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Geodesic Polyhedra

written by Rene K. Mueller, Copyright (c) 2007, last updated Sun, October 28, 2012

Geodesic Icosidodecahedron

Icosidodecahedron


Icosidodecahedron
  • Uniform Polyhedron: U24
  • Archimedean Solid: A4
  • Wythoff symbol: 2|3 5
  • Symmetry Group: icosahedral
  • Vertex Configuration: {3, 5, 3, 5}
  • Dual: rhombic triacontahedron
  • V: s3 / 6 * (45 + 17 * √5)
  • A: s2 * (5 * √3 + 3 * √5 * √(5 + 2 * √5))
  • rinner: s / 8 * (5 + 3 * √5)
  • router: s * (1 + √5) / 2
  • Vertices/Connectors: 30 (4-way)
  • Faces: 32
    • 20 x 3-sided
    • 12 x 5-sided
  • Edges/Struts:
    • A x 60: 0.61803

Geodesic Icosidodecahedron L1


Geodesic Icosidodecahedron L1
  • Vertices/Connectors: 42
    • 12 x 5-way
    • 30 x 6-way
  • Faces: 80 (3-sided)
  • Edges/Struts:
    • A x 60: 0.54653
    • B x 60: 0.61803
    • total 120 struts (2 kinds)
    • strut variance 13.0%


Geodesic Icosidodecahedron Dome L1


Geodesic Icosidodecahedron Dome L1

Geodesic Icosidodecahedron Dome L1
  • Vertices/Connectors: 26
    • 10 x 4-way
    • 6 x 5-way
    • 10 x 6-way
  • Faces: 40 (3-sided)

  • Icosidodecahedron Dome L1 Construction Map
  • Edges/Struts:
    • A x 30: 0.54653
    • B x 35: 0.61803
    • total 65 struts (2 kinds)
    • strut variance 13.0%

d= A= x 30, B= x 35,
After triangulating it's the same as the Icosahedron 2V or L2. It's a bit of redundancy to list it anyway.

Geodesic Icosidodecahedron L2


Geodesic Icosidodecahedron L2
  • Vertices/Connectors: 162
    • 12 x 5-way
    • 150 x 6-way
  • Faces: 320 (3-sided)
  • Edges/Struts:
    • A x 120: 0.27590
    • B x 120: 0.28547
    • C x 120: 0.31287
    • D x 60: 0.32124
    • E x 60: 0.32492
    • total 480 struts (5 kinds)
    • strut variance 17.8%


Geodesic Icosidodecahedron Dome L2


Geodesic Icosidodecahedron Dome L2

Geodesic Icosidodecahedron Dome L2
  • Vertices/Connectors: 91
    • 20 x 4-way
    • 6 x 5-way
    • 65 x 6-way
  • Faces: 160 (3-sided)

  • Icosidodecahedron Dome L2 Construction Map
  • Edges/Struts:
    • A x 60: 0.27590
    • B x 60: 0.28547
    • C x 70: 0.31287
    • D x 30: 0.32124
    • E x 30: 0.32492
    • total 250 struts (5 kinds)
    • strut variance 17.8%

d= A= x 60, B= x 60, C= x 70, D= x 30, E= x 30,
The L2 is the same as a Icosahedron with 4V or L3.

Geodesic Icosidodecahedron L2T


Geodesic Icosidodecahedron L2T
  • Vertices/Connectors: 242
    • 120 x 4-way
    • 80 x 6-way
    • 12 x 10-way
    • 30 x 12-way
  • Faces: 480 (3-sided)
  • Edges/Struts:
    • A x 60: 0.15841
    • B x 120: 0.17931
    • C x 60: 0.18843
    • D x 120: 0.27590
    • E x 60: 0.30389
    • F x 120: 0.31287
    • G x 120: 0.34893
    • H x 60: 0.36284
    • total 720 struts (8 kinds)
    • strut variance 129.7%


Geodesic Icosidodecahedron Dome L2T


Geodesic Icosidodecahedron Dome L2T

Geodesic Icosidodecahedron Dome L2T
  • Vertices/Connectors: 131
    • 10 x 3-way
    • 55 x 4-way
    • 40 x 6-way
    • 10 x 7-way
    • 6 x 10-way
    • 10 x 12-way
  • Faces: 240 (3-sided)

  • Icosidodecahedron Dome L2T Construction Map
  • Edges/Struts:
    • A x 30: 0.15841
    • B x 60: 0.17931
    • C x 30: 0.18843
    • D x 60: 0.27590
    • E x 30: 0.30389
    • F x 70: 0.31287
    • G x 60: 0.34893
    • H x 30: 0.36284
    • total 370 struts (8 kinds)
    • strut variance 129.7%

d= A= x 30, B= x 60, C= x 30, D= x 60, E= x 30, F= x 70, G= x 60, H= x 30,
Very beautiful construct, the same would have been achieved to triaconize a 2V or L2 Icosahedron (2V.2VT)


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