface Area: $1.52$ 
+Solid Angle: $3.36$

pretraining/mathematica/geometry/solids/23860.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.038 & 0.375 & 0.907 \\
+ 0.689 & 0.417 & 0.776 \\
+ 0.364 & 0.323 & 0.305 \\
+ 0.305 & 0.082 & 0.413 \\
+\end{array}
+\right)$. 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: $0.2$ 
+Volume: $0.01$ 
+Surface Area: $0.52$

pretraining/mathematica/geometry/solids/24703.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.609 & 0.429 & 0.894 \\
+ 0.429 & 0.152 & 0.927 \\
+ 0.235 & 0.883 & 0.342 \\
+ 0.366 & 0.96 & 0.617 \\
+\end{array}
+\right)$. 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: $0.45$ 
+Solid Angle: $0.42$

pretraining/mathematica/geometry/solids/2638.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.692 & 0.156 & 0.625 \\
+ 0.077 & 0.433 & 0.16 \\
+ 0.724 & 0.354 & 0.797 \\
+ 0.08 & 0.571 & 0.029 \\
+ 0.47 & 0.155 & 0.542 \\
+ 0.769 & 0.763 & 0.775 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.02$ 
+Solid Angle: $1.06$ 
+Surface Area: $0.85$

pretraining/mathematica/geometry/solids/32416.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.575 & 0.005 & 0.006 \\
+ 0.176 & 0.529 & 0.254 \\
+ 0.58 & 0.781 & 0.279 \\
+ 0.73 & 0.905 & 0.211 \\
+ 0.94 & 0.249 & 0.825 \\
+ 0.699 & 0.204 & 0.604 \\
+\end{array}
+\right)$. 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: $0.56$ 
+Volume: $0.07$ 
+Surface Area: $1.25$

pretraining/mathematica/geometry/solids/34106.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.401 & 0.995 & 0.122 \\
+ 0.698 & 0.056 & 0.592 \\
+ 0.129 & 0.062 & 0.629 \\
+ 0.403 & 0.607 & 0.85 \\
+ 0.291 & 0.46 & 0.674 \\
+ 0.218 & 0.129 & 0.223 \\
+ 0.969 & 0.733 & 0.774 \\
+ 0.557 & 0.784 & 0.68 \\
+\end{array}
+\right)$. 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:
+Volume: $0.13$ 
+Solid Angle: $0.52$ 
+Surface Area: $1.77$

pretraining/mathematica/geometry/solids/34290.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.295 & 0.649 & 0.124 \\
+ 0.761 & 0.788 & 0.025 \\
+ 0.685 & 0.403 & 0.969 \\
+ 0.753 & 0.652 & 0.053 \\
+ 0.633 & 0.014 & 0.768 \\
+ 0.227 & 0.24 & 0.063 \\
+ 0.392 & 0.935 & 0.939 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $2.79$ 
+Surface Area: $1.84$ 
+Volume: $0.14$

pretraining/mathematica/geometry/solids/37695.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.189 & 0.257 & 0.061 \\
+ 0.081 & 0.244 & 0.589 \\
+ 0.737 & 0.446 & 0.773 \\
+ 0.467 & 0.8 & 0.198 \\
+ 0.447 & 0.774 & 0.86 \\
+\end{array}
+\right)$. 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: $1.1$ 
+Solid Angle: $0.45$

pretraining/mathematica/geometry/solids/38166.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.858 & 0.784 & 0.297 \\
+ 0.223 & 0.231 & 0.601 \\
+ 0.659 & 0.754 & 0.979 \\
+ 0.945 & 0.428 & 0.447 \\
+\end{array}
+\right)$. 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: $0.57$ 
+Surface Area: $0.79$

pretraining/mathematica/geometry/solids/40234.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.294 & 0.015 & 0.04 \\
+ 0.727 & 0.413 & 0.25 \\
+ 0.269 & 0.417 & 0.924 \\
+ 0.642 & 0.405 & 0.765 \\
+ 0.397 & 0.962 & 0.126 \\
+ 0.712 & 0.488 & 0.071 \\
+ 0.782 & 0.92 & 0.406 \\
+ 0.404 & 0.156 & 0.972 \\
+\end{array}
+\right)$. 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: $1.81$ 
+Solid Angle: $0.66$ 
+Volume: $0.15$

pretraining/mathematica/geometry/solids/41192.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.504 & 0.1 & 0.288 \\
+ 0.779 & 0.738 & 0.344 \\
+ 0.576 & 0.857 & 0.413 \\
+ 0.565 & 0.104 & 0.181 \\
+ 0.245 & 0.006 & 0.294 \\
+ 0.361 & 0.614 & 0.42 \\
+ 0.657 & 0.744 & 0.457 \\
+ 0.872 & 0.585 & 0.47 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.02$ 
+Solid Angle: $4.16$ 
+Surface Area: $0.7$

pretraining/mathematica/geometry/solids/43676.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.692 & 0.72 & 0.273 \\
+ 0.532 & 0.086 & 0.223 \\
+ 0.891 & 0.434 & 0.24 \\
+ 0.122 & 0.286 & 0.541 \\
+ 0.527 & 0.613 & 0.816 \\
+ 0.75 & 0.607 & 0.72 \\
+ 0.725 & 0.12 & 0.443 \\
+\end{array}
+\right)$. 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: $1.44$ 
+Surface Area: $1.05$

pretraining/mathematica/geometry/solids/44954.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.084 & 0.086 & 0.414 \\
+ 0.612 & 0.991 & 0.2 \\
+ 0.228 & 0.02 & 0.071 \\
+ 0.436 & 0.034 & 0.612 \\
+\end{array}
+\right)$. 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: $0.78$ 
+Volume: $0.03$ 
+Solid Angle: $1.21$

pretraining/mathematica/geometry/solids/46435.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.224 & 0.806 & 0.167 \\
+ 0.183 & 0.187 & 0.055 \\
+ 0.549 & 0.513 & 0.041 \\
+ 0.041 & 0.334 & 0.526 \\
+ 0.535 & 0.443 & 0.778 \\
+ 0.727 & 0.088 & 0.082 \\
+ 0.759 & 0.404 & 0.648 \\
+ 0.235 & 0.914 & 0.332 \\
+ 0.975 & 0.188 & 0.28 \\
+\end{array}
+\right)$. 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: $0.13$ 
+Solid Angle: $2.24$ 
+Surface Area: $1.64$

pretraining/mathematica/geometry/solids/50464.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.002 & 0.169 & 0.315 \\
+ 0.005 & 0.204 & 0.132 \\
+ 0.145 & 0.722 & 0.813 \\
+ 0.446 & 0.082 & 0.385 \\
+ 0.274 & 0.65 & 0.11 \\
+ 0.46 & 0. & 0.969 \\
+ 0.687 & 0.934 & 0.248 \\
+ 0.816 & 0.475 & 0.546 \\
+\end{array}
+\right)$. 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: $2.62$ 
+Surface Area: $1.95$ 
+Volume: $0.18$

pretraining/mathematica/geometry/solids/52475.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.454 & 0.961 & 0.379 \\
+ 0.957 & 0.692 & 0.566 \\
+ 0.719 & 0.517 & 0.045 \\
+ 0.018 & 0.782 & 0.268 \\
+\end{array}
+\right)$. 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: $0.65$ 
+Solid Angle: $1.13$

pretraining/mathematica/geometry/solids/53529.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & 0. & 0.588 \\
+ 0.425 & -0.309 & 0.263 \\
+ -0.162 & 0.5 & 0.263 \\
+ 0.162 & -0.5 & -0.263 \\
+ -0.425 & 0.309 & -0.263 \\
+ 0. & 0. & -0.588 \\
+ 0.425 & 0.309 & 0.263 \\
+ -0.425 & -0.309 & -0.263 \\
+ -0.162 & -0.5 & 0.263 \\
+ -0.526 & 0. & 0.263 \\
+ 0.526 & 0. & -0.263 \\
+ 0.162 & 0.5 & -0.263 \\
+\end{array}
+\right)$. Determine the Circumradius.
+Answer:
+$0.59$

pretraining/mathematica/geometry/solids/54064.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.269 & 0.732 & 0.313 \\
+ 0.785 & 0.221 & 0.523 \\
+ 0.737 & 0.485 & 0.938 \\
+ 0.973 & 0.888 & 0.664 \\
+\end{array}
+\right)$. 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: $0.03$ 
+Surface Area: $0.77$ 
+Solid Angle: $0.23$

pretraining/mathematica/geometry/solids/55274.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.463 & 0.169 & 0.405 \\
+ 0.056 & 0.137 & 0.607 \\
+ 0.362 & 0.858 & 0.549 \\
+ 0.821 & 0.151 & 0.36 \\
+\end{array}
+\right)$. 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: $0.6$ 
+Solid Angle: $3.15$

pretraining/mathematica/geometry/solids/60534.txt

@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{-5.868,1.029,5.847\}$ has radii $\{5.737,4.527,7.496\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Volume: $815.47$ 
+Surface Area: $436.38$

pretraining/mathematica/geometry/solids/60646.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.782 & 0.433 & 0.614 \\
+ 0.891 & 0.813 & 0.539 \\
+ 0.427 & 0.6 & 0.724 \\
+ 0.274 & 0.155 & 0.807 \\
+\end{array}
+\right)$. 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: $0.04$ 
+Surface Area: $0.36$

pretraining/mathematica/geometry/solids/60906.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.8 & 0.332 & 0.726 \\
+ 0.085 & 0.117 & 0.545 \\
+ 0.965 & 0.738 & 0.033 \\
+ 0.774 & 0.708 & 0.593 \\
+ 0.364 & 0.759 & 0.057 \\
+ 0.719 & 0.197 & 0.585 \\
+ 0.674 & 0.302 & 0.363 \\
+ 0.227 & 0.811 & 0.189 \\
+ 0.204 & 0.494 & 0.872 \\
+ 0.119 & 0.139 & 0.821 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.17$ 
+Surface Area: $1.85$ 
+Solid Angle: $2.41$

pretraining/mathematica/geometry/solids/63398.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.074 & 0.225 & 0.197 \\
+ 0.511 & 0.585 & 0.215 \\
+ 0.916 & 0.298 & 0.654 \\
+ 0.975 & 0.38 & 0.205 \\
+\end{array}
+\right)$. 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: $0.13$ 
+Volume: $0.02$ 
+Surface Area: $0.64$

pretraining/mathematica/geometry/solids/63768.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.107 & 0.257 & 0.234 \\
+ 0.21 & 0.098 & 0.388 \\
+ 0.867 & 0.29 & 0.277 \\
+ 0.875 & 0.829 & 0.919 \\
+ 0.328 & 0.606 & 0.126 \\
+ 0.092 & 0.402 & 0.705 \\
+ 0.027 & 0.081 & 0.66 \\
+ 0.927 & 0.227 & 0.444 \\
+\end{array}
+\right)$. 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: $0.14$ 
+Surface Area: $1.71$ 
+Solid Angle: $2.09$

pretraining/mathematica/geometry/solids/64594.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.525 & 0.611 & 0.329 \\
+ 0.151 & 0.043 & 0.982 \\
+ 0.914 & 0.362 & 0.608 \\
+ 0.98 & 0.241 & 0.215 \\
+\end{array}
+\right)$. 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: $0.03$ 
+Surface Area: $0.8$ 
+Solid Angle: $0.53$

pretraining/mathematica/geometry/solids/65018.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.335 & 0.326 & 0.579 \\
+ 0.619 & 0.92 & 0.091 \\
+ 0.219 & 0.496 & 0.394 \\
+ 0.297 & 0.926 & 0.034 \\
+ 0.629 & 0.828 & 0.717 \\
+ 0.972 & 0.26 & 0.108 \\
+ 0.455 & 0.059 & 0.522 \\
+ 0.423 & 0.646 & 0.969 \\
+ 0.347 & 0.035 & 0.216 \\
+\end{array}
+\right)$. 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: $1.92$ 
+Solid Angle: $5.39$

pretraining/mathematica/geometry/solids/66597.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.417 & 0.831 & 0.412 \\
+ 0.165 & 0.57 & 0.403 \\
+ 0.474 & 0.461 & 0.338 \\
+ 0.233 & 0.834 & 0.751 \\
+\end{array}
+\right)$. 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: $0.27$ 
+Solid Angle: $0.72$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/68882.txt

@@ -0,0 +1,5 @@
+Problem:
+A sphere centered at $\{-6.035,3.397,7.027\}$ has radius $5.401$. Estimate the sphere's surface area and volume.
+Answer:
+Volume: $660.03$ 
+Surface Area: $366.6$

pretraining/mathematica/geometry/solids/69301.txt

@@ -0,0 +1,39 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -\frac{1}{2} \sqrt{5+\frac{11}{\sqrt{5}}} & 0 & \frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ \sqrt{\frac{5}{4}+\frac{11}{4 \sqrt{5}}} & 0 & -\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ -\frac{1}{2} \sqrt{\frac{1}{2}+\frac{1}{\sqrt{5}}} & -\frac{1}{8} \left(3+\sqrt{5}\right)^{3/2} & \frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ -\frac{1}{2} \sqrt{\frac{1}{2}+\frac{1}{\sqrt{5}}} & \frac{1}{8} \left(3+\sqrt{5}\right)^{3/2} & \frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ \frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} & -\frac{3+\sqrt{5}}{4 \sqrt{2}} & \frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ \frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} & \frac{1}{4} \sqrt{7+3 \sqrt{5}} & \frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ -\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} & -\frac{3+\sqrt{5}}{4 \sqrt{2}} & \frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ -\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} & \frac{1}{4} \sqrt{7+3 \sqrt{5}} & \frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ -\frac{1}{4} \sqrt{5+\frac{11}{\sqrt{5}}} & -\frac{1}{4} \sqrt{3+\sqrt{5}} & -\frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ -\frac{1}{4} \sqrt{5+\frac{11}{\sqrt{5}}} & \frac{\sqrt{3+\sqrt{5}}}{4} & -\frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ \frac{1}{4} \sqrt{5+\frac{11}{\sqrt{5}}} & -\frac{1}{4} \sqrt{3+\sqrt{5}} & \frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ \frac{1}{4} \sqrt{5+\frac{11}{\sqrt{5}}} & \frac{\sqrt{3+\sqrt{5}}}{4} & \frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ \sqrt{\frac{1}{2}+\frac{1}{\sqrt{5}}} & 0 & -\frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ -\frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} & -\frac{1}{4} \sqrt{7+3 \sqrt{5}} & -\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ -\frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} & \frac{1}{4} \sqrt{7+3 \sqrt{5}} & -\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ -\sqrt{\frac{1}{2}+\frac{1}{\sqrt{5}}} & 0 & \frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ \frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} & -\frac{1}{4} \sqrt{7+3 \sqrt{5}} & -\frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ \frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} & \frac{1}{4} \sqrt{7+3 \sqrt{5}} & -\frac{1}{4} \sqrt{13+\frac{29}{\sqrt{5}}} \\
+ \sqrt{\frac{1}{8}+\frac{1}{4 \sqrt{5}}} & -\frac{1}{8} \left(3+\sqrt{5}\right)^{3/2} & -\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ \sqrt{\frac{1}{8}+\frac{1}{4 \sqrt{5}}} & \frac{1}{8} \left(3+\sqrt{5}\right)^{3/2} & -\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{5}}} \\
+ 0 & 0 & -\frac{1}{4} \sqrt{5 \left(5+\sqrt{5}\right)} \\
+ 0 & 0 & \frac{1}{4} \sqrt{5 \left(5+\sqrt{5}\right)} \\
+ \frac{\sqrt{5-\sqrt{5}}}{4} & -\frac{1}{4} \sqrt{5 \left(3+\sqrt{5}\right)} & \frac{\sqrt{5+\sqrt{5}}}{4} \\
+ \frac{\sqrt{5-\sqrt{5}}}{4} & \frac{1}{4} \sqrt{5 \left(3+\sqrt{5}\right)} & \frac{\sqrt{5+\sqrt{5}}}{4} \\
+ \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{4}} & -\frac{\sqrt{\frac{5}{2}}}{2} & -\frac{1}{4} \sqrt{5+\sqrt{5}} \\
+ \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{4}} & \frac{\sqrt{\frac{5}{2}}}{2} & -\frac{1}{4} \sqrt{5+\sqrt{5}} \\
+ -\frac{1}{2} \sqrt{\frac{5}{2}+\sqrt{5}} & -\frac{\sqrt{\frac{5}{2}}}{2} & \frac{\sqrt{5+\sqrt{5}}}{4} \\
+ -\frac{1}{2} \sqrt{\frac{5}{2}+\sqrt{5}} & \frac{\sqrt{\frac{5}{2}}}{2} & \frac{\sqrt{5+\sqrt{5}}}{4} \\
+ \frac{\sqrt{5+\sqrt{5}}}{2} & 0 & \frac{\sqrt{5+\sqrt{5}}}{4} \\
+ -\frac{1}{2} \sqrt{5+\sqrt{5}} & 0 & -\frac{1}{4} \sqrt{5+\sqrt{5}} \\
+ -\frac{1}{4} \sqrt{5-\sqrt{5}} & -\frac{1}{4} \sqrt{5 \left(3+\sqrt{5}\right)} & -\frac{1}{4} \sqrt{5+\sqrt{5}} \\
+ -\frac{1}{4} \sqrt{5-\sqrt{5}} & \frac{1}{4} \sqrt{5 \left(3+\sqrt{5}\right)} & -\frac{1}{4} \sqrt{5+\sqrt{5}} \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$120$

pretraining/mathematica/geometry/solids/71180.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.638 & 0.969 & 0.908 \\
+ 0.231 & 0.913 & 0.134 \\
+ 0.679 & 0.849 & 0.32 \\
+ 0.008 & 0.039 & 0.921 \\
+ 0.068 & 0.181 & 0.94 \\
+ 0.166 & 0.706 & 0.48 \\
+ 0.982 & 0.05 & 0.258 \\
+ 0.398 & 0.384 & 0.933 \\
+ 0.009 & 0.191 & 0.248 \\
+\end{array}
+\right)$. 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: $1.08$ 
+Surface Area: $2.66$ 
+Volume: $0.3$

pretraining/mathematica/geometry/solids/73297.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.799 & 0.401 & 0.565 \\
+ 0.067 & 0.835 & 0.594 \\
+ 0.172 & 0.757 & 0.394 \\
+ 0.656 & 0.147 & 0.687 \\
+ 0.953 & 0.161 & 0.725 \\
+ 0.26 & 0.907 & 0.772 \\
+ 0.845 & 0.215 & 0.303 \\
+ 0.573 & 0.905 & 0.871 \\
+ 0.052 & 0.313 & 0.361 \\
+\end{array}
+\right)$. 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: $6.08$

pretraining/mathematica/geometry/solids/73901.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.668 & 0.853 & 0.322 \\
+ 0.295 & 0.698 & 0.988 \\
+ 0.938 & 0.346 & 0.643 \\
+ 0.455 & 0.281 & 0.649 \\
+ 0.423 & 0.683 & 0.067 \\
+ 0.26 & 0.322 & 0.26 \\
+ 0.024 & 0.932 & 0.93 \\
+ 0.088 & 0.621 & 0.668 \\
+ 0.68 & 0.843 & 0.238 \\
+\end{array}
+\right)$. 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: $1.61$ 
+Solid Angle: $3.76$ 
+Volume: $0.14$