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Graphics3D[GraphicsComplex[{{-Sqrt[1 - 2/Sqrt[5]]/4, -1/4, -Sqrt[1 + 2/Sqrt[5]]}, {-Sqrt[1 - 2/Sqrt[5]]/4, 1/4, -Sqrt[1 + 2/Sqrt[5]]}, {Sqrt[1 - 2/Sqrt[5]]/4, -1/4, Sqrt[1 + 2/Sqrt[5]]}, {Sqrt[1 - 2/Sqrt[5]]/4, 1/4, Sqrt[1 + 2/Sqrt[5]]},
   {Sqrt[1/8 - 1/(8*Sqrt[5])], 0, Sqrt[1 + 2/Sqrt[5]]}, {Sqrt[1/8 - 1/(8*Sqrt[5])], (-3 - Sqrt[5])/4, Sqrt[1/8 + 1/(8*Sqrt[5])]}, {Sqrt[1/8 - 1/(8*Sqrt[5])], (-1 - Sqrt[5])/4, Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[1/8 - 1/(8*Sqrt[5])], (1 + Sqrt[5])/4, Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0]}, {Sqrt[1/8 - 1/(8*Sqrt[5])], (3 + Sqrt[5])/4, Sqrt[1/8 + 1/(8*Sqrt[5])]}, {Sqrt[1/32 - 1/(32*Sqrt[5])], (-3*(1 + Sqrt[5]))/8, Sqrt[1/4 + 1/(2*Sqrt[5])]},
   {Sqrt[1/32 - 1/(32*Sqrt[5])], (3*(1 + Sqrt[5]))/8, Sqrt[1/4 + 1/(2*Sqrt[5])]}, {Sqrt[1 + 2/Sqrt[5]]/4, (-2 - Sqrt[5])/4, Sqrt[(5 + Sqrt[5])/10]}, {Sqrt[1 + 2/Sqrt[5]]/4, (2 + Sqrt[5])/4, Sqrt[(5 + Sqrt[5])/10]},
   {Sqrt[1/8 + 1/(8*Sqrt[5])], (-3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]}, {Sqrt[1/8 + 1/(8*Sqrt[5])], (3 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]}, {Sqrt[5 + 2/Sqrt[5]]/4, (-2 - Sqrt[5])/4, Sqrt[1/4 + 1/(2*Sqrt[5])]},
   {Sqrt[5 + 2/Sqrt[5]]/4, (2 + Sqrt[5])/4, Sqrt[1/4 + 1/(2*Sqrt[5])]}, {Sqrt[5/32 + 11/(32*Sqrt[5])], (-3*(1 + Sqrt[5]))/8, Sqrt[1/8 + 1/(8*Sqrt[5])]}, {Sqrt[5/32 + 11/(32*Sqrt[5])], (3*(1 + Sqrt[5]))/8, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {Sqrt[1/4 + 1/(2*Sqrt[5])], -1/2, Sqrt[5/8 + 11/(8*Sqrt[5])]}, {Sqrt[1/4 + 1/(2*Sqrt[5])], 1/2, Sqrt[5/8 + 11/(8*Sqrt[5])]}, {Sqrt[13/32 + 19/(32*Sqrt[5])], (-5 - Sqrt[5])/8, -Sqrt[1 + 2/Sqrt[5]]/2},
   {Sqrt[13/32 + 19/(32*Sqrt[5])], (5 + Sqrt[5])/8, -Sqrt[1 + 2/Sqrt[5]]/2}, {Sqrt[13/32 + 29/(32*Sqrt[5])], (-3 - Sqrt[5])/8, Root[1 - 5*#1^2 + 5*#1^4 & , 1, 0]}, {Sqrt[13/32 + 29/(32*Sqrt[5])], (3 + Sqrt[5])/8, Root[1 - 5*#1^2 + 5*#1^4 & , 1, 0]},
   {Sqrt[17/32 + 31/(32*Sqrt[5])], (-5 - Sqrt[5])/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {Sqrt[17/32 + 31/(32*Sqrt[5])], (5 + Sqrt[5])/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Sqrt[25/32 + 41/(32*Sqrt[5])], (-3 - Sqrt[5])/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {Sqrt[25/32 + 41/(32*Sqrt[5])], (3 + Sqrt[5])/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {Sqrt[5/8 + 11/(8*Sqrt[5])], -1/2, -Sqrt[1 + 2/Sqrt[5]]/2},
   {Sqrt[5/8 + 11/(8*Sqrt[5])], 0, Sqrt[(5 + Sqrt[5])/10]}, {Sqrt[5/8 + 11/(8*Sqrt[5])], 1/2, -Sqrt[1 + 2/Sqrt[5]]/2}, {Sqrt[5/8 + 11/(8*Sqrt[5])], (-1 - Sqrt[5])/4, Sqrt[1/8 - 1/(8*Sqrt[5])]},
   {Sqrt[5/8 + 11/(8*Sqrt[5])], (1 + Sqrt[5])/4, Sqrt[1/8 - 1/(8*Sqrt[5])]}, {Sqrt[13 + 22/Sqrt[5]]/4, -1/4, Sqrt[1/4 + 1/(2*Sqrt[5])]}, {Sqrt[13 + 22/Sqrt[5]]/4, 1/4, Sqrt[1/4 + 1/(2*Sqrt[5])]},
   {Sqrt[29/32 + 61/(32*Sqrt[5])], (1 - Sqrt[5])/8, Sqrt[1/8 + 1/(8*Sqrt[5])]}, {Sqrt[29/32 + 61/(32*Sqrt[5])], (-1 + Sqrt[5])/8, Sqrt[1/8 + 1/(8*Sqrt[5])]}, {-Sqrt[1 + 2/Sqrt[5]], 0, Sqrt[1/8 - 1/(8*Sqrt[5])]},
   {-Sqrt[1 + 2/Sqrt[5]]/2, -1/2, Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0]}, {-Sqrt[1 + 2/Sqrt[5]]/2, 1/2, Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0]}, {-Sqrt[1 + 2/Sqrt[5]]/4, (-2 - Sqrt[5])/4, Root[1 - 5*#1^2 + 5*#1^4 & , 1, 0]},
   {-Sqrt[1 + 2/Sqrt[5]]/4, (2 + Sqrt[5])/4, Root[1 - 5*#1^2 + 5*#1^4 & , 1, 0]}, {Sqrt[1 + 2/Sqrt[5]], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]}, {-Sqrt[5 + 2/Sqrt[5]]/4, (-2 - Sqrt[5])/4, -Sqrt[1 + 2/Sqrt[5]]/2},
   {-Sqrt[5 + 2/Sqrt[5]]/4, (2 + Sqrt[5])/4, -Sqrt[1 + 2/Sqrt[5]]/2}, {-Sqrt[25/2 + 41/(2*Sqrt[5])]/4, (-3 - Sqrt[5])/8, Sqrt[1/8 + 1/(8*Sqrt[5])]}, {-Sqrt[25/2 + 41/(2*Sqrt[5])]/4, (3 + Sqrt[5])/8, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {-Sqrt[13 + 22/Sqrt[5]]/4, -1/4, -Sqrt[1 + 2/Sqrt[5]]/2}, {-Sqrt[13 + 22/Sqrt[5]]/4, 1/4, -Sqrt[1 + 2/Sqrt[5]]/2}, {-Sqrt[29/2 + 61/(2*Sqrt[5])]/4, (1 - Sqrt[5])/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {-Sqrt[29/2 + 61/(2*Sqrt[5])]/4, (-1 + Sqrt[5])/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {-Sqrt[(5 + Sqrt[5])/10]/4, (1 - Sqrt[5])/8, Sqrt[1 + 2/Sqrt[5]]}, {-Sqrt[(5 + Sqrt[5])/10]/4, (-1 + Sqrt[5])/8, Sqrt[1 + 2/Sqrt[5]]},
   {Sqrt[(5 + Sqrt[5])/10]/4, (1 - Sqrt[5])/8, -Sqrt[1 + 2/Sqrt[5]]}, {Sqrt[(5 + Sqrt[5])/10]/4, (-1 + Sqrt[5])/8, -Sqrt[1 + 2/Sqrt[5]]}, {Sqrt[(5 + Sqrt[5])/10], 0, Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0]},
   {-Sqrt[(65 + 19*Sqrt[5])/10]/4, (-5 - Sqrt[5])/8, Sqrt[1/4 + 1/(2*Sqrt[5])]}, {-Sqrt[(65 + 19*Sqrt[5])/10]/4, (5 + Sqrt[5])/8, Sqrt[1/4 + 1/(2*Sqrt[5])]}, {-Sqrt[(85 + 31*Sqrt[5])/10]/4, (-5 - Sqrt[5])/8, Sqrt[1/8 + 1/(8*Sqrt[5])]},
   {-Sqrt[(85 + 31*Sqrt[5])/10]/4, (5 + Sqrt[5])/8, Sqrt[1/8 + 1/(8*Sqrt[5])]}, {Root[1 - 5*#1^2 + 5*#1^4 & , 1, 0], 0, Sqrt[5/8 + 11/(8*Sqrt[5])]}, {Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0], -1/2, Sqrt[1/4 + 1/(2*Sqrt[5])]},
   {Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0], 0, Root[1 - 5*#1^2 + 5*#1^4 & , 1, 0]}, {Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0], 1/2, Sqrt[1/4 + 1/(2*Sqrt[5])]}, {Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0], (-1 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]},
   {Root[1 - 100*#1^2 + 80*#1^4 & , 1, 0], (1 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]}, {Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0], (-3 - Sqrt[5])/4, Sqrt[1/8 - 1/(8*Sqrt[5])]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0], (3 + Sqrt[5])/4, Sqrt[1/8 - 1/(8*Sqrt[5])]}, {Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0], 0, -Sqrt[1 + 2/Sqrt[5]]}, {Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0], (-3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0], (-1 - Sqrt[5])/4, Sqrt[5/8 + 11/(8*Sqrt[5])]}, {Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0], (1 + Sqrt[5])/4, Sqrt[5/8 + 11/(8*Sqrt[5])]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0], (3 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {Root[1 - 1040*#1^2 + 1280*#1^4 & , 1, 0], (-3 - Sqrt[5])/8, Sqrt[(5 + Sqrt[5])/10]},
   {Root[1 - 1040*#1^2 + 1280*#1^4 & , 1, 0], (3 + Sqrt[5])/8, Sqrt[(5 + Sqrt[5])/10]}, {Root[1 - 400*#1^2 + 1280*#1^4 & , 1, 0], (-3*(1 + Sqrt[5]))/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Root[1 - 400*#1^2 + 1280*#1^4 & , 1, 0], (3*(1 + Sqrt[5]))/8, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]}, {Root[1 - 80*#1^2 + 1280*#1^4 & , 2, 0], (-3*(1 + Sqrt[5]))/8, -Sqrt[1 + 2/Sqrt[5]]/2},
   {Root[1 - 80*#1^2 + 1280*#1^4 & , 2, 0], (3*(1 + Sqrt[5]))/8, -Sqrt[1 + 2/Sqrt[5]]/2}}, Polygon[{{73, 65, 63, 72, 5}, {70, 8, 32, 30, 7}, {7, 30, 33, 6, 71}, {30, 32, 34, 31, 33}, {32, 8, 74, 9, 34}, {8, 70, 64, 67, 74}, {70, 7, 71, 66, 64},
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    {55, 8, 27, 44, 24}, {60, 77, 14, 16, 72}, {14, 24, 44, 35, 16}, {44, 27, 19, 21, 35}, {19, 69, 76, 54, 21}, {76, 39, 60, 72, 54}, {20, 36, 17, 73, 53}, {56, 7, 45, 49, 41}, {41, 49, 39, 61, 78}, {49, 45, 68, 75, 39}, {45, 7, 26, 18, 68},
    {7, 56, 25, 44, 26}, {56, 41, 78, 15, 25}, {18, 26, 44, 36, 20}, {44, 25, 15, 17, 36}, {15, 78, 61, 73, 17}, {61, 39, 75, 53, 73}, {75, 68, 18, 20, 53}, {21, 11, 59, 62, 3}, {2, 57, 22, 79, 40}, {40, 79, 68, 47, 51}, {79, 22, 33, 12, 68},
    {22, 57, 29, 38, 33}, {57, 2, 43, 15, 29}, {2, 40, 51, 67, 43}, {38, 29, 15, 11, 21}, {15, 43, 67, 59, 11}, {67, 51, 47, 62, 59}, {47, 68, 12, 3, 62}, {12, 33, 38, 21, 3}}]]]

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