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Geodesic Polyhedra

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

Geodesic Snub Cube

Snub Cube


Snub Cube
  • Uniform Polyhedron: U12
  • aka Cubus Simus
  • aka Snub Cuboctahedron
  • Archimedean Solid: A7
  • Wythoff symbol: |2 3 4
  • Symmetry Group: octahedral
  • Vertex Configuration: {3, 3, 3, 3, 4}
  • Dual: pentagonal icositetrahedron
  • t: 1/3 * (1 + (10-3*√33)(1/3) + (19+3*√33)(1/3) )
  • V: s3 * ( 8/3 * √(3 * (3-t)/(4*(2-t)) - 1) + √(4 * (3-t)/(4*(2-t)) -2) )
  • V: s3 * √((613 * t + 203)/(9*(35*t-62)))
  • A: s2 * (6 + 8 * √3)
  • rinner: s * √(abs(1-t)/(4*(2-t)))
  • router: s * √((3-t)/(4*(2-t)))
  • Vertices/Connectors: 24 (5-way)
  • Faces: 38
    • 32 x 3-sided
    • 6 x 4-sided
  • Edges/Struts:
    • A x 60: 0.74421

Geodesic Snub Cube L1


Geodesic Snub Cube L1
  • Vertices/Connectors: 30
    • 6 x 4-way
    • 24 x 6-way
  • Faces: 56 (3-sided)
  • Edges/Struts:
    • A x 24: 0.54710
    • B x 60: 0.74421
    • total 84 struts (2 kinds)
    • strut variance 36.0%

Geodesic Snub Cube L2


Geodesic Snub Cube L2
  • Vertices/Connectors: 114
    • 6 x 4-way
    • 108 x 6-way
  • Faces: 224 (3-sided)
  • Edges/Struts:
    • A x 48: 0.27620
    • B x 48: 0.28731
    • C x 120: 0.37897
    • D x 24: 0.38686
    • E x 96: 0.40089
    • total 336 struts (5 kinds)
    • strut variance 45.3%

Geodesic Snub Cube L2T


Geodesic Snub Cube L2T
  • Vertices/Connectors: 170
    • 84 x 4-way
    • 56 x 6-way
    • 6 x 8-way
    • 24 x 12-way
  • Faces: 336 (3-sided)
  • Edges/Struts:
    • A x 24: 0.14348
    • B x 48: 0.20649
    • C x 96: 0.23304
    • D x 24: 0.26808
    • E x 48: 0.27620
    • F x 120: 0.37897
    • G x 48: 0.40339
    • H x 96: 0.44048
    • total 504 struts (8 kinds)
    • strut variance 207.7%
At the first sight it looks as if there is a horizontal base, yet, it's slightly distorted and unsuitable therefore for a dome consideration, unfortunately.


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