diff --git a/pretraining/mathematica/geometry/solids/10403.txt b/pretraining/mathematica/geometry/solids/10403.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ca9cfd64f0a6023863014e31b47024e404a3852f
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/10403.txt
@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.533 & 0.273 & 0.215 \\
+ 0.176 & 0.838 & 0.849 \\
+ 0.011 & 0.241 & 0.233 \\
+ 0.311 & 0.249 & 0.12 \\
+ 0.013 & 0.956 & 0.788 \\
+ 0.543 & 0.441 & 0.753 \\
+ 0.628 & 0.956 & 0.341 \\
+ 0.038 & 0.559 & 0.745 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.11$ 
+Solid Angle: $1.74$ 
+Surface Area: $1.49$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/10637.txt b/pretraining/mathematica/geometry/solids/10637.txt
new file mode 100644
index 0000000000000000000000000000000000000000..14e9688a9e12702e060bdd3adff82ad66b666d88
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/10637.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.326 & 0.731 & 0.387 \\
+ 0.985 & 0.577 & 0.637 \\
+ 0.163 & 0.766 & 0.823 \\
+ 0.201 & 0.509 & 0.907 \\
+ 0.364 & 0.243 & 0.492 \\
+ 0.169 & 0.549 & 0.402 \\
+\end{array}
+\right)$. 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: $1.81$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/1125.txt b/pretraining/mathematica/geometry/solids/1125.txt
new file mode 100644
index 0000000000000000000000000000000000000000..010076262d96ef660b6bf49d0eb9a5a96cff4738
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/1125.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -\frac{1}{4} \sqrt{2+\sqrt{3}} & \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & \frac{1}{2 \sqrt{2}} \\
+ -\frac{1}{4} \sqrt{2+\sqrt{3}} & \frac{\sqrt{2-\sqrt{3}}}{4} & -\frac{1}{2 \sqrt{2}} \\
+ -\frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} \\
+ -\frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & -\frac{1}{4} \sqrt{2+\sqrt{3}} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & \frac{\sqrt{2+\sqrt{3}}}{4} & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2-\sqrt{3}}}{4} & -\frac{1}{4} \sqrt{2+\sqrt{3}} & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2-\sqrt{3}}}{4} & \frac{\sqrt{2+\sqrt{3}}}{4} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2+\sqrt{3}}}{4} & \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2+\sqrt{3}}}{4} & \frac{\sqrt{2-\sqrt{3}}}{4} & \frac{1}{2 \sqrt{2}} \\
+\end{array}
+\right)$. Determine the Centroid.
+Answer:
+$\{0,0,0\}$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/13225.txt b/pretraining/mathematica/geometry/solids/13225.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dcca58b4d658b5f5a167de3c29df22c0a1081583
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/13225.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.953 & 0.843 & 0.735 \\
+ 0.082 & 0.661 & 0.148 \\
+ 0.01 & 0.05 & 0.314 \\
+ 0.673 & 0.636 & 0.158 \\
+ 0.417 & 0.901 & 0.832 \\
+ 0.634 & 0.498 & 0.29 \\
+ 0.316 & 0.893 & 0.945 \\
+ 0.719 & 0.566 & 0.784 \\
+ 0.048 & 0.453 & 0.111 \\
+ 0.812 & 0.919 & 0.21 \\
+\end{array}
+\right)$. 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: $1.94$ 
+Volume: $0.17$ 
+Solid Angle: $1.18$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/14573.txt b/pretraining/mathematica/geometry/solids/14573.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8fc0b14d2b5957f935ad4edd0c36cf3201119ae3
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/14573.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.829 & 0.996 & 0.191 \\
+ 0.885 & 0.411 & 0.785 \\
+ 0.197 & 0.295 & 0.687 \\
+ 0.955 & 0.742 & 0.28 \\
+ 0.817 & 0.772 & 0.215 \\
+ 0.386 & 0.582 & 0.421 \\
+\end{array}
+\right)$. 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: $0.82$ 
+Solid Angle: $0.46$ 
+Volume: $0.02$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/15700.txt b/pretraining/mathematica/geometry/solids/15700.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dc10a997e9648150bca1469f1b21f2591fb59a61
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/15700.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.424 & 0.826 & 0.876 \\
+ 0.664 & 0.373 & 0.057 \\
+ 0.789 & 0.416 & 0.182 \\
+ 0.82 & 0.491 & 0.524 \\
+ 0.923 & 0.352 & 0.587 \\
+ 0.111 & 0.926 & 0.795 \\
+\end{array}
+\right)$. 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: $0.81$ 
+Solid Angle: $0.44$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/19583.txt b/pretraining/mathematica/geometry/solids/19583.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3f6048d72b3b887ef5ebb34a05c070f17cea5597
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/19583.txt
@@ -0,0 +1,77 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ -\frac{1}{2} & 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} & 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{2} & 0 \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & -\frac{1}{2} & 0 \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{2} & 0 \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & -\frac{1}{2} & 0 \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \\
+ -\frac{1}{2} & 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} & 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{3}{4}+\frac{13}{4 \sqrt{5}} & \frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ \frac{3}{4}+\frac{13}{4 \sqrt{5}} & -\frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ \frac{5}{4}+\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+ 1+\frac{9}{2 \sqrt{5}} & 0 & \frac{1}{20} \left(15+\sqrt{5}\right) \\
+ \frac{5}{4}+\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+ -\frac{3}{4}-\frac{13}{4 \sqrt{5}} & \frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ -\frac{3}{4}-\frac{13}{4 \sqrt{5}} & -\frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ -\frac{5}{4}-\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+ -1-\frac{9}{2 \sqrt{5}} & 0 & \frac{1}{20} \left(15+\sqrt{5}\right) \\
+ -\frac{5}{4}-\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+\end{array}
+\right)$. Determine the SurfaceArea.
+Answer:
+$\frac{1}{2} \left(20+15 \sqrt{3}+50 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/19870.txt b/pretraining/mathematica/geometry/solids/19870.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9f68bdabc70d572f33492bb839e9112398258b2d
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/19870.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.682 & 0.384 & 0.234 \\
+ 0.935 & 0.431 & 0.951 \\
+ 0.851 & 0.177 & 0.746 \\
+ 0.877 & 0.579 & 0.577 \\
+ 0.028 & 0.474 & 0.714 \\
+ 0.14 & 0.181 & 0.526 \\
+\end{array}
+\right)$. 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: $1.09$ 
+Volume: $0.06$ 
+Solid Angle: $1.02$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/22420.txt b/pretraining/mathematica/geometry/solids/22420.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6be856e5c815d8f16c20f7093987a869ee79ee1b
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/22420.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.738 & 0.808 & 0.683 \\
+ 0.777 & 0.329 & 0.728 \\
+ 0.913 & 0.51 & 0.611 \\
+ 0.407 & 0.9 & 0.938 \\
+ 0.779 & 0.559 & 0.047 \\
+\end{array}
+\right)$. 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: $0.68$ 
+Volume: $0.02$ 
+Solid Angle: $2.55$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/22547.txt b/pretraining/mathematica/geometry/solids/22547.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d4e2851240def632e2ff8a10e613311b8533dbf9
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/22547.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.138 & 0.392 & 0.973 \\
+ 0.808 & 0.238 & 0.18 \\
+ 0.781 & 0.944 & 0.931 \\
+ 0.789 & 0.5 & 0.52 \\
+ 0.212 & 0.96 & 0.716 \\
+\end{array}
+\right)$. 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: $1.23$ 
+Solid Angle: $0.55$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/24321.txt b/pretraining/mathematica/geometry/solids/24321.txt
new file mode 100644
index 0000000000000000000000000000000000000000..327c53245a286f588230fb69e57e2515d43f3529
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/24321.txt
@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.207 & 0.901 & 0.595 \\
+ 0.976 & 0.894 & 0.99 \\
+ 0.244 & 0.157 & 0.405 \\
+ 0.989 & 0.635 & 0.494 \\
+ 0.474 & 0.953 & 0.299 \\
+ 0.419 & 0.759 & 0.285 \\
+ 0.305 & 0.316 & 0.728 \\
+ 0.722 & 0.034 & 0.351 \\
+ 0.835 & 0.273 & 0.756 \\
+ 0.51 & 0.972 & 0.892 \\
+ 0.621 & 0.332 & 0.893 \\
+\end{array}
+\right)$. 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: $2.08$ 
+Volume: $0.22$ 
+Solid Angle: $2.12$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/26253.txt b/pretraining/mathematica/geometry/solids/26253.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c351b77e31516ffb63f700d015204b8fe128b2a4
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/26253.txt
@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.984 & 0.386 & 0.72 \\
+ 0.269 & 0.492 & 0.843 \\
+ 0.225 & 0.936 & 0.221 \\
+ 0.755 & 0.315 & 0.816 \\
+ 0.334 & 0.997 & 0.966 \\
+ 0.248 & 0.333 & 0.198 \\
+ 0.925 & 0.457 & 0.432 \\
+ 0.734 & 0.862 & 0.461 \\
+ 0.315 & 0.927 & 0.045 \\
+ 0.474 & 0.214 & 0.082 \\
+ 0.967 & 0.44 & 0.954 \\
+\end{array}
+\right)$. 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: $2.55$ 
+Surface Area: $2.2$ 
+Volume: $0.23$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/26276.txt b/pretraining/mathematica/geometry/solids/26276.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6eea4374d432a3643de548666f2707c6bace0d75
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/26276.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.038 & 0.854 & 0.853 \\
+ 0.567 & 0.032 & 0.75 \\
+ 0.94 & 0.204 & 0.338 \\
+ 0.158 & 0.667 & 0.207 \\
+ 0.666 & 0.638 & 0.562 \\
+ 0.016 & 0.764 & 0.827 \\
+ 0.862 & 0.467 & 0.279 \\
+ 0.271 & 0.2 & 0.449 \\
+ 0.45 & 0.4 & 0.944 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.65$ 
+Solid Angle: $1.04$ 
+Volume: $0.14$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/2681.txt b/pretraining/mathematica/geometry/solids/2681.txt
new file mode 100644
index 0000000000000000000000000000000000000000..874d105299cdbb67329aba2a9720b98c68bf0309
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/2681.txt
@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.478 & 0.256 & 0.414 \\
+ 0.496 & 0.722 & 0.023 \\
+ 0.169 & 0.452 & 0.72 \\
+ 0.709 & 0.346 & 0.047 \\
+ 0.345 & 0.744 & 0.155 \\
+ 0.871 & 0.724 & 0.014 \\
+ 0.815 & 0.473 & 0.322 \\
+\end{array}
+\right)$. 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: $1.65$ 
+Surface Area: $0.88$ 
+Volume: $0.04$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/27848.txt b/pretraining/mathematica/geometry/solids/27848.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b5b36414e5d5ef31ab7bc1a9abcd19fe7cfc9b4a
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/27848.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.251 & 0.382 & 0.863 \\
+ 0.619 & 0.288 & 0.291 \\
+ 0.909 & 0.965 & 0.848 \\
+ 0.677 & 0.37 & 0.809 \\
+ 0.825 & 0.193 & 0.387 \\
+ 0.335 & 0.289 & 0.596 \\
+\end{array}
+\right)$. 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: $0.91$ 
+Volume: $0.04$ 
+Solid Angle: $0.54$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/28086.txt b/pretraining/mathematica/geometry/solids/28086.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b2db14ae59e33d4d0a515207945d14c2b247d903
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/28086.txt
@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.248 & 0.749 & 0.539 \\
+ 0.334 & 0. & 0.487 \\
+ 0.127 & 0.216 & 0.882 \\
+ 0.632 & 0.57 & 0.057 \\
+ 0.671 & 0.913 & 0.278 \\
+ 0.568 & 0.112 & 0.54 \\
+ 0.721 & 0.458 & 0.864 \\
+ 0.562 & 0.043 & 0.899 \\
+\end{array}
+\right)$. 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: $1.57$ 
+Solid Angle: $1.69$ 
+Volume: $0.12$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/28570.txt b/pretraining/mathematica/geometry/solids/28570.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3f9ff2be9e0db97781eabfbbda7be9dc5f5736a7
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/28570.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.691 & 0.649 & 0.727 \\
+ 0.808 & 0.123 & 0.345 \\
+ 0.366 & 0.364 & 0.653 \\
+ 0.88 & 0.14 & 0.983 \\
+ 0.612 & 0.68 & 0.92 \\
+ 0.433 & 0.39 & 0.81 \\
+ 0.648 & 0.82 & 0.094 \\
+ 0.664 & 0.398 & 0.961 \\
+ 0.363 & 0.553 & 0.15 \\
+\end{array}
+\right)$. 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: $0.1$ 
+Solid Angle: $5.17$ 
+Surface Area: $1.38$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/30401.txt b/pretraining/mathematica/geometry/solids/30401.txt
new file mode 100644
index 0000000000000000000000000000000000000000..62102bb34431b07500ef0a300334e4c0257ce2e5
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/30401.txt
@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.346 & 0.984 & 0.993 \\
+ 0.943 & 0.364 & 0.754 \\
+ 0.244 & 0.022 & 0.508 \\
+ 0.403 & 0.797 & 0.13 \\
+ 0.711 & 0.678 & 0.048 \\
+ 0.836 & 0.419 & 0.554 \\
+ 0.907 & 0.492 & 0.993 \\
+ 0.233 & 0.038 & 0.761 \\
+\end{array}
+\right)$. 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:
+Volume: $0.18$ 
+Surface Area: $2.05$ 
+Solid Angle: $0.76$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/31232.txt b/pretraining/mathematica/geometry/solids/31232.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b9602e430f02b850009aa2c05772277fff682d04
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/31232.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.63 & 0.464 & 0.652 \\
+ 0.319 & 0.517 & 0.376 \\
+ 0.844 & 0.592 & 0.732 \\
+ 0.88 & 0.57 & 0.656 \\
+ 0.004 & 0.729 & 0.2 \\
+\end{array}
+\right)$. 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: $1.1$ 
+Surface Area: $0.3$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/32177.txt b/pretraining/mathematica/geometry/solids/32177.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b13508586c2201f8dc1e426d4045b22fb4f123d3
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/32177.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.894 & 0.19 & 0.505 \\
+ 0.071 & 0.899 & 0.56 \\
+ 0.005 & 0.807 & 0.937 \\
+ 0.963 & 0.292 & 0.051 \\
+ 0.968 & 0.883 & 0.239 \\
+ 0.247 & 0.563 & 0.9 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $0.88$ 
+Surface Area: $1.61$ 
+Volume: $0.09$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/32186.txt b/pretraining/mathematica/geometry/solids/32186.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a248f0dd9445a1bbbaf5d83d8acd9c4d5dfcbb75
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/32186.txt
@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.414 & 0.3 & 0.51 \\
+ 0.951 & 0.128 & 0.502 \\
+ 0.511 & 0.929 & 0.96 \\
+ 0.837 & 0.223 & 0.471 \\
+\end{array}
+\right)$. 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: $0.15$ 
+Surface Area: $0.46$ 
+Volume: $0.$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/32500.txt b/pretraining/mathematica/geometry/solids/32500.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb7ba98c85d1e609962182266ebcc209b2193686
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/32500.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.007 & 0.121 & 0.156 \\
+ 0.729 & 0.932 & 0.337 \\
+ 0.927 & 0.755 & 0.795 \\
+ 0.693 & 0.186 & 0.546 \\
+ 0.268 & 0.091 & 0.393 \\
+ 0.861 & 0.522 & 0.919 \\
+\end{array}
+\right)$. 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: $0.15$ 
+Volume: $0.04$ 
+Surface Area: $1.22$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/32778.txt b/pretraining/mathematica/geometry/solids/32778.txt
new file mode 100644
index 0000000000000000000000000000000000000000..33966f778e32c9fa01a3078471edd13c11cecb2a
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/32778.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.242 & 0.209 & 0.964 \\
+ 0.261 & 0.647 & 0.113 \\
+ 0.079 & 0.511 & 0.812 \\
+ 0.536 & 0.592 & 0.015 \\
+ 0.987 & 0.108 & 0.211 \\
+\end{array}
+\right)$. 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: $1.22$ 
+Solid Angle: $0.16$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/33446.txt b/pretraining/mathematica/geometry/solids/33446.txt
new file mode 100644
index 0000000000000000000000000000000000000000..60359ccd838a318eef0e21f6ef39aa8186f797fa
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/33446.txt
@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.866 & 0.262 & 0.368 \\
+ 0.331 & 0.256 & 0.489 \\
+ 0.223 & 0.172 & 0.913 \\
+ 0.368 & 0.909 & 0.507 \\
+ 0.253 & 0.493 & 0.073 \\
+ 0.081 & 0.4 & 0.75 \\
+ 0.756 & 0.635 & 0.137 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.09$ 
+Surface Area: $1.36$ 
+Solid Angle: $0.86$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/35631.txt b/pretraining/mathematica/geometry/solids/35631.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c5e3288ccff07d33889f42923180ad75c18f55d3
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/35631.txt
@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.687 & 0.546 & 0.353 \\
+ 0.767 & 0.581 & 0.818 \\
+ 0.093 & 0.136 & 0.563 \\
+ 0.351 & 0.39 & 0.433 \\
+ 0.414 & 0.12 & 0.482 \\
+ 0.795 & 0.911 & 0.368 \\
+ 0.463 & 0.182 & 0.539 \\
+ 0.871 & 0.391 & 0.626 \\
+\end{array}
+\right)$. 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: $0.84$ 
+Solid Angle: $3.47$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/36988.txt b/pretraining/mathematica/geometry/solids/36988.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f1653be082814a2c03acfe76508eee695cd46bb7
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/36988.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.48 & 0.871 & 0.132 \\
+ 0.823 & 0.176 & 0.774 \\
+ 0.763 & 0.422 & 0.919 \\
+ 0.941 & 0.515 & 0.244 \\
+ 0.979 & 0.425 & 0.807 \\
+ 0.146 & 0.16 & 0.041 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.09$ 
+Solid Angle: $0.72$ 
+Surface Area: $1.41$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/37187.txt b/pretraining/mathematica/geometry/solids/37187.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9c6293061ac535f22c318ca2c2247301d1462e6b
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/37187.txt
@@ -0,0 +1,21 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -1 & 0 & -\frac{1}{2} \\
+ -1 & 0 & \frac{1}{2} \\
+ -\frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ -\frac{1}{2} & \frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ \frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ \frac{1}{2} & \frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ 1 & 0 & -\frac{1}{2} \\
+ 1 & 0 & \frac{1}{2} \\
+ \frac{1}{4} \left(-3-\sqrt{6}\right) & \frac{1}{4} \sqrt{5+2 \sqrt{6}} & 0 \\
+ \frac{1}{4} \left(3+\sqrt{6}\right) & \frac{1}{4} \sqrt{5+2 \sqrt{6}} & 0 \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$26$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/37946.txt b/pretraining/mathematica/geometry/solids/37946.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f358dd1789737007e27752ec39a3f52c07070738
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/37946.txt
@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.864 & 0.643 & 0.707 \\
+ 0.798 & 0.187 & 0.46 \\
+ 0.234 & 0.205 & 0.109 \\
+ 0.811 & 0.146 & 0.862 \\
+ 0.138 & 0.039 & 0.418 \\
+ 0.239 & 0.795 & 0.24 \\
+ 0.985 & 0.482 & 0.852 \\
+ 0.106 & 0.933 & 0.648 \\
+ 0.866 & 0.241 & 0.326 \\
+ 0.821 & 0.824 & 0.287 \\
+ 0.209 & 0.341 & 0.113 \\
+\end{array}
+\right)$. 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: $4.96$ 
+Surface Area: $2.22$ 
+Volume: $0.24$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/38952.txt b/pretraining/mathematica/geometry/solids/38952.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a29659c904dd3724eae2ea77f859a6eb8b7957cf
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/38952.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.915 & 0.736 & 0.564 \\
+ 0.244 & 0.426 & 0.83 \\
+ 0.14 & 0.188 & 0.033 \\
+ 0.716 & 0.685 & 0.879 \\
+ 0.312 & 0.883 & 0.047 \\
+ 0.151 & 0.104 & 0.593 \\
+ 0.202 & 0.522 & 0.024 \\
+ 0.105 & 0.703 & 0.657 \\
+ 0.357 & 0.999 & 0.52 \\
+ 0.861 & 0.174 & 0.022 \\
+\end{array}
+\right)$. 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: $0.27$ 
+Solid Angle: $2.01$ 
+Surface Area: $2.39$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/41691.txt b/pretraining/mathematica/geometry/solids/41691.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b056e42229d7ef3e7a1f1534d0a54e8183f8878f
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/41691.txt
@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.073 & 0.959 & 0.309 \\
+ 0.026 & 0.947 & 0.271 \\
+ 0.867 & 0.348 & 0.47 \\
+ 0.226 & 0.43 & 0.866 \\
+ 0.075 & 0.153 & 0.059 \\
+ 0.235 & 0.509 & 0.019 \\
+ 0.687 & 0.195 & 0.493 \\
+ 0.196 & 0.983 & 0.628 \\
+ 0.024 & 0.829 & 0.414 \\
+ 0.773 & 0.662 & 0.872 \\
+ 0.832 & 0.911 & 0.709 \\
+\end{array}
+\right)$. 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: $0.22$ 
+Solid Angle: $4.03$ 
+Surface Area: $2.15$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/41966.txt b/pretraining/mathematica/geometry/solids/41966.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69d7ba5aa5b6d9c42a4611d1ef03c0540555d820
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/41966.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.947 & 0.154 & 0.043 \\
+ 0.593 & 0.374 & 0.313 \\
+ 0.469 & 0.345 & 0.77 \\
+ 0.238 & 0.894 & 0.61 \\
+ 0.029 & 0.901 & 0.423 \\
+ 0.262 & 0.852 & 0.991 \\
+\end{array}
+\right)$. 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: $1.13$ 
+Volume: $0.04$ 
+Solid Angle: $0.1$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/42211.txt b/pretraining/mathematica/geometry/solids/42211.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9e498b840c69bfefd4a7537ff116a5b69591d045
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/42211.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.763 & 0.511 & 0.768 \\
+ 0.261 & 0.115 & 0.742 \\
+ 0.216 & 0.37 & 0.172 \\
+ 0.032 & 0.892 & 0.75 \\
+ 0.537 & 0.926 & 0.002 \\
+ 0.78 & 0.944 & 0.231 \\
+ 0.126 & 0.078 & 0.974 \\
+ 0.276 & 0.272 & 0.372 \\
+ 0.229 & 0.852 & 0.954 \\
+ 0.981 & 0.795 & 0.476 \\
+\end{array}
+\right)$. 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: $2.38$ 
+Volume: $0.22$ 
+Surface Area: $2.26$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/42352.txt b/pretraining/mathematica/geometry/solids/42352.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07a11958cf85f72ea7dacfd3f3a5adcf78a92c14
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/42352.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.657 & 0.622 & 0.113 \\
+ 0.27 & 0.776 & 0.085 \\
+ 0.901 & 0.623 & 0.954 \\
+ 0.195 & 0.422 & 0.809 \\
+ 0.327 & 0.618 & 0.846 \\
+ 0.315 & 0.893 & 0.826 \\
+ 0.286 & 0.813 & 0.074 \\
+ 0.56 & 0.248 & 0.42 \\
+ 0.081 & 0.633 & 0.462 \\
+ 0.902 & 0.924 & 0.123 \\
+\end{array}
+\right)$. 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: $3.62$ 
+Volume: $0.18$ 
+Surface Area: $1.87$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/42724.txt b/pretraining/mathematica/geometry/solids/42724.txt
new file mode 100644
index 0000000000000000000000000000000000000000..321494e22ecee17f807cf81988e6fe3e6e8d6d1d
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/42724.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.879 & 0.199 & 0.1 \\
+ 0.935 & 0.754 & 0.894 \\
+ 0.824 & 0.686 & 0.244 \\
+ 0.625 & 0.191 & 0.835 \\
+ 0.144 & 0.754 & 0.575 \\
+ 0.676 & 0.851 & 0.455 \\
+ 0.424 & 0.185 & 0.58 \\
+ 0.436 & 0.577 & 0.181 \\
+ 0.584 & 0.523 & 0.952 \\
+\end{array}
+\right)$. 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: $0.93$ 
+Surface Area: $1.7$ 
+Volume: $0.17$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/43559.txt b/pretraining/mathematica/geometry/solids/43559.txt
new file mode 100644
index 0000000000000000000000000000000000000000..db8becbc27ef69a5918b8b6e35154721171d2e6d
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/43559.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.649 & 0.717 & 0.212 \\
+ 0.025 & 0.268 & 0.372 \\
+ 0.608 & 0.894 & 0.957 \\
+ 0.25 & 0.735 & 0.006 \\
+ 0.031 & 0.775 & 0.04 \\
+ 0.723 & 0.588 & 0.844 \\
+ 0.289 & 0.19 & 0.875 \\
+ 0.304 & 0.736 & 0.782 \\
+ 0.103 & 0.13 & 0.544 \\
+\end{array}
+\right)$. 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: $1.42$ 
+Volume: $0.13$ 
+Surface Area: $1.73$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/47225.txt b/pretraining/mathematica/geometry/solids/47225.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8535ddab70c767d6fd2b685658ed5f6bc3d843d2
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/47225.txt
@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.482 & 0.827 & 0.444 \\
+ 0.717 & 0.09 & 0.571 \\
+ 0.422 & 0.168 & 0.335 \\
+ 0.611 & 0.35 & 0.147 \\
+\end{array}
+\right)$. 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: $0.43$ 
+Volume: $0.01$ 
+Solid Angle: $0.13$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/47674.txt b/pretraining/mathematica/geometry/solids/47674.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ceaaff2a0ca8407522da43d910d993ef9439eb61
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/47674.txt
@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{-9.009,9.625,7.589\}$ has radii $\{5.837,9.789,0.137\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Surface Area: $359.59$ 
+Volume: $32.71$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/48383.txt b/pretraining/mathematica/geometry/solids/48383.txt
new file mode 100644
index 0000000000000000000000000000000000000000..82bf45b23113307ab409c56b5dfe634427865e62
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/48383.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.098 & 0.215 & 0.079 \\
+ 0.058 & 0.243 & 0.075 \\
+ 0.113 & 0.525 & 0.941 \\
+ 0.43 & 0.314 & 0.796 \\
+ 0.057 & 0. & 0.121 \\
+ 0.285 & 0.692 & 0.914 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.72$ 
+Volume: $0.03$ 
+Solid Angle: $2.83$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/52500.txt b/pretraining/mathematica/geometry/solids/52500.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c2ee7468eb0d9428a04184bda714710a1832518
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/52500.txt
@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.255 & 0.973 & 0.532 \\
+ 0.882 & 0.463 & 0.099 \\
+ 0.075 & 0.908 & 0.084 \\
+ 0.727 & 0.489 & 0.875 \\
+ 0.676 & 0.071 & 0.175 \\
+ 0.366 & 0.683 & 0.812 \\
+ 0.249 & 0.31 & 0.835 \\
+\end{array}
+\right)$. 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: $1.64$ 
+Volume: $0.16$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/52600.txt b/pretraining/mathematica/geometry/solids/52600.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e53cf358df6e49bbfe3c012a1c576445468453e0
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/52600.txt
@@ -0,0 +1,6 @@
+Problem:
+A cone with radius $1.666$ has its base centered at$\{7.487,4.707,5.466\}$ and its tip is at $\{2.384,8.789,2.599\}$. Estimate the cone's surface area, volume, and centroid.
+Answer:
+Surface Area: $47.07$ 
+Centroid: $\{6.21,5.73,4.75\}$ 
+Volume: $20.74$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/54182.txt b/pretraining/mathematica/geometry/solids/54182.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dfe5d61bdebc8495236ee7b65a0c5fd8e056e2e4
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/54182.txt
@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.302 & 0.355 & 0.096 \\
+ 0.121 & 0.847 & 0.418 \\
+ 0.709 & 0.131 & 0.13 \\
+ 0.047 & 0.259 & 0.921 \\
+ 0.499 & 0.052 & 0.395 \\
+ 0.159 & 0.553 & 0.089 \\
+ 0.87 & 0.28 & 0.577 \\
+\end{array}
+\right)$. 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: $3.26$ 
+Surface Area: $1.49$ 
+Volume: $0.1$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/5442.txt b/pretraining/mathematica/geometry/solids/5442.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ab2c4559b71380d2bd41488692638a5e5e0cff17
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/5442.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.499 & 0.866 & 0.059 \\
+ 0.823 & 0.843 & 0.148 \\
+ 0.371 & 0.642 & 0.134 \\
+ 0.827 & 0.205 & 0.124 \\
+ 0.193 & 0.327 & 0.793 \\
+ 0.693 & 0.276 & 0.329 \\
+ 0.625 & 0.971 & 0.294 \\
+ 0.301 & 0.236 & 0.814 \\
+ 0.12 & 0.565 & 0.91 \\
+ 0.058 & 0.643 & 0.357 \\
+\end{array}
+\right)$. 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:
+Solid Angle: $2.34$ 
+Surface Area: $1.61$ 
+Volume: $0.11$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/56677.txt b/pretraining/mathematica/geometry/solids/56677.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c033af576c3141f321041124f99a4dcc773f9dbf
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/56677.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.336 & 0.885 & 0.049 \\
+ 0.753 & 0.61 & 0.959 \\
+ 0.008 & 0.479 & 0.498 \\
+ 0.942 & 0.393 & 0.521 \\
+ 0.427 & 0.814 & 0.776 \\
+ 0.428 & 0.751 & 0.832 \\
+ 0.584 & 0.164 & 0.372 \\
+ 0.509 & 0.965 & 0.115 \\
+ 0.383 & 0.652 & 0.803 \\
+ 0.591 & 0.412 & 0.019 \\
+\end{array}
+\right)$. 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: $1.8$ 
+Volume: $0.16$ 
+Surface Area: $1.75$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/56783.txt b/pretraining/mathematica/geometry/solids/56783.txt
new file mode 100644
index 0000000000000000000000000000000000000000..43ca0e2aab464d26ccb9d6a117ec61ae5963872f
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/56783.txt
@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.622 & 0.947 & 0.1 \\
+ 0.34 & 0.029 & 0.712 \\
+ 0.797 & 0.18 & 0.316 \\
+ 0.437 & 0.733 & 0.475 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.01$ 
+Surface Area: $0.72$ 
+Solid Angle: $0.08$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/57100.txt b/pretraining/mathematica/geometry/solids/57100.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ea99dc2331d48ef855b6899ffa3163fe07aa5ef4
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/57100.txt
@@ -0,0 +1,99 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -2.412 & 0. & -0.843 \\
+ -2.412 & 0. & 0.157 \\
+ -2.285 & -0.934 & -0.509 \\
+ -2.285 & -0.934 & 0.491 \\
+ -2.285 & 0.934 & -0.509 \\
+ -2.285 & 0.934 & 0.491 \\
+ -2.157 & 0. & 0.824 \\
+ -2.079 & -0.577 & -1.588 \\
+ -2.079 & 0.577 & -1.588 \\
+ -1.951 & -1.512 & -1.255 \\
+ -1.951 & -1.512 & -0.255 \\
+ -1.951 & 1.512 & -1.255 \\
+ -1.951 & 1.512 & -0.255 \\
+ -1.745 & 0. & -2.333 \\
+ -1.618 & -0.934 & -2. \\
+ -1.618 & -0.934 & 1.236 \\
+ -1.618 & 0.934 & -2. \\
+ -1.618 & 0.934 & 1.236 \\
+ -1.539 & -1.512 & 0.824 \\
+ -1.539 & 1.512 & 0.824 \\
+ -1.491 & 0. & 1.569 \\
+ -1.206 & -2.089 & -0.921 \\
+ -1.206 & -2.089 & 0.079 \\
+ -1.206 & 2.089 & -0.921 \\
+ -1.206 & 2.089 & 0.079 \\
+ -1.079 & -1.868 & -1.588 \\
+ -1.079 & 1.868 & -1.588 \\
+ -0.873 & -1.512 & 1.569 \\
+ -0.873 & -0.357 & -2.667 \\
+ -0.873 & 0.357 & -2.667 \\
+ -0.873 & 1.512 & 1.569 \\
+ -0.745 & -1.291 & -2.333 \\
+ -0.745 & -0.577 & 1.903 \\
+ -0.745 & 0.577 & 1.903 \\
+ -0.745 & 1.291 & -2.333 \\
+ -0.539 & -2.089 & 0.824 \\
+ -0.539 & 2.089 & 0.824 \\
+ -0.333 & -2.446 & -1.255 \\
+ -0.333 & -2.446 & -0.255 \\
+ -0.333 & 2.446 & -1.255 \\
+ -0.333 & 2.446 & -0.255 \\
+ -0.127 & -0.934 & 1.903 \\
+ -0.127 & 0.934 & 1.903 \\
+ 0. & -1.868 & -2. \\
+ 0. & -1.868 & 1.236 \\
+ 0. & 0. & -3. \\
+ 0. & 0. & 2.236 \\
+ 0. & 1.868 & -2. \\
+ 0. & 1.868 & 1.236 \\
+ 0.127 & -0.934 & -2.667 \\
+ 0.127 & 0.934 & -2.667 \\
+ 0.333 & -2.446 & -0.509 \\
+ 0.333 & -2.446 & 0.491 \\
+ 0.333 & 2.446 & -0.509 \\
+ 0.333 & 2.446 & 0.491 \\
+ 0.539 & -2.089 & -1.588 \\
+ 0.539 & 2.089 & -1.588 \\
+ 0.745 & -1.291 & 1.569 \\
+ 0.745 & -0.577 & -2.667 \\
+ 0.745 & 0.577 & -2.667 \\
+ 0.745 & 1.291 & 1.569 \\
+ 0.873 & -1.512 & -2.333 \\
+ 0.873 & -0.357 & 1.903 \\
+ 0.873 & 0.357 & 1.903 \\
+ 0.873 & 1.512 & -2.333 \\
+ 1.079 & -1.868 & 0.824 \\
+ 1.079 & 1.868 & 0.824 \\
+ 1.206 & -2.089 & -0.843 \\
+ 1.206 & -2.089 & 0.157 \\
+ 1.206 & 2.089 & -0.843 \\
+ 1.206 & 2.089 & 0.157 \\
+ 1.491 & 0. & -2.333 \\
+ 1.539 & -1.512 & -1.588 \\
+ 1.539 & 1.512 & -1.588 \\
+ 1.618 & -0.934 & -2. \\
+ 1.618 & -0.934 & 1.236 \\
+ 1.618 & 0.934 & -2. \\
+ 1.618 & 0.934 & 1.236 \\
+ 1.745 & 0. & 1.569 \\
+ 1.951 & -1.512 & -0.509 \\
+ 1.951 & -1.512 & 0.491 \\
+ 1.951 & 1.512 & -0.509 \\
+ 1.951 & 1.512 & 0.491 \\
+ 2.079 & -0.577 & 0.824 \\
+ 2.079 & 0.577 & 0.824 \\
+ 2.157 & 0. & -1.588 \\
+ 2.285 & -0.934 & -1.255 \\
+ 2.285 & -0.934 & -0.255 \\
+ 2.285 & 0.934 & -1.255 \\
+ 2.285 & 0.934 & -0.255 \\
+ 2.412 & 0. & -0.921 \\
+ 2.412 & 0. & 0.079 \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$180.$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/57829.txt b/pretraining/mathematica/geometry/solids/57829.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2a3e448bed94baf4ed4250fc840d33dab1ffd898
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/57829.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.618 & 0.681 & 0.011 \\
+ 0.231 & 0.142 & 0.098 \\
+ 0.545 & 0.928 & 0.645 \\
+ 0.592 & 0.199 & 0.044 \\
+ 0.806 & 0.685 & 0.606 \\
+ 0.205 & 0.447 & 0.383 \\
+\end{array}
+\right)$. 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: $1.03$ 
+Solid Angle: $1.3$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/58247.txt b/pretraining/mathematica/geometry/solids/58247.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a3b885a6e11b5d64043cad8e57d53d207f76f4d
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/58247.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.836 & 0.08 & 0.111 \\
+ 0.551 & 0.149 & 0.582 \\
+ 0.443 & 0.924 & 0.401 \\
+ 0.213 & 0.885 & 0.461 \\
+ 0.834 & 0.837 & 0.845 \\
+ 0.463 & 0.242 & 0.691 \\
+\end{array}
+\right)$. 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: $0.35$ 
+Surface Area: $1.24$ 
+Volume: $0.08$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/60347.txt b/pretraining/mathematica/geometry/solids/60347.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b41d9ff90c958629266540b0a8a24f16611cedae
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/60347.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.074 & 0.896 & 0.412 \\
+ 0.057 & 0.026 & 0.731 \\
+ 0.367 & 0.498 & 0.134 \\
+ 0.08 & 0.098 & 0.387 \\
+ 0.311 & 0.071 & 0.825 \\
+\end{array}
+\right)$. 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: $0.83$ 
+Solid Angle: $0.28$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/60963.txt b/pretraining/mathematica/geometry/solids/60963.txt
new file mode 100644
index 0000000000000000000000000000000000000000..88e36148cb7af3f0a50d32f1847ad95691855a1d
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/60963.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.288 & 0.425 & 0.06 \\
+ 0.417 & 0.673 & 0.696 \\
+ 0.464 & 0.186 & 0.382 \\
+ 0.374 & 0.067 & 0.563 \\
+ 0.615 & 0.847 & 0.699 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.61$ 
+Solid Angle: $0.3$ 
+Volume: $0.02$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/61810.txt b/pretraining/mathematica/geometry/solids/61810.txt
new file mode 100644
index 0000000000000000000000000000000000000000..89e41de127f18d6fe54832544f6fe4f334843af2
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/61810.txt
@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.916 & 0.207 & 0.873 \\
+ 0.766 & 0.053 & 0.573 \\
+ 0.981 & 0.135 & 0.814 \\
+ 0.115 & 0.69 & 0.991 \\
+ 0.912 & 0.553 & 0.574 \\
+ 0.072 & 0.65 & 0.319 \\
+ 0.226 & 0.412 & 0.843 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.09$ 
+Surface Area: $1.37$ 
+Solid Angle: $2.32$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/62503.txt b/pretraining/mathematica/geometry/solids/62503.txt
new file mode 100644
index 0000000000000000000000000000000000000000..64bd32cccd27b04dde3e35d96565c39528f331df
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/62503.txt
@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.765 & 0.251 & 0.437 \\
+ 0.785 & 0.75 & 0.199 \\
+ 0.814 & 0.525 & 0.614 \\
+ 0.257 & 0.829 & 0.681 \\
+\end{array}
+\right)$. 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: $0.45$ 
+Surface Area: $0.52$ 
+Volume: $0.02$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/62880.txt b/pretraining/mathematica/geometry/solids/62880.txt
new file mode 100644
index 0000000000000000000000000000000000000000..43cc40dbc0b1a0a67355348f1afd6b01d4bf2be2
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/62880.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.26 & 0.176 & 0.646 \\
+ 0.641 & 0.109 & 0.329 \\
+ 0.583 & 0.818 & 0.036 \\
+ 0.899 & 0.85 & 0.571 \\
+ 0.612 & 0.925 & 0.57 \\
+ 0.377 & 0.408 & 0.229 \\
+\end{array}
+\right)$. 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: $1.11$ 
+Volume: $0.07$ 
+Solid Angle: $0.6$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/64587.txt b/pretraining/mathematica/geometry/solids/64587.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e68f8d51a6411261b557e7c7847671594f7b1a48
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/64587.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.007 & 0.499 & 0.539 \\
+ 0.803 & 0.876 & 0.165 \\
+ 0.787 & 0.74 & 0.819 \\
+ 0.566 & 0.663 & 0.936 \\
+ 0.269 & 0.685 & 0.236 \\
+ 0.4 & 0.031 & 0.901 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.08$ 
+Solid Angle: $0.89$ 
+Surface Area: $1.39$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/67913.txt b/pretraining/mathematica/geometry/solids/67913.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c037e0e5a4cf9d0446ec6eeb98f35c5eeea20fbc
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/67913.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.138 & 0.511 & 0.583 \\
+ 0.147 & 0.78 & 0.9 \\
+ 0.706 & 0.037 & 0.873 \\
+ 0.826 & 0.699 & 0.854 \\
+ 0.252 & 0.905 & 0.289 \\
+ 0.718 & 0.885 & 0.179 \\
+\end{array}
+\right)$. 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: $1.54$ 
+Solid Angle: $2.26$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/68415.txt b/pretraining/mathematica/geometry/solids/68415.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fe3c89095782e0f033d4b5d78db3d314cd4be789
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/68415.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.866 & 0.888 & 0.205 \\
+ 0.37 & 0.914 & 0.956 \\
+ 0.216 & 0.963 & 0.086 \\
+ 0.387 & 0.349 & 0.71 \\
+ 0.859 & 0.201 & 0.981 \\
+ 0.458 & 0.361 & 0.601 \\
+\end{array}
+\right)$. 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: $0.11$ 
+Solid Angle: $0.77$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/70352.txt b/pretraining/mathematica/geometry/solids/70352.txt
new file mode 100644
index 0000000000000000000000000000000000000000..acb6a852de2d1a800d842687521b273cf17b5d03
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/70352.txt
@@ -0,0 +1,39 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0 & 0 & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ 0 & 0 & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{10} \left(5-\sqrt{5}\right) & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{10} \left(5-\sqrt{5}\right) & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(5+3 \sqrt{5}\right) \\
+ \frac{2}{\sqrt{5}} & 0 & \frac{1}{10} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{10} \left(5+3 \sqrt{5}\right) & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(5+\sqrt{5}\right) \\
+ \frac{1}{10} \left(5+3 \sqrt{5}\right) & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(\sqrt{5}-5\right) \\
+ \frac{1}{10} \left(5+3 \sqrt{5}\right) & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(5+\sqrt{5}\right) \\
+ \frac{1}{10} \left(5+3 \sqrt{5}\right) & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(\sqrt{5}-5\right) \\
+ -\frac{2}{\sqrt{5}} & 0 & \frac{1}{10} \left(-5-3 \sqrt{5}\right) \\
+ -\frac{1}{\sqrt{5}} & -\sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(5+\sqrt{5}\right) \\
+ -\frac{1}{\sqrt{5}} & -\sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(\sqrt{5}-5\right) \\
+ -\frac{1}{\sqrt{5}} & \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(5+\sqrt{5}\right) \\
+ -\frac{1}{\sqrt{5}} & \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(\sqrt{5}-5\right) \\
+ \frac{1}{\sqrt{5}} & -\sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(5-\sqrt{5}\right) \\
+ \frac{1}{\sqrt{5}} & -\sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{\sqrt{5}} & \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(5-\sqrt{5}\right) \\
+ \frac{1}{\sqrt{5}} & \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{10} \left(-5-\sqrt{5}\right) \\
+ -1-\frac{1}{\sqrt{5}} & 0 & \frac{1}{10} \left(5+\sqrt{5}\right) \\
+ -1-\frac{1}{\sqrt{5}} & 0 & \frac{1}{10} \left(\sqrt{5}-5\right) \\
+ \frac{1}{10} \left(-5-\sqrt{5}\right) & -\sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{10} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{10} \left(-5-\sqrt{5}\right) & \sqrt{\frac{2}{5+\sqrt{5}}} & \frac{1}{10} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{10} \left(5+\sqrt{5}\right) & -\sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{10} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{10} \left(5+\sqrt{5}\right) & \sqrt{\frac{2}{5+\sqrt{5}}} & \frac{1}{10} \left(-5-3 \sqrt{5}\right) \\
+ 1+\frac{1}{\sqrt{5}} & 0 & \frac{1}{10} \left(5-\sqrt{5}\right) \\
+ 1+\frac{1}{\sqrt{5}} & 0 & \frac{1}{10} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{10} \left(-5-3 \sqrt{5}\right) & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(5-\sqrt{5}\right) \\
+ \frac{1}{10} \left(-5-3 \sqrt{5}\right) & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{10} \left(-5-3 \sqrt{5}\right) & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(5-\sqrt{5}\right) \\
+ \frac{1}{10} \left(-5-3 \sqrt{5}\right) & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(-5-\sqrt{5}\right) \\
+ \frac{1}{10} \left(\sqrt{5}-5\right) & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{10} \left(\sqrt{5}-5\right) & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{10} \left(-5-3 \sqrt{5}\right) \\
+\end{array}
+\right)$. Determine the GeneralizedDiameter.
+Answer:
+$1+\sqrt{5}$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/73558.txt b/pretraining/mathematica/geometry/solids/73558.txt
new file mode 100644
index 0000000000000000000000000000000000000000..15b95eee76863e77ed5ab22ea08fa0b6db242955
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/73558.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.574 & 0.054 & 0.32 \\
+ 0.424 & 0.166 & 0.727 \\
+ 0.483 & 0.134 & 0.081 \\
+ 0.229 & 0.988 & 0.968 \\
+ 0.125 & 0.926 & 0.068 \\
+ 0.35 & 0.255 & 0.768 \\
+ 0.222 & 0.527 & 0.816 \\
+ 0.739 & 0.862 & 0.881 \\
+ 0.161 & 0.751 & 0.244 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.15$ 
+Solid Angle: $1.36$ 
+Surface Area: $1.93$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/74044.txt b/pretraining/mathematica/geometry/solids/74044.txt
new file mode 100644
index 0000000000000000000000000000000000000000..26e273480526fe035bb6581a93832758779801b5
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/74044.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.218 & 0.544 & 0.734 \\
+ 0.946 & 0.923 & 0.573 \\
+ 0.188 & 0.484 & 0.14 \\
+ 0.439 & 0.295 & 0.043 \\
+ 0.334 & 0.344 & 0.889 \\
+ 0.488 & 0.194 & 0.103 \\
+\end{array}
+\right)$. 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: $1.18$ 
+Volume: $0.07$ 
+Solid Angle: $2.03$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/74083.txt b/pretraining/mathematica/geometry/solids/74083.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6ab0caad6f23b2da07eb652e42a8958443e4eec2
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/74083.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.495 & 0.525 & 0.303 \\
+ 0.168 & 0.689 & 0.548 \\
+ 0.149 & 0.893 & 0.463 \\
+ 0.59 & 0.946 & 0.821 \\
+ 0.099 & 0.664 & 0.164 \\
+\end{array}
+\right)$. 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: $0.42$ 
+Surface Area: $0.53$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/75518.txt b/pretraining/mathematica/geometry/solids/75518.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fafd7ccd2aca4488f5cfd89fd92084e4a71bc079
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/75518.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0. & 0. & 1.192 \\
+ 0.607 & 0. & 0.397 \\
+ -0.304 & 0.526 & 0.397 \\
+ 0.304 & 0.526 & -0.397 \\
+ -0.304 & -0.526 & 0.397 \\
+ 0.304 & -0.526 & -0.397 \\
+ -0.607 & 0. & -0.397 \\
+ 0. & 0. & -1.192 \\
+\end{array}
+\right)$. Determine the GeneralizedDiameter.
+Answer:
+$2.38$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/77284.txt b/pretraining/mathematica/geometry/solids/77284.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d2b7353659a938708841902bea407c90ef658a89
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/77284.txt
@@ -0,0 +1,27 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0 & -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\
+ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\
+ 0 & -\sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ 0 & \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ -\frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\
+ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\
+ \frac{1}{2} \left(-1-\sqrt{2}\right) & -\frac{1}{2} & 0 \\
+ -\sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} & 0 & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ \sqrt{\frac{1}{2} \left(2+\sqrt{2}\right)} & 0 & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ -\frac{1}{2} \sqrt{2+\sqrt{2}} & -\frac{1}{2} \sqrt{2+\sqrt{2}} & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ -\frac{1}{2} \sqrt{2+\sqrt{2}} & \frac{\sqrt{2+\sqrt{2}}}{2} & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ \frac{\sqrt{2+\sqrt{2}}}{2} & -\frac{1}{2} \sqrt{2+\sqrt{2}} & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ \frac{\sqrt{2+\sqrt{2}}}{2} & \frac{\sqrt{2+\sqrt{2}}}{2} & -\sqrt{-1-\sqrt{2}+\sqrt{\frac{1}{2} \left(10+7 \sqrt{2}\right)}} \\
+ -\frac{1}{2} & \frac{1}{2} \left(-1-\sqrt{2}\right) & 0 \\
+ \frac{1}{2} & \frac{1}{2} \left(1+\sqrt{2}\right) & 0 \\
+ \frac{1}{2} & \frac{1}{2} \left(-1-\sqrt{2}\right) & 0 \\
+ -\frac{1}{2} & \frac{1}{2} \left(1+\sqrt{2}\right) & 0 \\
+ \frac{1}{2} \left(1+\sqrt{2}\right) & -\frac{1}{2} & 0 \\
+ \frac{1}{2} \left(-1-\sqrt{2}\right) & \frac{1}{2} & 0 \\
+ \frac{1}{2} \left(1+\sqrt{2}\right) & \frac{1}{2} & 0 \\
+\end{array}
+\right)$. Determine the GeneralizedDiameter.
+Answer:
+$\sqrt{1+\sqrt{20+14 \sqrt{2}}}$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/79145.txt b/pretraining/mathematica/geometry/solids/79145.txt
new file mode 100644
index 0000000000000000000000000000000000000000..78706864770802c08fdb2fc76a9c5b9eed97abc4
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/79145.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.464 & 0.567 & 0.351 \\
+ 0.547 & 0.377 & 0.119 \\
+ 0.095 & 0.576 & 0.514 \\
+ 0.385 & 0.586 & 0.872 \\
+ 0.83 & 0.774 & 0.952 \\
+ 0.049 & 0.415 & 0.139 \\
+ 0.213 & 0.209 & 0.792 \\
+ 0.83 & 0.409 & 0.985 \\
+ 0.761 & 0.117 & 0.172 \\
+\end{array}
+\right)$. 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: $4.89$ 
+Surface Area: $1.73$ 
+Volume: $0.15$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/80582.txt b/pretraining/mathematica/geometry/solids/80582.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ddc088af029b5541e869112be7ccf0595ef4d7e2
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/80582.txt
@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.531 & 0.875 & 0.449 \\
+ 0.869 & 0.078 & 0.917 \\
+ 0.097 & 0.403 & 0.415 \\
+ 0.74 & 0.502 & 0.285 \\
+ 0.621 & 0.284 & 0.579 \\
+ 0.274 & 0.665 & 0.108 \\
+ 0.136 & 0.249 & 0.903 \\
+\end{array}
+\right)$. 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: $1.42$ 
+Solid Angle: $1.38$ 
+Volume: $0.09$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/81637.txt b/pretraining/mathematica/geometry/solids/81637.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4a21db28bc44ce45d067c5cfa34c46d5587124e0
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/81637.txt
@@ -0,0 +1,32 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ 0 & \frac{1}{2} \left(-1-\sqrt{5}\right) & 0 \\
+ 0 & \frac{1}{2} \left(1+\sqrt{5}\right) & 0 \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & 0 & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & 0 & \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) & \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) & \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & 0 & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ -\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(-3-\sqrt{5}\right) & 0 \\
+ -\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(3+\sqrt{5}\right) & 0 \\
+ \frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(-3-\sqrt{5}\right) & 0 \\
+ \frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & \frac{1}{4} \left(3+\sqrt{5}\right) & 0 \\
+ -\sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & -\frac{1}{2} & \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ -\sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & \frac{1}{2} & \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} \\
+ -\frac{1}{2} & -\sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ -\frac{1}{2} & \sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ \frac{1}{2} & -\sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ \frac{1}{2} & \sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & -\sqrt{\frac{1}{2} \left(-4-2 \sqrt{5}+\sqrt{2 \left(25+11 \sqrt{5}\right)}\right)} \\
+ -\sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & -\frac{1}{2} & 0 \\
+ -\sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & \frac{1}{2} & 0 \\
+ \sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & -\frac{1}{2} & 0 \\
+ \sqrt{\frac{5}{4}+\frac{\sqrt{5}}{2}} & \frac{1}{2} & 0 \\
+\end{array}
+\right)$. Determine the FaceCount.
+Answer:
+$32$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/82319.txt b/pretraining/mathematica/geometry/solids/82319.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5fd056394b8980decdfe3db704b54129c123b966
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/82319.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.971 & 0.691 & 0.182 \\
+ 0.516 & 0.137 & 0.221 \\
+ 0.59 & 0.694 & 0.679 \\
+ 0.3 & 0.668 & 0.365 \\
+ 0.465 & 0.094 & 0.324 \\
+ 0.982 & 0.12 & 0.659 \\
+ 0.834 & 0.395 & 0.819 \\
+ 0.09 & 0.234 & 0.81 \\
+ 0.67 & 0.768 & 0.034 \\
+\end{array}
+\right)$. 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: $1.78$ 
+Solid Angle: $1.41$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/8517.txt b/pretraining/mathematica/geometry/solids/8517.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3c82217f953aae985c557f9f8ed61af6c2e0b1ab
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/8517.txt
@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.495 & 0.713 & 0.792 \\
+ 0.376 & 0.28 & 0.013 \\
+ 0.681 & 0.485 & 0.887 \\
+ 0.8 & 0.141 & 0.037 \\
+ 0.857 & 0.57 & 0.189 \\
+ 0.741 & 0.699 & 0.278 \\
+ 0.557 & 0.621 & 0.363 \\
+ 0.395 & 0.415 & 0.865 \\
+ 0.378 & 0.136 & 0.195 \\
+ 0.957 & 0.04 & 0.611 \\
+\end{array}
+\right)$. 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: $1.55$ 
+Volume: $0.14$ 
+Surface Area: $1.56$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/86221.txt b/pretraining/mathematica/geometry/solids/86221.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d83210b60743b1a03c12c83298aa3ce130c605db
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/86221.txt
@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.124 & 0.076 & 0.484 \\
+ 0.187 & 0.155 & 0.209 \\
+ 0.763 & 0.677 & 0.906 \\
+ 0.262 & 0.05 & 0.286 \\
+\end{array}
+\right)$. 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:
+Surface Area: $0.35$ 
+Solid Angle: $0.57$ 
+Volume: $0.01$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/87961.txt b/pretraining/mathematica/geometry/solids/87961.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c6e6093dcc0b951608a1194f7d77d6ad80090925
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/87961.txt
@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.57 & 0.785 & 0.094 \\
+ 0.31 & 0.954 & 0.456 \\
+ 0.416 & 0.684 & 0.541 \\
+ 0.588 & 0.468 & 0.302 \\
+ 0.545 & 0.408 & 0.459 \\
+ 0.221 & 0.752 & 0.26 \\
+ 0.275 & 0.534 & 0.54 \\
+\end{array}
+\right)$. 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: $0.59$ 
+Surface Area: $0.5$ 
+Volume: $0.02$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/88755.txt b/pretraining/mathematica/geometry/solids/88755.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8c0415c92cb080d2f9e4d97a38ecd1d790bb1674
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/88755.txt
@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.841 & 0.342 & 0.059 \\
+ 0.485 & 0.39 & 0.58 \\
+ 0.839 & 0.022 & 0.793 \\
+ 0.768 & 0.801 & 0.542 \\
+ 0.383 & 0.186 & 0.547 \\
+\end{array}
+\right)$. 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: $0.46$ 
+Surface Area: $0.85$ 
+Volume: $0.04$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/91435.txt b/pretraining/mathematica/geometry/solids/91435.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1bd81e68df53c7fdd918e320ac255db244ec28b4
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/91435.txt
@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.229 & 0.724 & 0.887 \\
+ 0.578 & 0.607 & 0.201 \\
+ 0.888 & 0.776 & 0.125 \\
+ 0.785 & 0.093 & 0.001 \\
+ 0.698 & 0.661 & 0.527 \\
+ 0.328 & 0.432 & 0.459 \\
+ 0.187 & 0.643 & 0.938 \\
+ 0.664 & 0.3 & 0.354 \\
+\end{array}
+\right)$. 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: $1.$ 
+Surface Area: $1.06$ 
+Volume: $0.05$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/92428.txt b/pretraining/mathematica/geometry/solids/92428.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4feb9c9effe0657c0ddb90c02f53904a6de7c774
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/92428.txt
@@ -0,0 +1,5 @@
+Problem:
+A sphere centered at $\{2.553,-3.937,-5.833\}$ has radius $4.181$. Estimate the sphere's surface area and volume.
+Answer:
+Surface Area: $219.68$ 
+Volume: $306.18$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/9531.txt b/pretraining/mathematica/geometry/solids/9531.txt
new file mode 100644
index 0000000000000000000000000000000000000000..368c7c00e35491b2e3f66b80c7816e165c72f2c6
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/9531.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.09 & 0.073 & 0.413 \\
+ 0.559 & 0.949 & 0.254 \\
+ 0.248 & 0.067 & 0.101 \\
+ 0.288 & 0.003 & 0.599 \\
+ 0.964 & 0.047 & 0.189 \\
+ 0.877 & 0.12 & 0.506 \\
+ 0.136 & 0.342 & 0.941 \\
+ 0.355 & 0.888 & 0.309 \\
+ 0.395 & 0.91 & 0.784 \\
+\end{array}
+\right)$. 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: $0.22$ 
+Solid Angle: $2.45$ 
+Surface Area: $2.23$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/96881.txt b/pretraining/mathematica/geometry/solids/96881.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1126723cf787de75fd31f25e2dd782112b886497
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/96881.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.545 & 0.867 & 0.291 \\
+ 0.951 & 0.729 & 0.643 \\
+ 0.321 & 0.211 & 0.768 \\
+ 0.3 & 0.616 & 0.481 \\
+ 0.077 & 0.715 & 0.109 \\
+ 0.585 & 0.333 & 0.149 \\
+\end{array}
+\right)$. 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: $1.64$ 
+Surface Area: $1.19$ 
+Volume: $0.07$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/97328.txt b/pretraining/mathematica/geometry/solids/97328.txt
new file mode 100644
index 0000000000000000000000000000000000000000..603d54b67d76e2c6c07b98cef8f00a3143babe43
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/97328.txt
@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.681 & 0.657 & 0.599 \\
+ 0.869 & 0.423 & 0.774 \\
+ 0.336 & 0.634 & 0.346 \\
+ 0.343 & 0.714 & 0.637 \\
+ 0.561 & 0.589 & 0.168 \\
+ 0.962 & 0.112 & 0.687 \\
+\end{array}
+\right)$. 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: $0.67$ 
+Solid Angle: $3.09$ 
+Volume: $0.02$
\ No newline at end of file
diff --git a/pretraining/mathematica/geometry/solids/99589.txt b/pretraining/mathematica/geometry/solids/99589.txt
new file mode 100644
index 0000000000000000000000000000000000000000..89f777927eae673351affc0e31b2348c66e9af8b
--- /dev/null
+++ b/pretraining/mathematica/geometry/solids/99589.txt
@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.78 & 0.813 & 0.496 \\
+ 0.959 & 0.235 & 0.324 \\
+ 0.139 & 0.951 & 0.787 \\
+ 0.039 & 0.008 & 0.711 \\
+ 0.361 & 0.745 & 0.904 \\
+ 0.66 & 0.959 & 0.258 \\
+ 0.677 & 0.709 & 0.91 \\
+ 0.317 & 0.569 & 0.998 \\
+ 0.262 & 0.598 & 0.09 \\
+\end{array}
+\right)$. 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: $2.28$ 
+Solid Angle: $3.95$ 
+Volume: $0.25$
\ No newline at end of file