Hellenica World

Gyroelongated pentagonal cupolarotunda

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"GyroelongatedPentagonalCupolarotunda_11.gif"

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"GyroelongatedPentagonalCupolarotunda_13.gif"

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"GyroelongatedPentagonalCupolarotunda_18.gif"

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Graphics3D[GraphicsComplex[{{0, (-1 - Sqrt[5])/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1,
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        3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 +
        10894704640000*#1^8 & , 3, 0]}, {0, (1 + Sqrt[5])/2,
    Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {0, -Sqrt[1 + 2/Sqrt[5]], Root[361 + 1520*#1 - 13240*#1^2 + 19200*#1^3 + 7760*#1^4 - 25600*#1^5 +
        6400*#1^8 & , 4, 0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 -
        28990840217600*#1^3 + 3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 -
        47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]}, {0, Sqrt[(5 + Sqrt[5])/10],
    Root[-479 - 6240*#1 - 8600*#1^2 + 16000*#1^3 + 49360*#1^4 - 44800*#1^5 - 12800*#1^6 + 6400*#1^8 & , 4,
      0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 +
        3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 +
        10894704640000*#1^8 & , 3, 0]}, {(-1 - Sqrt[5])/2, 0,
    Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {Sqrt[(5 + Sqrt[5])/10], 0, Root[641 + 7760*#1 + 8360*#1^2 - 22400*#1^3 - 11440*#1^4 + 19200*#1^5 +
        6400*#1^8 & , 2, 0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 -
        28990840217600*#1^3 + 3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 -
        47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]}, {-1/2, -Sqrt[5 + 2*Sqrt[5]]/2,
    Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0], (-1 - Sqrt[5])/4,
    Root[641 + 7760*#1 + 8360*#1^2 - 22400*#1^3 - 11440*#1^4 + 19200*#1^5 + 6400*#1^8 & , 2, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0], (1 + Sqrt[5])/4,
    Root[641 + 7760*#1 + 8360*#1^2 - 22400*#1^3 - 11440*#1^4 + 19200*#1^5 + 6400*#1^8 & , 2, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(1 + Sqrt[5])/2, 0, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {-Sqrt[(5 + Sqrt[5])/2]/2, (-3 - Sqrt[5])/4, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {-Sqrt[(5 + Sqrt[5])/2]/2, (3 + Sqrt[5])/4, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {Sqrt[5/8 + Sqrt[5]/8], (3 + Sqrt[5])/4, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {-Sqrt[1 + 2/Sqrt[5]]/2, -1/2, Root[641 + 7760*#1 + 8360*#1^2 - 22400*#1^3 - 11440*#1^4 + 19200*#1^5 +
        6400*#1^8 & , 2, 0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 -
        28990840217600*#1^3 + 3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 -
        47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]}, {-Sqrt[1 + 2/Sqrt[5]]/2, 1/2,
    Root[641 + 7760*#1 + 8360*#1^2 - 22400*#1^3 - 11440*#1^4 + 19200*#1^5 + 6400*#1^8 & , 2, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {-1/2, Sqrt[5 + 2*Sqrt[5]]/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {1/2, -Sqrt[5 + 2*Sqrt[5]]/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {1/2, Sqrt[5 + 2*Sqrt[5]]/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(-3 - Sqrt[5])/4, -Sqrt[(5 + Sqrt[5])/2]/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(-3 - Sqrt[5])/4, Sqrt[5/8 + Sqrt[5]/8], Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(3 + Sqrt[5])/4, -Sqrt[(5 + Sqrt[5])/2]/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(3 + Sqrt[5])/4, Sqrt[5/8 + Sqrt[5]/8], Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {-Sqrt[5 + 2*Sqrt[5]]/2, -1/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {-Sqrt[5 + 2*Sqrt[5]]/2, 1/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {Sqrt[5 + 2*Sqrt[5]]/2, -1/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {Sqrt[5 + 2*Sqrt[5]]/2, 1/2, Root[1 + 8*#1^2 - 176*#1^4 + 512*#1^6 + 256*#1^8 & , 1, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(3 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0],
    Root[361 + 1520*#1 - 13240*#1^2 + 19200*#1^3 + 7760*#1^4 - 25600*#1^5 + 6400*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(1 + Sqrt[5])/4, Sqrt[5/8 + 11/(8*Sqrt[5])],
    Root[361 + 1520*#1 - 13240*#1^2 + 19200*#1^3 + 7760*#1^4 - 25600*#1^5 + 6400*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(-1 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0],
    Root[-479 - 6240*#1 - 8600*#1^2 + 16000*#1^3 + 49360*#1^4 - 44800*#1^5 - 12800*#1^6 + 6400*#1^8 & , 4,
      0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 +
        3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 +
        10894704640000*#1^8 & , 3, 0]}, {-1/2, -Sqrt[1 + 2/Sqrt[5]]/2,
    Root[-479 - 6240*#1 - 8600*#1^2 + 16000*#1^3 + 49360*#1^4 - 44800*#1^5 - 12800*#1^6 + 6400*#1^8 & , 4,
      0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 +
        3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 +
        10894704640000*#1^8 & , 3, 0]}, {(-3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0],
    Root[361 + 1520*#1 - 13240*#1^2 + 19200*#1^3 + 7760*#1^4 - 25600*#1^5 + 6400*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(-1 - Sqrt[5])/4, Sqrt[5/8 + 11/(8*Sqrt[5])],
    Root[361 + 1520*#1 - 13240*#1^2 + 19200*#1^3 + 7760*#1^4 - 25600*#1^5 + 6400*#1^8 & , 4, 0] -
     Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 + 3719440179200*#1^4 +
        76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {1/2, -Sqrt[1 + 2/Sqrt[5]]/2, Root[-479 - 6240*#1 - 8600*#1^2 + 16000*#1^3 + 49360*#1^4 - 44800*#1^5 -
        12800*#1^6 + 6400*#1^8 & , 4, 0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 -
        28990840217600*#1^3 + 3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 -
        47248834560000*#1^7 + 10894704640000*#1^8 & , 3, 0]},
   {(1 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0],
    Root[-479 - 6240*#1 - 8600*#1^2 + 16000*#1^3 + 49360*#1^4 - 44800*#1^5 - 12800*#1^6 + 6400*#1^8 & , 4,
      0] - Root[482477187239 + 2343512990720*#1 - 5105030091520*#1^2 - 28990840217600*#1^3 +
        3719440179200*#1^4 + 76573704192000*#1^5 + 32992002048000*#1^6 - 47248834560000*#1^7 +
        10894704640000*#1^8 & , 3, 0]}}, Polygon[{{27, 23, 10}, {14, 19, 23}, {2, 17, 19}, {12, 21, 17},
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    {18, 22, 28, 34, 3}, {10, 23, 29, 35, 28}}]]]

In[575]:=

"GyroelongatedPentagonalCupolarotunda_19.gif"

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"GyroelongatedPentagonalCupolarotunda_20.gif"

In[576]:=

"GyroelongatedPentagonalCupolarotunda_21.gif"

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"GyroelongatedPentagonalCupolarotunda_22.gif"

In[577]:=

"GyroelongatedPentagonalCupolarotunda_23.gif"

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"GyroelongatedPentagonalCupolarotunda_24.gif"

Johnson Polyhedra

Geometry