Hellenica World

# Pentagonal gyrocupolarotunda

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Graphics3D[GraphicsComplex[{{0, (-1 - Sqrt[5])/2, (-9*Sqrt[1 - 2/Sqrt[5]])/8},
{0, (1 + Sqrt[5])/2, (-9*Sqrt[1 - 2/Sqrt[5]])/8}, {Sqrt[1/2 + 1/(2*Sqrt[5])], 0,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 - Sqrt[(5 - Sqrt[5])/10]}, {Sqrt[(5 - Sqrt[5])/10]/2, (-1 - Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 - Sqrt[(5 - Sqrt[5])/10]}, {Sqrt[(5 - Sqrt[5])/10]/2, (1 + Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 - Sqrt[(5 - Sqrt[5])/10]}, {-Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8}, {-Sqrt[5/8 + Sqrt[5]/8], (3 + Sqrt[5])/4, (-9*Sqrt[1 - 2/Sqrt[5]])/8},
{Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4, (-9*Sqrt[1 - 2/Sqrt[5]])/8},
{Sqrt[5/8 + Sqrt[5]/8], (3 + Sqrt[5])/4, (-9*Sqrt[1 - 2/Sqrt[5]])/8},
{-Sqrt[1/4 + 1/(2*Sqrt[5])], -1/2, (-9*Sqrt[1 - 2/Sqrt[5]])/8 - Sqrt[(5 - Sqrt[5])/10]},
{-Sqrt[1/4 + 1/(2*Sqrt[5])], 1/2, (-9*Sqrt[1 - 2/Sqrt[5]])/8 - Sqrt[(5 - Sqrt[5])/10]},
{-Sqrt[5/4 + Sqrt[5]/2], -1/2, (-9*Sqrt[1 - 2/Sqrt[5]])/8}, {-Sqrt[5/4 + Sqrt[5]/2], 1/2,
(-9*Sqrt[1 - 2/Sqrt[5]])/8}, {Sqrt[5/4 + Sqrt[5]/2], -1/2, (-9*Sqrt[1 - 2/Sqrt[5]])/8},
{Sqrt[5/4 + Sqrt[5]/2], 1/2, (-9*Sqrt[1 - 2/Sqrt[5]])/8}, {Sqrt[(5 + 2*Sqrt[5])/5], 0,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[1/2 + 1/(2*Sqrt[5])]}, {Sqrt[1/8 + 1/(8*Sqrt[5])], (-3 - Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[1/2 + 1/(2*Sqrt[5])]}, {Sqrt[1/8 + 1/(8*Sqrt[5])], (3 + Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[1/2 + 1/(2*Sqrt[5])]}, {-Sqrt[5/8 + 11/(8*Sqrt[5])], (-1 - Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[1/2 + 1/(2*Sqrt[5])]}, {-Sqrt[5/8 + 11/(8*Sqrt[5])], (1 + Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[1/2 + 1/(2*Sqrt[5])]}, {-Sqrt[1/2 + 1/(2*Sqrt[5])], 0,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[(5 + 2*Sqrt[5])/5]}, {-Sqrt[(5 - Sqrt[5])/10]/2, (-1 - Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[(5 + 2*Sqrt[5])/5]}, {-Sqrt[(5 - Sqrt[5])/10]/2, (1 + Sqrt[5])/4,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[(5 + 2*Sqrt[5])/5]}, {Sqrt[1/4 + 1/(2*Sqrt[5])], -1/2,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[(5 + 2*Sqrt[5])/5]}, {Sqrt[1/4 + 1/(2*Sqrt[5])], 1/2,
(-9*Sqrt[1 - 2/Sqrt[5]])/8 + Sqrt[(5 + 2*Sqrt[5])/5]}},
Polygon[{{23, 21, 22, 24, 25}, {20, 21, 23}, {19, 22, 21}, {17, 24, 22}, {16, 25, 24}, {18, 23, 25},
{9, 2, 18}, {7, 13, 20}, {12, 6, 19}, {1, 8, 17}, {14, 15, 16}, {2, 7, 20, 23, 18}, {13, 12, 19, 21, 20},
{6, 1, 17, 22, 19}, {8, 14, 16, 24, 17}, {15, 9, 18, 25, 16}, {3, 4, 10, 11, 5}, {7, 2, 5, 11},
{12, 13, 11, 10}, {1, 6, 10, 4}, {14, 8, 4, 3}, {9, 15, 3, 5}, {5, 2, 9}, {11, 13, 7}, {10, 6, 12},
{4, 8, 1}, {3, 15, 14}}]]]

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Johnson Polyhedra

Geometry