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Geodesic Polyhedra

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

Geodesic Octahedron

Octahedron


Octahedron
  • Uniform Polyhedron: U5
  • Platonic Solid
  • Platonic Element: Air
  • Wythoff symbol: 4|2 3
  • Symmetry Group: octahedral
  • Vertex Configuration: {3, 3, 3, 3}
  • Dual: cube
  • V: s3 / 3 * √2
  • A: s2 * 8 / 4 * √3
  • rinner: s / 6 * √6
  • router: s / 2 * √2
  • Vertices/Connectors: 6 (4-way)
  • Faces: 8 (3-sided)
  • Edges/Struts:
    • A x 12: 1.41421
Octahedron looks very suitable for a dome construction, straight hemisphere line.

The L1 is the same as the original aka L0, since there are just triangles, so jump direct on the L2.

Geodesic Octahedron L2


Geodesic Octahedron L2
  • Vertices/Connectors: 18
    • 6 x 4-way
    • 12 x 6-way
  • Faces: 32 (3-sided)
  • Edges/Struts:
    • A x 24: 0.76537
    • B x 24: 1.00000
    • total 48 struts (2 kinds)
    • strut variance 30.7%


Geodesic Octahedron Dome L2


Geodesic Octahedron Dome L2

Geodesic Octahedron Dome L2
  • Vertices/Connectors: 13
    • 4 x 3-way
    • 5 x 4-way
    • 4 x 6-way
  • Faces: 16 (3-sided)

  • Octahedron Dome L2 Construction Map
  • Edges/Struts:
    • A x 16: 0.76537
    • B x 12: 1.00000
    • total 28 struts (2 kinds)
    • strut variance 30.7%

d= A= x 16, B= x 12,

Geodesic Octahedron L3


Geodesic Octahedron L3
  • Vertices/Connectors: 66
    • 6 x 4-way
    • 60 x 6-way
  • Faces: 128 (3-sided)
  • Edges/Struts:
    • A x 48: 0.39018
    • B x 48: 0.42291
    • C x 48: 0.51764
    • D x 24: 0.54120
    • E x 24: 0.57735
    • total 192 struts (5 kinds)
    • strut variance 47.9%


Geodesic Octahedron Dome L3


Geodesic Octahedron Dome L3

Geodesic Octahedron Dome L3
  • Vertices/Connectors: 41
    • 4 x 3-way
    • 13 x 4-way
    • 24 x 6-way
  • Faces: 64 (3-sided)

  • Octahedron Dome L3 Construction Map
  • Edges/Struts:
    • A x 32: 0.39018
    • B x 24: 0.42291
    • C x 24: 0.51764
    • D x 12: 0.54120
    • E x 12: 0.57735
    • total 104 struts (5 kinds)
    • strut variance 47.9%

d= A= x 32, B= x 24, C= x 24, D= x 12, E= x 12,
The L3 has even a square skylight, but likely it needs to be composed by triangles so the rain flows down from the top. I likely build a L3 as a model to explore the details.

Geodesic Octahedron L2T


Geodesic Octahedron L2T
  • Vertices/Connectors: 26
    • 12 x 4-way
    • 8 x 6-way
    • 6 x 8-way
  • Faces: 48 (3-sided)
  • Edges/Struts:
    • A x 24: 0.60581
    • B x 24: 0.76537
    • C x 24: 0.91940
    • total 72 struts (3 kinds)
    • strut variance 51.7%


Geodesic Octahedron Dome L2T


Geodesic Octahedron Dome L2T

Geodesic Octahedron Dome L2T
  • Vertices/Connectors: 17
    • 4 x 3-way
    • 4 x 4-way
    • 4 x 5-way
    • 4 x 6-way
    • 1 x 8-way
  • Faces: 24 (3-sided)

  • Octahedron Dome L2T Construction Map
  • Edges/Struts:
    • A x 12: 0.60581
    • B x 16: 0.76537
    • C x 12: 0.91940
    • total 40 struts (3 kinds)
    • strut variance 51.7%

d= A= x 12, B= x 16, C= x 12,

Geodesic Octahedron L3T


Geodesic Octahedron L3T
  • Vertices/Connectors: 146
    • 72 x 4-way
    • 48 x 6-way
    • 12 x 8-way
    • 8 x 12-way
    • 6 x 16-way
  • Faces: 288 (3-sided)
  • Edges/Struts:
    • A x 48: 0.19241
    • B x 48: 0.24650
    • C x 48: 0.27801
    • D x 48: 0.30653
    • E x 48: 0.34535
    • F x 48: 0.39018
    • G x 48: 0.46472
    • H x 48: 0.47313
    • I x 48: 0.54543
    • total 432 struts (9 kinds)
    • strut variance 183.9%


Geodesic Octahedron Dome L3T


Geodesic Octahedron Dome L3T

Geodesic Octahedron Dome L3T
  • Vertices/Connectors: 81
    • 8 x 3-way
    • 32 x 4-way
    • 4 x 5-way
    • 24 x 6-way
    • 4 x 8-way
    • 4 x 9-way
    • 4 x 12-way
    • 1 x 16-way
  • Faces: 144 (3-sided)

  • Octahedron Dome L3T Construction Map
  • Edges/Struts:
    • A x 24: 0.19241
    • B x 24: 0.24650
    • C x 24: 0.27801
    • D x 24: 0.30653
    • E x 24: 0.34535
    • F x 32: 0.39018
    • G x 24: 0.46472
    • H x 24: 0.47313
    • I x 24: 0.54543
    • total 224 struts (9 kinds)
    • strut variance 183.9%

d= A= x 24, B= x 24, C= x 24, D= x 24, E= x 24, F= x 32, G= x 24, H= x 24, I= x 24,


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