Hellenica World

# Tetrahedron 5-Compound

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Graphics3D[GraphicsComplex[{{-Sqrt[1 + 1/Sqrt[5]]/2, 0, Root[1 - 80*#1^2 + 320*#1^4 & , 2, 0]},
{Sqrt[1 + 1/Sqrt[5]]/2, 0, Sqrt[1/2 - 1/Sqrt[5]]/2}, {-Sqrt[1 - 1/Sqrt[5]]/2, 0, -Sqrt[1/2 + 1/Sqrt[5]]/2},
{Sqrt[1 - 1/Sqrt[5]]/2, 0, Sqrt[1/8 + 1/(4*Sqrt[5])]}, {-Sqrt[1/2 + 1/Sqrt[5]]/2, -1/(2*Sqrt[2]), Sqrt[1/2 - 1/Sqrt[5]]/2},
{-Sqrt[1/2 + 1/Sqrt[5]]/2, 1/(2*Sqrt[2]), Sqrt[1/2 - 1/Sqrt[5]]/2}, {Sqrt[1/8 + 1/(4*Sqrt[5])], -1/(2*Sqrt[2]),
Root[1 - 80*#1^2 + 320*#1^4 & , 2, 0]}, {Sqrt[1/8 + 1/(4*Sqrt[5])], 1/(2*Sqrt[2]), Root[1 - 80*#1^2 + 320*#1^4 & , 2, 0]},
{-Sqrt[1 + 1/Sqrt[5]]/4, -1/(2*Sqrt[3 + Sqrt[5]]), Sqrt[1/8 + 1/(4*Sqrt[5])]}, {-Sqrt[1 + 1/Sqrt[5]]/4, 1/(2*Sqrt[3 + Sqrt[5]]),
Sqrt[1/8 + 1/(4*Sqrt[5])]}, {Sqrt[1 + 1/Sqrt[5]]/4, -1/(2*Sqrt[3 + Sqrt[5]]), -Sqrt[1/2 + 1/Sqrt[5]]/2},
{Sqrt[1 + 1/Sqrt[5]]/4, 1/(2*Sqrt[3 + Sqrt[5]]), -Sqrt[1/2 + 1/Sqrt[5]]/2}, {-Sqrt[1 - 1/Sqrt[5]]/4, -Sqrt[3 + Sqrt[5]]/4,
Root[1 - 80*#1^2 + 320*#1^4 & , 2, 0]}, {-Sqrt[1 - 1/Sqrt[5]]/4, Sqrt[3 + Sqrt[5]]/4, Root[1 - 80*#1^2 + 320*#1^4 & , 2, 0]},
{Root[1 - 80*#1^2 + 320*#1^4 & , 2, 0], -1/(2*Sqrt[2]), -Sqrt[1/2 + 1/Sqrt[5]]/2}, {Root[1 - 80*#1^2 + 320*#1^4 & , 2, 0], 1/(2*Sqrt[2]),
-Sqrt[1/2 + 1/Sqrt[5]]/2}, {Sqrt[1/2 - 1/Sqrt[5]]/2, -1/(2*Sqrt[2]), Sqrt[1/8 + 1/(4*Sqrt[5])]},
{Sqrt[1/2 - 1/Sqrt[5]]/2, 1/(2*Sqrt[2]), Sqrt[1/8 + 1/(4*Sqrt[5])]}, {Sqrt[1 - 1/Sqrt[5]]/4, -Sqrt[3 + Sqrt[5]]/4, Sqrt[1/2 - 1/Sqrt[5]]/2},
{Sqrt[1 - 1/Sqrt[5]]/4, Sqrt[3 + Sqrt[5]]/4, Sqrt[1/2 - 1/Sqrt[5]]/2}},
Polygon[{{1, 11, 17}, {20, 11, 1}, {1, 17, 20}, {20, 17, 11}, {14, 9, 2}, {2, 9, 15}, {15, 14, 2}, {9, 14, 15}, {10, 8, 3}, {3, 8, 19},
{19, 10, 3}, {8, 10, 19}, {12, 6, 4}, {4, 6, 13}, {13, 12, 4}, {6, 12, 13}, {16, 7, 5}, {5, 7, 18}, {18, 16, 5}, {7, 16, 18}}]]]

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