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Geodesic Polyhedra

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

Geodesic Rhombicuboctahedron

Rhombicuboctahedron


Rhombicuboctahedron
  • Uniform Polyhedron: U10
  • aka Small Rhombicuboctahedron
  • Archimedean Solid: A6
  • Wythoff symbol: 3 4|2
  • Symmetry Group: octahedral
  • Vertex Configuration: {4, 3, 4, 4}
  • Dual: deltoidal icositetrahedron
  • V: s3 / 3 * (12 + 10 * √2)
  • A: s2 * (18 + 2 * √3)
  • rinner: s / 17 * (6 + √2) * √(5 + 2 * √2)
  • router: s / 2 * √(5 + 2 * √2)
  • Vertices/Connectors: 24 (4-way)
  • Faces: 26
    • 8 x 3-sided
    • 18 x 4-sided
  • Edges/Struts:
    • A x 48: 0.71481

Geodesic Rhombicuboctahedron L1


Geodesic Rhombicuboctahedron L1
  • Vertices/Connectors: 42
    • 18 x 4-way
    • 24 x 7-way
  • Faces: 80 (3-sided)
  • Edges/Struts:
    • A x 72: 0.52372
    • B x 48: 0.71481
    • total 120 struts (2 kinds)
    • strut variance 36.5%

Geodesic Rhombicuboctahedron L2


Geodesic Rhombicuboctahedron L2
  • Vertices/Connectors: 162
    • 18 x 4-way
    • 120 x 6-way
    • 24 x 7-way
  • Faces: 320 (3-sided)
  • Edges/Struts:
    • A x 144: 0.26418
    • B x 144: 0.27386
    • C x 96: 0.36346
    • D x 72: 0.37033
    • E x 24: 0.38268
    • total 480 struts (5 kinds)
    • strut variance 45.1%
Two straight hemispherical lines, at 1/3 or 2/3 height approximately.

Geodesic Rhombicuboctahedron L2T


Geodesic Rhombicuboctahedron L2T
  • Vertices/Connectors: 242
    • 120 x 4-way
    • 80 x 6-way
    • 18 x 8-way
    • 24 x 14-way
  • Faces: 480 (3-sided)
  • Edges/Struts:
    • A x 72: 0.13612
    • B x 144: 0.19744
    • C x 24: 0.22232
    • D x 72: 0.25577
    • E x 144: 0.26418
    • F x 96: 0.36346
    • G x 144: 0.38653
    • H x 24: 0.42221
    • total 720 struts (8 kinds)
    • strut variance 210.3%


Geodesic Rhombicuboctahedron Dome L2T


Geodesic Rhombicuboctahedron Dome L2T

Geodesic Rhombicuboctahedron Dome L2T
  • Vertices/Connectors: 133
    • 8 x 3-way
    • 64 x 4-way
    • 4 x 5-way
    • 36 x 6-way
    • 11 x 8-way
    • 10 x 14-way
  • Faces: 240 (3-sided)

  • Rhombicuboctahedron Dome L2T Construction Map
  • Edges/Struts:
    • A x 38: 0.13612
    • B x 72: 0.19744
    • C x 14: 0.22232
    • D x 38: 0.25577
    • E x 76: 0.26418
    • F x 48: 0.36346
    • G x 72: 0.38653
    • H x 14: 0.42221
    • total 372 struts (8 kinds)
    • strut variance 210.3%

d= A= x 38, B= x 72, C= x 14, D= x 38, E= x 76, F= x 48, G= x 72, H= x 14,


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