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Geodesic Polyhedra

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

Geodesic Truncated Cuboctahedron

Truncated Cuboctahedron


Truncated Cuboctahedron
  • Uniform Polyhedron: U11
  • aka Great Rhombicuboctahedron
  • Archimedean Solid: A3
  • Wythoff symbol: 2 3 4|
  • Symmetry Group: octahedral
  • Vertex Configuration: {4, 6, 8}
  • Dual: disdyakis dodecahedron
  • V: s3 * (22 + 14 * √2)
  • A: s2 * 12 * (2 + √2 + √3)
  • rinner: s * 3/97 * (14 + √2) * √(13 + 6 * √2)
  • router: s / 2 * √(13 + 6 * √2)
  • Vertices/Connectors: 48 (3-way)
  • Faces: 26
    • 12 x 4-sided
    • 8 x 6-sided
    • 6 x 8-sided
  • Edges/Struts:
    • A x 72: 0.43148

Geodesic Truncated Cuboctahedron L1


Geodesic Truncated Cuboctahedron L1
  • Vertices/Connectors: 74
    • 12 x 4-way
    • 56 x 6-way
    • 6 x 8-way
  • Faces: 144 (3-sided)
  • Edges/Struts:
    • A x 48: 0.30880
    • B x 72: 0.43148
    • C x 48: 0.44244
    • D x 48: 0.59001
    • total 216 struts (4 kinds)
    • strut variance 90.9%
The L1 looks very good, the Truncate Cuboctahedron has 8-, 6-, and 4-sided polygons, once centerpoint triangulated make up a beautiful shape. Unfortunately no straight hemisphere line to derive a dome from.

Geodesic Truncated Cuboctahedron L2


Geodesic Truncated Cuboctahedron L2
  • Vertices/Connectors: 290
    • 12 x 4-way
    • 272 x 6-way
    • 6 x 8-way
  • Faces: 576 (3-sided)
  • Edges/Struts:
    • A x 96: 0.15487
    • B x 96: 0.15676
    • C x 144: 0.21702
    • D x 48: 0.21836
    • E x 48: 0.22122
    • F x 96: 0.22260
    • G x 48: 0.22579
    • H x 96: 0.22669
    • I x 96: 0.29834
    • J x 96: 0.30464
    • total 864 struts (10 kinds)
    • strut variance 96.8%

Geodesic Truncated Cuboctahedron L2T


Geodesic Truncated Cuboctahedron L2T
  • Vertices/Connectors: 434
    • 216 x 4-way
    • 144 x 6-way
    • 12 x 8-way
    • 56 x 12-way
    • 6 x 16-way
  • Faces: 864 (3-sided)
  • Edges/Struts:
    • A x 48: 0.07529
    • B x 96: 0.11553
    • C x 96: 0.12908
    • D x 48: 0.13215
    • E x 48: 0.14734
    • F x 96: 0.14838
    • G x 96: 0.15487
    • H x 48: 0.18805
    • I x 144: 0.21702
    • J x 96: 0.22260
    • K x 96: 0.22942
    • L x 96: 0.25328
    • M x 48: 0.25972
    • N x 96: 0.28571
    • O x 96: 0.29834
    • P x 48: 0.37211
    • total 1296 struts (16 kinds)
    • strut variance 396.0%


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