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Geodesic Polyhedra

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

Geodesic Rhombicosidodecahedron

Rhombicosidodecahedron


Rhombicosidodecahedron
  • Uniform Polyhedron: U27
  • aka Small Rhombicosidodecahedron
  • Archimedean Solid: A5
  • Wythoff symbol: 3 5|2
  • Symmetry Group: icosahedral
  • Vertex Configuration: {4, 3, 4, 5}
  • Dual: deltoidal hexecontahedron
  • V: s3 / 3 * (60 + 29 * √5)
  • A: s2 * (30 + √(30 * (10 + 3 * √5 + √(15 * (5 + 2 * √5)))))
  • rinner: s / 41 * (15 + 2 *√5) * √(11 + 4 * √5)
  • router: s / 2 * √(11 + 4 * √5)
  • Vertices/Connectors: 60 (4-way)
  • Faces: 62
    • 20 x 3-sided
    • 30 x 4-sided
    • 12 x 5-sided
  • Edges/Struts:
    • A x 120: 0.44784

Geodesic Rhombicosidodecahedron L1


Geodesic Rhombicosidodecahedron L1
  • Vertices/Connectors: 102
    • 30 x 4-way
    • 12 x 5-way
    • 60 x 7-way
  • Faces: 200 (3-sided)
  • Edges/Struts:
    • A x 120: 0.32082
    • B x 60: 0.38835
    • C x 120: 0.44784
    • total 300 struts (3 kinds)
    • strut variance 39.6%

Geodesic Rhombicosidodecahedron L2


Geodesic Rhombicosidodecahedron L2
  • Vertices/Connectors: 402
    • 30 x 4-way
    • 12 x 5-way
    • 300 x 6-way
    • 60 x 7-way
  • Faces: 800 (3-sided)
  • Edges/Struts:
    • A x 240: 0.16093
    • B x 240: 0.16306
    • C x 120: 0.19510
    • D x 120: 0.19848
    • E x 240: 0.22535
    • F x 120: 0.22686
    • G x 60: 0.22826
    • H x 60: 0.22975
    • total 1200 struts (8 kinds)
    • strut variance 42.9%

Geodesic Rhombicosidodecahedron L2T


Geodesic Rhombicosidodecahedron L2T
  • Vertices/Connectors: 602
    • 300 x 4-way
    • 200 x 6-way
    • 30 x 8-way
    • 12 x 10-way
    • 60 x 14-way
  • Faces: 1200 (3-sided)
  • Edges/Struts:
    • A x 120: 0.07843
    • B x 60: 0.10864
    • C x 240: 0.12006
    • D x 120: 0.12647
    • E x 60: 0.13294
    • F x 120: 0.15322
    • G x 240: 0.16093
    • H x 120: 0.19510
    • I x 60: 0.21265
    • J x 240: 0.22535
    • K x 240: 0.23829
    • L x 120: 0.24957
    • M x 60: 0.26079
    • total 1800 struts (13 kinds)
    • strut variance 234.6%


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