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pretraining/mathematica/geometry/solids/10345.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.519 & 0.64 & 0.712 \\
+ 0.774 & 0.509 & 0.418 \\
+ 0.05 & 0.123 & 0.09 \\
+ 0.005 & 0.881 & 0.734 \\
+\end{array}
+\right)$. 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: $0.02$ 
+Surface Area: $0.89$

pretraining/mathematica/geometry/solids/11994.txt

@@ -0,0 +1,37 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & -1.618 & -0.5 \\
+ 0. & -1.618 & 0.5 \\
+ 0. & 1.618 & -0.5 \\
+ 0. & 1.618 & 0.5 \\
+ 0.851 & 0. & -1.026 \\
+ 0.851 & 0. & 1.026 \\
+ 0.263 & -0.809 & -1.026 \\
+ 0.263 & -0.809 & 1.026 \\
+ 0.263 & 0.809 & -1.026 \\
+ 0.263 & 0.809 & 1.026 \\
+ -0.951 & -1.309 & -0.5 \\
+ -0.951 & -1.309 & 0.5 \\
+ -0.951 & 1.309 & -0.5 \\
+ -0.951 & 1.309 & 0.5 \\
+ 0.951 & -1.309 & -0.5 \\
+ 0.951 & -1.309 & 0.5 \\
+ 0.951 & 1.309 & -0.5 \\
+ 0.951 & 1.309 & 0.5 \\
+ -0.688 & -0.5 & -1.026 \\
+ -0.688 & -0.5 & 1.026 \\
+ -0.688 & 0.5 & -1.026 \\
+ -0.688 & 0.5 & 1.026 \\
+ -1.539 & -0.5 & -0.5 \\
+ -1.539 & -0.5 & 0.5 \\
+ -1.539 & 0.5 & -0.5 \\
+ -1.539 & 0.5 & 0.5 \\
+ 1.539 & -0.5 & -0.5 \\
+ 1.539 & -0.5 & 0.5 \\
+ 1.539 & 0.5 & -0.5 \\
+ 1.539 & 0.5 & 0.5 \\
+\end{array}
+\right)$. Determine the Volume.
+Answer:
+$12.34$

pretraining/mathematica/geometry/solids/12238.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.238 & 0.897 & 0.015 \\
+ 0.802 & 0.749 & 0.256 \\
+ 0.507 & 0.218 & 0.08 \\
+ 0.047 & 0.842 & 0.203 \\
+ 0.685 & 0.898 & 0.281 \\
+ 0.626 & 0.644 & 0.616 \\
+ 0.01 & 0.954 & 0.639 \\
+ 0.528 & 0.036 & 0.919 \\
+ 0.037 & 0.674 & 0.479 \\
+ 0.368 & 0.29 & 0.016 \\
+ 0.019 & 0.591 & 0.774 \\
+\end{array}
+\right)$. 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: $0.21$ 
+Solid Angle: $1.92$ 
+Surface Area: $2.14$

pretraining/mathematica/geometry/solids/13851.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.961 & 0.945 & 0.372 \\
+ 0.703 & 0.027 & 0.704 \\
+ 0.568 & 0.572 & 0.335 \\
+ 0.657 & 0.552 & 0.906 \\
+ 0.576 & 0.522 & 0.671 \\
+\end{array}
+\right)$. 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: $0.21$ 
+Surface Area: $0.69$ 
+Volume: $0.03$

pretraining/mathematica/geometry/solids/14039.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.653 & 0.173 & 0.717 \\
+ 0.931 & 0.432 & 0.916 \\
+ 0.152 & 0.537 & 0.82 \\
+ 0.474 & 0.921 & 0.345 \\
+ 0.012 & 0.225 & 0.244 \\
+ 0.817 & 0.864 & 0.133 \\
+ 0.785 & 0.769 & 0.158 \\
+ 0.228 & 0.759 & 0.977 \\
+\end{array}
+\right)$. 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: $1.92$ 
+Solid Angle: $1.98$ 
+Volume: $0.17$

pretraining/mathematica/geometry/solids/14373.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.513 & 0.838 & 0.572 \\
+ 0.248 & 0.759 & 0.844 \\
+ 0.858 & 0.423 & 0.785 \\
+ 0.831 & 0.669 & 0.54 \\
+ 0.185 & 0.06 & 0.789 \\
+ 0.34 & 0.181 & 0.242 \\
+\end{array}
+\right)$. 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: $1.68$ 
+Surface Area: $1.22$

pretraining/mathematica/geometry/solids/16854.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.769 & 0.515 & 0.005 \\
+ 0.569 & 0.442 & 0.192 \\
+ 0.274 & 0.584 & 0.428 \\
+ 0.138 & 0.439 & 0.853 \\
+ 0.975 & 0.689 & 0.989 \\
+ 0.677 & 0.508 & 0.555 \\
+ 0.594 & 0.829 & 0.617 \\
+ 0.024 & 0.409 & 0.573 \\
+\end{array}
+\right)$. 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: $1.31$ 
+Volume: $0.07$ 
+Solid Angle: $0.4$

pretraining/mathematica/geometry/solids/19873.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.308 & 0.441 & 0.119 \\
+ 0.297 & 0.282 & 0.118 \\
+ 0.266 & 0.526 & 0.76 \\
+ 0.672 & 0.316 & 0.696 \\
+ 0.269 & 0.014 & 0.493 \\
+ 0.034 & 0.913 & 0.329 \\
+ 0.278 & 0.812 & 0.663 \\
+ 0.954 & 0.347 & 0.66 \\
+ 0.022 & 0.204 & 0.444 \\
+\end{array}
+\right)$. 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: $0.12$ 
+Surface Area: $1.48$ 
+Solid Angle: $2.92$

pretraining/mathematica/geometry/solids/21440.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.774 & 0.107 & 0.679 \\
+ 0.258 & 0.845 & 0.108 \\
+ 0.465 & 0.791 & 0.763 \\
+ 0.897 & 0.558 & 0.693 \\
+ 0.925 & 0.596 & 0.641 \\
+ 0.447 & 0.987 & 0.743 \\
+ 0.654 & 0.339 & 0.522 \\
+ 0.435 & 0.303 & 0.632 \\
+\end{array}
+\right)$. 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: $1.08$ 
+Solid Angle: $0.52$ 
+Volume: $0.06$

pretraining/mathematica/geometry/solids/21765.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.084 & 0.292 & 0.985 \\
+ 0.456 & 0.615 & 0.829 \\
+ 0.238 & 0.709 & 0.941 \\
+ 0.546 & 0.473 & 0.312 \\
+ 0.554 & 0.097 & 0.017 \\
+ 0.448 & 0.58 & 0.09 \\
+ 0.237 & 0.937 & 0.217 \\
+\end{array}
+\right)$. 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: $1.38$ 
+Solid Angle: $0.57$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/23177.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.825 & 0.464 & 0.76 \\
+ 0.716 & 0.757 & 0.589 \\
+ 0.43 & 0.585 & 0.409 \\
+ 0.75 & 0.971 & 0.126 \\
+\end{array}
+\right)$. 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: $0.38$ 
+Solid Angle: $0.17$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/23210.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.877 & 0.868 & 0.362 \\
+ 0.201 & 0.393 & 0.369 \\
+ 0.812 & 0.541 & 0.045 \\
+ 0.435 & 0.83 & 0.335 \\
+ 0.551 & 0.17 & 0.414 \\
+ 0.233 & 0.511 & 0.828 \\
+ 0.825 & 0.56 & 0.897 \\
+ 0.865 & 0.294 & 0.912 \\
+ 0.291 & 0.781 & 0.134 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.7$ 
+Volume: $0.16$ 
+Solid Angle: $1.67$

pretraining/mathematica/geometry/solids/30234.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.953 & 0.199 & 0.286 \\
+ 0.157 & 0.314 & 0.74 \\
+ 0.755 & 0.832 & 0.534 \\
+ 0.184 & 0.023 & 0.233 \\
+ 0.16 & 0.326 & 0.819 \\
+\end{array}
+\right)$. 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: $0.38$ 
+Surface Area: $1.1$ 
+Volume: $0.04$

pretraining/mathematica/geometry/solids/31396.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0 & 0 & \frac{1}{2} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \\
+ \frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(1-\sqrt{5}\right) & \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ -\frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & \frac{1}{2} & \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ \frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & -\frac{1}{2} & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ -\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(\sqrt{5}-1\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ 0 & 0 & -\frac{1}{2} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \\
+ \frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(\sqrt{5}-1\right) & \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ -\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(1-\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ -\frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & -\frac{1}{2} & \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ -\sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & 0 & \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & 0 & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ \frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & \frac{1}{2} & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$30$

pretraining/mathematica/geometry/solids/31550.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.388 & 0.738 & 0.966 \\
+ 0.593 & 0.322 & 0.861 \\
+ 0.752 & 0.626 & 0.011 \\
+ 0.776 & 0.678 & 0.869 \\
+ 0.428 & 0.944 & 0.125 \\
+ 0.975 & 0.98 & 0.78 \\
+ 0.927 & 0.848 & 0.267 \\
+ 0.207 & 0.7 & 0.008 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.44$ 
+Surface Area: $1.72$ 
+Volume: $0.15$

pretraining/mathematica/geometry/solids/32659.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.751 & 0.429 & 0.249 \\
+ 0.098 & 0.331 & 0.253 \\
+ 0.784 & 0.579 & 0.311 \\
+ 0.371 & 0.023 & 0.934 \\
+ 0.525 & 0.723 & 0.285 \\
+ 0.024 & 0.259 & 0.743 \\
+ 0.443 & 0.252 & 0.087 \\
+ 0.377 & 0.632 & 0.553 \\
+ 0.331 & 0.612 & 0.889 \\
+ 0.771 & 0.784 & 0.747 \\
+\end{array}
+\right)$. 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: $2.41$ 
+Volume: $0.14$ 
+Surface Area: $1.65$

pretraining/mathematica/geometry/solids/33613.txt

@@ -0,0 +1,6 @@
+Problem:
+A cone with radius $7.046$ has its base centered at$\{9.687,3.522,2.656\}$ and its tip is at $\{0.269,2.553,1.062\}$. Estimate the cone's surface area, volume, and centroid.
+Answer:
+Volume: $499.2$ 
+Centroid: $\{7.33,3.28,2.26\}$ 
+Surface Area: $419.62$

pretraining/mathematica/geometry/solids/34566.txt

@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{7.987,-1.663,1.373\}$ has radii $\{8.694,4.196,2.453\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Surface Area: $304.22$ 
+Volume: $374.84$

pretraining/mathematica/geometry/solids/35920.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.204 & 0.289 & 0.913 \\
+ 0.548 & 0.375 & 0.027 \\
+ 0.298 & 0.998 & 0.56 \\
+ 0.174 & 0.962 & 0.474 \\
+\end{array}
+\right)$. 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: $0.1$ 
+Volume: $0.02$ 
+Surface Area: $0.76$

pretraining/mathematica/geometry/solids/39140.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.27 & 0.003 & 0.756 \\
+ 0.769 & 0.951 & 0.745 \\
+ 0.013 & 0.431 & 0.207 \\
+ 0.134 & 0.305 & 0.418 \\
+ 0.521 & 0.286 & 0.9 \\
+\end{array}
+\right)$. 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: $0.93$ 
+Volume: $0.$ 
+Solid Angle: $0.04$

pretraining/mathematica/geometry/solids/39159.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.804 & 0.227 & 0.386 \\
+ 0.216 & 0.605 & 0.124 \\
+ 0.003 & 0.362 & 0.478 \\
+ 0.138 & 0.321 & 0.263 \\
+ 0.332 & 0.464 & 0.065 \\
+ 0.765 & 0.153 & 0.602 \\
+ 0.571 & 0.792 & 0.442 \\
+ 0.974 & 0.285 & 0.651 \\
+ 0.844 & 0.275 & 0.957 \\
+\end{array}
+\right)$. 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:
+Surface Area: $1.37$ 
+Solid Angle: $2.36$ 
+Volume: $0.1$

pretraining/mathematica/geometry/solids/39192.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.062 & 0.283 & 0.513 \\
+ 0.467 & 0.985 & 0.915 \\
+ 0.353 & 0.369 & 0.529 \\
+ 0.507 & 0.292 & 0.231 \\
+ 0.194 & 0.649 & 0.112 \\
+ 0.74 & 0.699 & 0.494 \\
+\end{array}
+\right)$. 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: $1.07$ 
+Volume: $0.06$ 
+Solid Angle: $0.92$

pretraining/mathematica/geometry/solids/40520.txt

@@ -0,0 +1,127 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -0.045 & -1.309 & 0.498 \\
+ -0.045 & 1.309 & 0.498 \\
+ 0.045 & -1.309 & -0.498 \\
+ 0.045 & 1.309 & -0.498 \\
+ -0.263 & -0.809 & 1.114 \\
+ -0.263 & 0.809 & 1.114 \\
+ 0.263 & -0.809 & -1.114 \\
+ 0.263 & 0.809 & -1.114 \\
+ -0.073 & -1.394 & 0.118 \\
+ -0.073 & 1.394 & 0.118 \\
+ 0.073 & -1.394 & -0.118 \\
+ 0.073 & 1.394 & -0.118 \\
+ -0.235 & -1.171 & -0.733 \\
+ -0.235 & 1.171 & -0.733 \\
+ 0.235 & -1.171 & 0.733 \\
+ 0.235 & 1.171 & 0.733 \\
+ -0.118 & -0.362 & -1.349 \\
+ -0.118 & -1.085 & 0.878 \\
+ -0.118 & 0.362 & -1.349 \\
+ -0.118 & 1.085 & 0.878 \\
+ 0.118 & -0.362 & 1.349 \\
+ 0.118 & -1.085 & -0.878 \\
+ 0.118 & 0.362 & 1.349 \\
+ 0.118 & 1.085 & -0.878 \\
+ -0.19 & -0.585 & 1.259 \\
+ -0.19 & 0.585 & 1.259 \\
+ 0.19 & -0.585 & -1.259 \\
+ 0.19 & 0.585 & -1.259 \\
+ -0.308 & -0.224 & 1.349 \\
+ -0.308 & 0.224 & 1.349 \\
+ 0.308 & -0.224 & -1.349 \\
+ 0.308 & 0.224 & -1.349 \\
+ -0.38 & 0. & -1.349 \\
+ 0.38 & 0. & 1.349 \\
+ -0.543 & -0.947 & 0.878 \\
+ -0.543 & 0.947 & 0.878 \\
+ 0.543 & -0.947 & -0.878 \\
+ 0.543 & 0.947 & -0.878 \\
+ -0.425 & -1.309 & 0.263 \\
+ -0.425 & 1.309 & 0.263 \\
+ 0.425 & -1.309 & -0.263 \\
+ 0.425 & 1.309 & -0.263 \\
+ -0.498 & -0.362 & -1.259 \\
+ -0.498 & -1.085 & -0.733 \\
+ -0.498 & 0.362 & -1.259 \\
+ -0.498 & 1.085 & -0.733 \\
+ 0.498 & -0.362 & 1.259 \\
+ 0.498 & -1.085 & 0.733 \\
+ 0.498 & 0.362 & 1.259 \\
+ 0.498 & 1.085 & 0.733 \\
+ -0.616 & 0. & 1.259 \\
+ 0.616 & 0. & -1.259 \\
+ -0.761 & -1.171 & 0.118 \\
+ -0.761 & 1.171 & 0.118 \\
+ 0.761 & -1.171 & -0.118 \\
+ 0.761 & 1.171 & -0.118 \\
+ -0.733 & -1.085 & 0.498 \\
+ -0.733 & -0.809 & -0.878 \\
+ -0.733 & 0.809 & -0.878 \\
+ -0.733 & 1.085 & 0.498 \\
+ 0.733 & -1.085 & -0.498 \\
+ 0.733 & -0.809 & 0.878 \\
+ 0.733 & 0.809 & 0.878 \\
+ 0.733 & 1.085 & -0.498 \\
+ -0.688 & -0.5 & -1.114 \\
+ -0.688 & 0.5 & -1.114 \\
+ 0.688 & -0.5 & 1.114 \\
+ 0.688 & 0.5 & 1.114 \\
+ -0.851 & 0. & 1.114 \\
+ 0.851 & 0. & -1.114 \\
+ -0.806 & -1.033 & -0.498 \\
+ -0.806 & 1.033 & -0.498 \\
+ 0.806 & -1.033 & 0.498 \\
+ 0.806 & 1.033 & 0.498 \\
+ -0.878 & -1.085 & -0.118 \\
+ -0.878 & -0.809 & 0.733 \\
+ -0.878 & 0.809 & 0.733 \\
+ -0.878 & 1.085 & -0.118 \\
+ 0.878 & -1.085 & 0.118 \\
+ 0.878 & -0.809 & -0.733 \\
+ 0.878 & 0.809 & -0.733 \\
+ 0.878 & 1.085 & 0.118 \\
+ -1.041 & -0.585 & 0.733 \\
+ -1.041 & 0.585 & 0.733 \\
+ 1.041 & -0.585 & -0.733 \\
+ 1.041 & 0.585 & -0.733 \\
+ -0.996 & -0.447 & -0.878 \\
+ -0.996 & 0.447 & -0.878 \\
+ 0.996 & -0.447 & 0.878 \\
+ 0.996 & 0.447 & 0.878 \\
+ -1.069 & -0.224 & 0.878 \\
+ -1.069 & 0.224 & 0.878 \\
+ 1.069 & -0.224 & -0.878 \\
+ 1.069 & 0.224 & -0.878 \\
+ -1.114 & -0.809 & -0.263 \\
+ -1.114 & 0.809 & -0.263 \\
+ 1.114 & -0.809 & 0.263 \\
+ 1.114 & 0.809 & 0.263 \\
+ -1.259 & -0.362 & 0.498 \\
+ -1.259 & 0.362 & 0.498 \\
+ 1.259 & -0.362 & -0.498 \\
+ 1.259 & 0.362 & -0.498 \\
+ -1.186 & 0.138 & -0.733 \\
+ -1.186 & -0.138 & -0.733 \\
+ 1.186 & 0.138 & 0.733 \\
+ 1.186 & -0.138 & 0.733 \\
+ -1.231 & -0.447 & -0.498 \\
+ -1.231 & 0.447 & -0.498 \\
+ 1.231 & -0.447 & 0.498 \\
+ 1.231 & 0.447 & 0.498 \\
+ -1.349 & -0.362 & 0.118 \\
+ -1.349 & 0.362 & 0.118 \\
+ 1.349 & -0.362 & -0.118 \\
+ 1.349 & 0.362 & -0.118 \\
+ -1.304 & -0.5 & -0.118 \\
+ -1.304 & 0.5 & -0.118 \\
+ 1.304 & -0.5 & 0.118 \\
+ 1.304 & 0.5 & 0.118 \\
+ -1.376 & 0. & 0.263 \\
+ 1.376 & 0. & -0.263 \\
+\end{array}
+\right)$. Determine the Circumradius.
+Answer:
+$1.4$

pretraining/mathematica/geometry/solids/40854.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.599 & 0.842 & 0.157 \\
+ 0.139 & 0.955 & 0.67 \\
+ 0.271 & 0.31 & 0.77 \\
+ 0.357 & 0.088 & 0.907 \\
+ 0.445 & 0.162 & 0.943 \\
+ 0.445 & 0.646 & 0.899 \\
+ 0.049 & 0.76 & 0.244 \\
+ 0.681 & 0.685 & 0.368 \\
+ 0.492 & 0.327 & 0.477 \\
+ 0.38 & 0.535 & 0.222 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.38$ 
+Solid Angle: $1.13$ 
+Volume: $0.11$

pretraining/mathematica/geometry/solids/41350.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.101 & 0.396 & 0.184 \\
+ 0.79 & 0.785 & 0.326 \\
+ 0.611 & 0.928 & 0.844 \\
+ 0.992 & 0.428 & 0.123 \\
+ 0.967 & 0.208 & 0.111 \\
+ 0.536 & 0.314 & 0.924 \\
+ 0.469 & 0.232 & 0.905 \\
+ 0.881 & 0.843 & 0.971 \\
+ 0.748 & 0.04 & 0.714 \\
+\end{array}
+\right)$. 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: $0.86$ 
+Surface Area: $2.09$ 
+Volume: $0.21$

pretraining/mathematica/geometry/solids/41763.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.251 & 0.815 & 0.861 \\
+ 0.745 & 0.938 & 0.476 \\
+ 0.31 & 0.848 & 0.367 \\
+ 0.122 & 0.101 & 0.134 \\
+ 0.249 & 0.063 & 0.837 \\
+\end{array}
+\right)$. 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: $1.05$ 
+Surface Area: $1.34$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/43280.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.484 & 0.113 & 0.16 \\
+ 0.231 & 0.064 & 0.803 \\
+ 0.36 & 0.783 & 0.168 \\
+ 0.996 & 0.616 & 0.366 \\
+ 0.292 & 0.433 & 0.027 \\
+ 0.798 & 0.909 & 0.891 \\
+ 0.334 & 0.114 & 0.089 \\
+\end{array}
+\right)$. 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: $1.81$ 
+Solid Angle: $2.75$

pretraining/mathematica/geometry/solids/44012.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.295 & 0.359 & 0.683 \\
+ 0.168 & 0.478 & 0.656 \\
+ 0.22 & 0.207 & 0.724 \\
+ 0.394 & 0.825 & 0.428 \\
+ 0.056 & 0.639 & 0.586 \\
+\end{array}
+\right)$. 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: $1.41$ 
+Volume: $0.$ 
+Surface Area: $0.22$

pretraining/mathematica/geometry/solids/44962.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.268 & 0.352 & 0.608 \\
+ 0.632 & 0.63 & 0.35 \\
+ 0.293 & 0.462 & 0.812 \\
+ 0.871 & 0.16 & 0.985 \\
+\end{array}
+\right)$. 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: $0.53$ 
+Solid Angle: $1.07$

pretraining/mathematica/geometry/solids/45371.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.783 & 0.206 & 0.911 \\
+ 0.242 & 0.711 & 0.147 \\
+ 0.015 & 0.586 & 0.099 \\
+ 0.454 & 0.404 & 0.897 \\
+ 0.905 & 0.664 & 0.149 \\
+ 0.578 & 0.988 & 0.604 \\
+\end{array}
+\right)$. 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: $0.59$ 
+Volume: $0.11$ 
+Surface Area: $1.49$

pretraining/mathematica/geometry/solids/45583.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.585 & 0.616 & 0.326 \\
+ 0.145 & 0.853 & 0.963 \\
+ 0.793 & 0.13 & 0.472 \\
+ 0.385 & 0.852 & 0.89 \\
+ 0.194 & 0.854 & 0.201 \\
+ 0.293 & 0.296 & 0.77 \\
+ 0.516 & 0.682 & 0.711 \\
+\end{array}
+\right)$. 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: $2.6$

pretraining/mathematica/geometry/solids/45865.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.629 & 0.125 & 0.292 \\
+ 0.071 & 0.231 & 0.933 \\
+ 0.031 & 0.677 & 0.892 \\
+ 0.608 & 0.593 & 0.316 \\
+ 0.762 & 0.039 & 0.769 \\
+ 0.002 & 0.233 & 0.521 \\
+ 0.82 & 0.914 & 0.526 \\
+ 0.061 & 0.942 & 0.659 \\
+ 0.038 & 0.62 & 0.291 \\
+ 0.681 & 0.143 & 0.3 \\
+\end{array}
+\right)$. 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: $2.17$ 
+Volume: $0.22$ 
+Solid Angle: $2.68$

pretraining/mathematica/geometry/solids/47457.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.049 & 0.048 & 0.544 \\
+ 0.456 & 0.053 & 0.934 \\
+ 0.036 & 0.353 & 0.632 \\
+ 0.467 & 0.774 & 0.483 \\
+ 0.79 & 0.899 & 0.856 \\
+ 0.964 & 0.157 & 0.897 \\
+ 0.827 & 0.676 & 0.444 \\
+ 0.739 & 0.423 & 0.534 \\
+ 0.976 & 0.963 & 0.57 \\
+ 0.93 & 0.195 & 0.701 \\
+\end{array}
+\right)$. 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: $0.86$ 
+Volume: $0.16$ 
+Surface Area: $1.82$

pretraining/mathematica/geometry/solids/48405.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.034 & 0.452 & 0.115 \\
+ 0.878 & 0.628 & 0.033 \\
+ 0.311 & 0.255 & 0.516 \\
+ 0.792 & 0.034 & 0.933 \\
+ 0.477 & 0.602 & 0.956 \\
+ 0.099 & 0.243 & 0.682 \\
+\end{array}
+\right)$. 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: $1.71$ 
+Solid Angle: $0.51$

pretraining/mathematica/geometry/solids/49505.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.435 & 0.256 & 0.661 \\
+ 0.411 & 0.239 & 0.281 \\
+ 0.843 & 0.917 & 0.912 \\
+ 0.199 & 0.079 & 0.859 \\
+ 0.211 & 0.463 & 0.86 \\
+ 0.656 & 0.775 & 0.432 \\
+ 0.029 & 0.076 & 0.787 \\
+ 0.147 & 0.898 & 0.692 \\
+ 0.138 & 0.411 & 0.276 \\
+\end{array}
+\right)$. 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: $1.62$ 
+Volume: $0.14$ 
+Solid Angle: $5.05$

pretraining/mathematica/geometry/solids/4955.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.9 & 0.552 & 0.022 \\
+ 0.149 & 0.086 & 0.514 \\
+ 0.897 & 0.862 & 0.518 \\
+ 0.574 & 0.708 & 0.754 \\
+ 0.554 & 0.918 & 0.065 \\
+ 0.292 & 0.761 & 0.415 \\
+ 0.661 & 0.409 & 0.905 \\
+ 0.288 & 0.942 & 0.706 \\
+ 0.472 & 0.235 & 0.357 \\
+\end{array}
+\right)$. 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: $1.13$ 
+Volume: $0.17$

pretraining/mathematica/geometry/solids/51533.txt

@@ -0,0 +1,21 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.793 & 0.838 & 0.388 \\
+ 0.075 & 0.603 & 0.92 \\
+ 0.055 & 0.852 & 0.476 \\
+ 0.093 & 0.792 & 0.188 \\
+ 0.697 & 0.304 & 0.816 \\
+ 0.474 & 0.909 & 0.063 \\
+ 0.428 & 0.995 & 0.396 \\
+ 0.962 & 0.596 & 0.491 \\
+ 0.329 & 0.117 & 0.308 \\
+ 0.169 & 0.112 & 0.954 \\
+ 0.514 & 0.806 & 0.105 \\
+ 0.246 & 0.95 & 0.932 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $3.22$ 
+Volume: $0.27$ 
+Surface Area: $2.37$

pretraining/mathematica/geometry/solids/51624.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.312 & 0.233 & 0.955 \\
+ 0.302 & 0.946 & 0.685 \\
+ 0.706 & 0.09 & 0.48 \\
+ 0.065 & 0.136 & 0.038 \\
+ 0.33 & 0.922 & 0.993 \\
+ 0.921 & 0.223 & 0.131 \\
+\end{array}
+\right)$. 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: $1.18$

pretraining/mathematica/geometry/solids/52943.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.928 & 0.923 & 0.833 \\
+ 0.796 & 0.906 & 0.969 \\
+ 0.26 & 0.107 & 0.685 \\
+ 0.432 & 0.246 & 0.338 \\
+ 0.239 & 0.206 & 0.402 \\
+ 0.851 & 0.217 & 0.442 \\
+ 0.231 & 0.674 & 0.7 \\
+\end{array}
+\right)$. 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: $1.25$ 
+Solid Angle: $0.69$ 
+Volume: $0.07$

pretraining/mathematica/geometry/solids/53586.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.899 & 0.533 & 0.309 \\
+ 0.767 & 0.254 & 0.203 \\
+ 0.707 & 0.952 & 0.057 \\
+ 0.42 & 0.986 & 0.403 \\
+\end{array}
+\right)$. 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: $0.46$ 
+Solid Angle: $1.1$ 
+Volume: $0.01$

pretraining/mathematica/geometry/solids/54431.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.707 & 0.48 & 0.142 \\
+ 0.184 & 0.255 & 0.877 \\
+ 0.113 & 0.908 & 0.356 \\
+ 0.489 & 0.914 & 0.25 \\
+ 0.966 & 0.116 & 0.895 \\
+ 0.435 & 0.905 & 0.002 \\
+ 0.278 & 0.443 & 0.207 \\
+ 0.697 & 0.852 & 0.337 \\
+ 0.315 & 0.246 & 0.71 \\
+ 0.549 & 0.186 & 0.826 \\
+\end{array}
+\right)$. 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: $1.84$ 
+Solid Angle: $2.31$ 
+Volume: $0.14$

pretraining/mathematica/geometry/solids/55538.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.366 & 0.584 & 0.374 \\
+ 0.904 & 0.771 & 0.604 \\
+ 0.263 & 0.788 & 0.21 \\
+ 0.838 & 0.159 & 0.217 \\
+ 0.96 & 0.623 & 0.179 \\
+ 0.843 & 0.991 & 0.365 \\
+ 0.486 & 0.455 & 0.036 \\
+ 0.087 & 0.055 & 0.154 \\
+ 0.719 & 0.096 & 0.412 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $4.64$ 
+Volume: $0.12$ 
+Surface Area: $1.59$

pretraining/mathematica/geometry/solids/57123.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.491 & 0.662 & 0.97 \\
+ 0.14 & 0.47 & 0.776 \\
+ 0.892 & 0.791 & 0.571 \\
+ 0.759 & 0.201 & 0.077 \\
+ 0.509 & 0.094 & 0.354 \\
+ 0.266 & 0.324 & 0.835 \\
+ 0.211 & 0.761 & 0.124 \\
+ 0.748 & 0.263 & 0.533 \\
+\end{array}
+\right)$. 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: $1.39$ 
+Volume: $0.15$

pretraining/mathematica/geometry/solids/58035.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.458 & 0.856 & 0.208 \\
+ 0.243 & 0.22 & 0.162 \\
+ 0.12 & 0.723 & 0.106 \\
+ 0.118 & 0.31 & 0.552 \\
+ 0.417 & 0.138 & 0.307 \\
+ 0.593 & 0.581 & 0.296 \\
+ 0.036 & 0.386 & 0.522 \\
+ 0.621 & 0.209 & 0.471 \\
+ 0.473 & 0.121 & 0.432 \\
+\end{array}
+\right)$. 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: $0.62$ 
+Surface Area: $0.89$ 
+Volume: $0.05$

pretraining/mathematica/geometry/solids/59455.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.995 & 0.724 & 0.539 \\
+ 0.317 & 0.059 & 0.976 \\
+ 0.066 & 0.205 & 0.343 \\
+ 0.046 & 0.912 & 0.844 \\
+ 0.658 & 0.241 & 0.833 \\
+ 0.701 & 0.754 & 0.076 \\
+ 0.906 & 0.805 & 0.538 \\
+ 0.748 & 0.681 & 0.86 \\
+ 0.498 & 0.263 & 0.269 \\
+ 0.066 & 0.986 & 0.922 \\
+\end{array}
+\right)$. 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: $2.33$ 
+Volume: $0.25$ 
+Solid Angle: $1.93$

pretraining/mathematica/geometry/solids/60280.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.276 & 0.964 & 0.193 \\
+ 0.289 & 0.468 & 0.778 \\
+ 0.441 & 0.127 & 0.447 \\
+ 0.477 & 0.02 & 0.926 \\
+\end{array}
+\right)$. 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: $0.02$ 
+Surface Area: $0.61$

pretraining/mathematica/geometry/solids/60434.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.985 & 0.695 & 0.877 \\
+ 0.025 & 0.281 & 0.571 \\
+ 0.774 & 0.007 & 0.505 \\
+ 0.251 & 0.686 & 0.175 \\
+ 0.669 & 0.885 & 0.464 \\
+\end{array}
+\right)$. 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: $0.08$ 
+Surface Area: $1.42$ 
+Solid Angle: $0.45$

pretraining/mathematica/geometry/solids/61345.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.964 & 0.584 & 0.386 \\
+ 0.722 & 0.202 & 0.565 \\
+ 0.731 & 0.862 & 0.661 \\
+ 0.517 & 0.765 & 0.334 \\
+ 0.109 & 0.877 & 0.452 \\
+ 0.05 & 0.527 & 0.07 \\
+ 0.922 & 0.662 & 0.564 \\
+ 0.184 & 0.835 & 0.663 \\
+ 0.42 & 0.417 & 0.064 \\
+ 0.037 & 0.304 & 0.401 \\
+\end{array}
+\right)$. 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: $1.61$ 
+Solid Angle: $1.76$

pretraining/mathematica/geometry/solids/65128.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.472 & 0.127 & 0.004 \\
+ 0.467 & 0.263 & 0.567 \\
+ 0.798 & 0.925 & 0.719 \\
+ 0.743 & 0.224 & 0.871 \\
+ 0.624 & 0.784 & 0.812 \\
+ 0.388 & 0.64 & 0.05 \\
+ 0.006 & 0.599 & 0.606 \\
+ 0.371 & 0.217 & 0.331 \\
+\end{array}
+\right)$. 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: $0.73$ 
+Volume: $0.13$ 
+Surface Area: $1.64$

pretraining/mathematica/geometry/solids/65355.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.101 & 0.853 & 0.507 \\
+ 0.355 & 0.269 & 0.268 \\
+ 0.469 & 0.495 & 0.048 \\
+ 0.065 & 0.522 & 0.853 \\
+ 0.193 & 0.886 & 0.719 \\
+ 0.302 & 0.612 & 0.831 \\
+ 0.086 & 0.571 & 0.596 \\
+ 0.076 & 0.973 & 0.143 \\
+ 0.666 & 0.56 & 0.39 \\
+\end{array}
+\right)$. 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: $5.47$ 
+Surface Area: $1.19$