Hellenica World

# Gyroelongated pentagonal bicupola

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{-(1 + Sqrt[5])^2/8, Sqrt[5/8 + Sqrt[5]/8], Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 4, 0]/2},
{-Sqrt[(5 + Sqrt[5])/2]/2, (-3 - Sqrt[5])/4, Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2},
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{0, (-1 - Sqrt[5])/2, Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2},
{0, Sqrt[(5 + Sqrt[5])/10], Root[1 - 5*#1^2 + 5*#1^4 & , 3, 0] +
Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 4, 0]/2},
{0, (1 + Sqrt[5])/2, Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2},
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Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2}, {Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0],
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{(1 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0], Root[1 - 5*#1^2 + 5*#1^4 & , 3, 0] +
Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 4, 0]/2}, {Sqrt[(5 + Sqrt[5])/10], 0,
Root[1 - 5*#1^2 + 5*#1^4 & , 2, 0] + Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2},
{Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4, Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2},
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{(3 + Sqrt[5])/4, Sqrt[5/8 + Sqrt[5]/8], Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 4, 0]/2},
{Sqrt[5 + 2*Sqrt[5]]/2, -1/2, Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2},
{Sqrt[5 + 2*Sqrt[5]]/2, 1/2, Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 1, 0]/2},
{(1 + Sqrt[5])/2, 0, Root[1 + 2*#1^2 - 11*#1^4 + 8*#1^6 + #1^8 & , 4, 0]/2}},
Polygon[{{1, 2, 4}, {1, 3, 2}, {1, 5, 3}, {1, 8, 5}, {2, 6, 4}, {2, 9, 6}, {3, 5, 7}, {3, 7, 10},
{4, 6, 11}, {4, 11, 12}, {5, 13, 7}, {6, 14, 11}, {7, 13, 16}, {11, 14, 19}, {13, 15, 21}, {13, 21, 16},
{14, 17, 24}, {14, 24, 19}, {16, 21, 25}, {16, 25, 18}, {19, 24, 26}, {19, 26, 20}, {21, 27, 25},
{22, 30, 27}, {23, 29, 28}, {24, 28, 26}, {25, 27, 29}, {26, 28, 30}, {27, 30, 29}, {28, 29, 30},
{12, 8, 1, 4}, {9, 2, 3, 10}, {15, 13, 5, 8}, {14, 6, 9, 17}, {10, 7, 16, 18}, {19, 20, 12, 11},
{27, 21, 15, 22}, {24, 17, 23, 28}, {23, 18, 25, 29}, {30, 22, 20, 26}, {22, 15, 8, 12, 20},
{17, 9, 10, 18, 23}}]]]

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Johnson Polyhedra

Geometry