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Graphics3D[GraphicsComplex[{{0, 0, -Sqrt[(5 - Sqrt[5])/10]}, {0, 0, Sqrt[(5 - Sqrt[5])/10]},
{Sqrt[1/2 + 1/(2*Sqrt[5])], 0, 0}, {Sqrt[(5 - Sqrt[5])/10]/2, (-1 - Sqrt[5])/4, 0},
{Sqrt[(5 - Sqrt[5])/10]/2, (1 + Sqrt[5])/4, 0}, {-Sqrt[1/4 + 1/(2*Sqrt[5])], -1/2, 0},
{-Sqrt[1/4 + 1/(2*Sqrt[5])], 1/2, 0}}, Polygon[{{5, 7, 2}, {7, 6, 2}, {6, 4, 2}, {4, 3, 2},
{3, 5, 2}, {1, 7, 5}, {1, 6, 7}, {1, 4, 6}, {1, 3, 4}, {1, 5, 3}}]]]
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Johnson Polyhedra
Geometry
