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Geodesic Polyhedra

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

Geodesic Dodecahedron

Dodecahedron


Dodecahedron
  • Uniform Polyhedron: U23
  • Platonic Solid
  • Platonic Element: Ether
  • Wythoff symbol: 3|2 5
  • Symmetry Group: icosahedral
  • Vertex Configuration: {5, 5, 5}
  • Dual: icosahedron
  • V: s3 / 4 * (15 + 7 * √5)
  • A: s2 * 12 / 4 * √(25 + 10 * √5)
  • rinner: s / 20 * √(250 + 110 * √5)
  • router: s / 4 * (√15 + √3)
  • Vertices/Connectors: 20 (3-way)
  • Faces: 12 (5-sided)
  • Edges/Struts:
    • A x 30: 0.71364

Geodesic Dodecahedron L1


Geodesic Dodecahedron L1
  • Vertices/Connectors: 32
    • 12 x 5-way
    • 20 x 6-way
  • Faces: 60 (3-sided)
  • Edges/Struts:
    • A x 60: 0.64085
    • B x 30: 0.71364
    • total 90 struts (2 kinds)
    • strut variance 11.4%

Geodesic Dodecahedron L2


Geodesic Dodecahedron L2
  • Vertices/Connectors: 122
    • 12 x 5-way
    • 110 x 6-way
  • Faces: 240 (3-sided)
  • Edges/Struts:
    • A x 120: 0.32474
    • B x 120: 0.34034
    • C x 60: 0.36284
    • D x 60: 0.37668
    • total 360 struts (4 kinds)
    • strut variance 16.0%
Looks very symmertrical, L1 & L2 - yet, no straight hemisphere line.

Geodesic Dodecahedron L2T


Geodesic Dodecahedron L2T
  • Vertices/Connectors: 182
    • 90 x 4-way
    • 60 x 6-way
    • 12 x 10-way
    • 20 x 12-way
  • Faces: 360 (3-sided)
  • Edges/Struts:
    • A x 60: 0.19071
    • B x 120: 0.21151
    • C x 120: 0.32474
    • D x 60: 0.36059
    • E x 60: 0.36284
    • F x 120: 0.40698
    • total 540 struts (6 kinds)
    • strut variance 113.1%


Geodesic Dodecahedron Dome L2T


Geodesic Dodecahedron Dome L2T

Geodesic Dodecahedron Dome L2T
  • Vertices/Connectors: 101
    • 8 x 3-way
    • 45 x 4-way
    • 32 x 6-way
    • 4 x 7-way
    • 4 x 10-way
    • 8 x 12-way
  • Faces: 180 (3-sided)

  • Dodecahedron Dome L2T Construction Map
  • Edges/Struts:
    • A x 32: 0.19071
    • B x 60: 0.21151
    • C x 64: 0.32473
    • D x 32: 0.36059
    • E x 32: 0.36284
    • F x 60: 0.40698
    • total 280 struts (6 kinds)
    • strut variance 113.1%

d= A= x 32, B= x 60, C= x 64, D= x 32, E= x 32, F= x 60,


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