Hellenica World

Truncated icosahedron

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Graphics3D[GraphicsComplex[{{-Sqrt[1 - 2/Sqrt[5]]/2, -1 - Sqrt[5]/2, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {-Sqrt[1 - 2/Sqrt[5]]/2, (2 + Sqrt[5])/2, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {Sqrt[1 - 2/Sqrt[5]]/2, -1 - Sqrt[5]/2, (-3*Sqrt[(5 + Sqrt[5])/10])/2},
   {Sqrt[1 - 2/Sqrt[5]]/2, (2 + Sqrt[5])/2, (-3*Sqrt[(5 + Sqrt[5])/10])/2},
   {-Sqrt[2 - 2/Sqrt[5]]/4, (1 - Sqrt[5])^(-1), -Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {-Sqrt[2 - 2/Sqrt[5]]/4, (-3*(1 + Sqrt[5]))/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {-Sqrt[2 - 2/Sqrt[5]]/4, (1 + Sqrt[5])/4, -Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {-Sqrt[2 - 2/Sqrt[5]]/4, (3*(1 + Sqrt[5]))/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[2 - 2/Sqrt[5]]/4, (1 - Sqrt[5])^(-1), Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {Sqrt[2 - 2/Sqrt[5]]/4, (-3*(1 + Sqrt[5]))/4, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {Sqrt[2 - 2/Sqrt[5]]/4, (1 + Sqrt[5])/4, Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {Sqrt[2 - 2/Sqrt[5]]/4, (3*(1 + Sqrt[5]))/4, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {Sqrt[1/4 + 1/(2*Sqrt[5])], -1/2, -Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {Sqrt[1/4 + 1/(2*Sqrt[5])], 1/2, -Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {Sqrt[5/4 + 1/(2*Sqrt[5])], -1 - Sqrt[5]/2, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {Sqrt[5/4 + 1/(2*Sqrt[5])], (2 + Sqrt[5])/2, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {(-3*Sqrt[1 + 2/Sqrt[5]])/2, -1/2, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {(-3*Sqrt[1 + 2/Sqrt[5]])/2, 1/2, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {-Sqrt[1 + 2/Sqrt[5]], -1, Sqrt[26 + 58/Sqrt[5]]/4}, {-Sqrt[1 + 2/Sqrt[5]], 1,
    Sqrt[26 + 58/Sqrt[5]]/4}, {-Sqrt[1 + 2/Sqrt[5]], -2/(-1 + Sqrt[5]),
    (-3*Sqrt[(5 + Sqrt[5])/10])/2}, {-Sqrt[1 + 2/Sqrt[5]], (1 + Sqrt[5])/2,
    (-3*Sqrt[(5 + Sqrt[5])/10])/2}, {-Sqrt[1 + 2/Sqrt[5]]/2, -1/2, Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {-Sqrt[1 + 2/Sqrt[5]]/2, 1/2, Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {Sqrt[1 + 2/Sqrt[5]], -1, Root[1 - 260*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[1 + 2/Sqrt[5]], 1, Root[1 - 260*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[1 + 2/Sqrt[5]], -2/(-1 + Sqrt[5]), Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {Sqrt[1 + 2/Sqrt[5]], (1 + Sqrt[5])/2, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {-Sqrt[2 + 2/Sqrt[5]], 0, Root[1 - 260*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[2 + 2/Sqrt[5]], 0, Sqrt[26 + 58/Sqrt[5]]/4}, {-Sqrt[5 + 2/Sqrt[5]]/2, -1 - Sqrt[5]/2,
    Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {-Sqrt[5 + 2/Sqrt[5]]/2, (2 + Sqrt[5])/2,
    Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {-Sqrt[17/8 + 31/(8*Sqrt[5])], (1 - Sqrt[5])^(-1),
    (-3*Sqrt[(5 + Sqrt[5])/10])/2}, {-Sqrt[17/8 + 31/(8*Sqrt[5])], (1 + Sqrt[5])/4,
    (-3*Sqrt[(5 + Sqrt[5])/10])/2}, {Sqrt[9/4 + 9/(2*Sqrt[5])], -1/2,
    (-3*Sqrt[(5 + Sqrt[5])/10])/2}, {Sqrt[9/4 + 9/(2*Sqrt[5])], 1/2,
    (-3*Sqrt[(5 + Sqrt[5])/10])/2}, {Sqrt[5/2 + 11/(2*Sqrt[5])], -1,
    Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {Sqrt[5/2 + 11/(2*Sqrt[5])], 1,
    Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {Sqrt[13/4 + 11/(2*Sqrt[5])], -1/2,
    Sqrt[1/8 + 1/(8*Sqrt[5])]}, {Sqrt[13/4 + 11/(2*Sqrt[5])], 1/2, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {-Sqrt[10 + 22/Sqrt[5]]/4, (-5 - Sqrt[5])/4, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {-Sqrt[10 + 22/Sqrt[5]]/4, (5 + Sqrt[5])/4, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {Sqrt[10 + 22/Sqrt[5]]/4, (-5 - Sqrt[5])/4, (-3*Sqrt[(5 + Sqrt[5])/10])/2},
   {Sqrt[10 + 22/Sqrt[5]]/4, (5 + Sqrt[5])/4, (-3*Sqrt[(5 + Sqrt[5])/10])/2},
   {-Sqrt[13 + 22/Sqrt[5]]/2, -1/2, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {-Sqrt[13 + 22/Sqrt[5]]/2, 1/2, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {-Sqrt[26 + 38/Sqrt[5]]/4, (-5 - Sqrt[5])/4, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {-Sqrt[26 + 38/Sqrt[5]]/4, (5 + Sqrt[5])/4, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {Sqrt[26 + 38/Sqrt[5]]/4, (-5 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[26 + 38/Sqrt[5]]/4, (5 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[34 + 62/Sqrt[5]]/4, (1 - Sqrt[5])^(-1), Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {Sqrt[34 + 62/Sqrt[5]]/4, (1 + Sqrt[5])/4, Sqrt[9/8 + 9/(8*Sqrt[5])]},
   {Sqrt[(5 + Sqrt[5])/10], 0, Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {Root[1 - 25*#1^2 + 5*#1^4 & , 1, 0], -1, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {Root[1 - 25*#1^2 + 5*#1^4 & , 1, 0], 1, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {Root[1 - 5*#1^2 + 5*#1^4 & , 1, 0], 0, -Sqrt[25/8 + 41/(8*Sqrt[5])]},
   {Root[1 - 5*#1^2 + 5*#1^4 & , 2, 0], -2/(-1 + Sqrt[5]), Root[1 - 260*#1^2 + 80*#1^4 & , 1,
     0]}, {Root[1 - 5*#1^2 + 5*#1^4 & , 2, 0], (1 + Sqrt[5])/2,
    Root[1 - 260*#1^2 + 80*#1^4 & , 1, 0]}, {Root[1 - 5*#1^2 + 5*#1^4 & , 3, 0],
    -2/(-1 + Sqrt[5]), Sqrt[26 + 58/Sqrt[5]]/4}, {Root[1 - 5*#1^2 + 5*#1^4 & , 3, 0],
    (1 + Sqrt[5])/2, Sqrt[26 + 58/Sqrt[5]]/4}},
  Polygon[{{53, 11, 24, 23, 9}, {51, 39, 40, 52, 30}, {60, 28, 16, 12, 2}, {20, 42, 48, 55, 18},
    {19, 17, 54, 47, 41}, {1, 10, 15, 27, 59}, {36, 26, 44, 50, 38}, {4, 58, 22, 32, 8},
    {34, 29, 33, 45, 46}, {21, 57, 3, 6, 31}, {37, 49, 43, 25, 35}, {13, 5, 56, 7, 14},
    {9, 59, 27, 51, 30, 53}, {53, 30, 52, 28, 60, 11}, {11, 60, 2, 42, 20, 24},
    {24, 20, 18, 17, 19, 23}, {23, 19, 41, 1, 59, 9}, {13, 25, 43, 3, 57, 5},
    {5, 57, 21, 33, 29, 56}, {56, 29, 34, 22, 58, 7}, {7, 58, 4, 44, 26, 14},
    {14, 26, 36, 35, 25, 13}, {40, 38, 50, 16, 28, 52}, {16, 50, 44, 4, 8, 12},
    {12, 8, 32, 48, 42, 2}, {48, 32, 22, 34, 46, 55}, {55, 46, 45, 54, 17, 18},
    {54, 45, 33, 21, 31, 47}, {47, 31, 6, 10, 1, 41}, {10, 6, 3, 43, 49, 15},
    {15, 49, 37, 39, 51, 27}, {39, 37, 35, 36, 38, 40}}]]]

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Archimedean Solid

Geometry

Index

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