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Geodesic Polyhedra

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

Geodesic Cube

Cube


Cube
  • Uniform Polyhedron: U6
  • aka Hexahedron
  • Platonic Solid
  • Platonic Element: Earth
  • Wythoff symbol: 3|2 4
  • Symmetry Group: octahedral
  • Vertex Configuration: {4, 4, 4}
  • Dual: octahedron
  • V: s3
  • A: s2 * 6
  • rinner: s / 2
  • router: s / 2 * √3
  • Vertices/Connectors: 8 (3-way)
  • Faces: 6 (4-sided)
  • Edges/Struts:
    • A x 12: 1.15470

Geodesic Cube L1


Geodesic Cube L1
  • Vertices/Connectors: 14
    • 6 x 4-way
    • 8 x 6-way
  • Faces: 24 (3-sided)
  • Edges/Struts:
    • A x 24: 0.91940
    • B x 12: 1.15470
    • total 36 struts (2 kinds)
    • strut variance 25.7%


Geodesic Cube Dome L1


Geodesic Cube Dome L1

Geodesic Cube Dome L1
  • Vertices/Connectors: 10
    • 2 x 3-way
    • 6 x 4-way
    • 2 x 6-way
  • Faces: 12 (3-sided)

  • Cube Dome L1 Construction Map
  • Edges/Struts:
    • A x 14: 0.91940
    • B x 7: 1.15470
    • total 21 struts (2 kinds)
    • strut variance 25.7%

d= A= x 14, B= x 7,

Geodesic Cube L2


Geodesic Cube L2
  • Vertices/Connectors: 50
    • 6 x 4-way
    • 44 x 6-way
  • Faces: 96 (3-sided)
  • Edges/Struts:
    • A x 48: 0.47313
    • B x 48: 0.53327
    • C x 24: 0.60581
    • D x 24: 0.65012
    • total 144 struts (4 kinds)
    • strut variance 37.4%


Geodesic Cube Dome L2


Geodesic Cube Dome L2

Geodesic Cube Dome L2
  • Vertices/Connectors: 31
    • 2 x 3-way
    • 12 x 4-way
    • 17 x 6-way
  • Faces: 48 (3-sided)

  • Cube Dome L2 Construction Map
  • Edges/Struts:
    • A x 28: 0.47313
    • B x 24: 0.53327
    • C x 14: 0.60581
    • D x 12: 0.65012
    • total 78 struts (4 kinds)
    • strut variance 37.4%

d= A= x 28, B= x 24, C= x 14, D= x 12,

Geodesic Cube L2T


Geodesic Cube L2T
  • Vertices/Connectors: 74
    • 36 x 4-way
    • 24 x 6-way
    • 6 x 8-way
    • 8 x 12-way
  • Faces: 144 (3-sided)
  • Edges/Struts:
    • A x 24: 0.29239
    • B x 48: 0.35693
    • C x 48: 0.47313
    • D x 24: 0.48701
    • E x 24: 0.60581
    • F x 48: 0.66092
    • total 216 struts (6 kinds)
    • strut variance 126.4%


Geodesic Cube Dome L2T


Geodesic Cube Dome L2T

Geodesic Cube Dome L2T
  • Vertices/Connectors: 43
    • 6 x 3-way
    • 15 x 4-way
    • 2 x 5-way
    • 12 x 6-way
    • 4 x 7-way
    • 2 x 8-way
    • 2 x 12-way
  • Faces: 72 (3-sided)

  • Cube Dome L2T Construction Map
  • Edges/Struts:
    • A x 12: 0.29239
    • B x 24: 0.35693
    • C x 28: 0.47313
    • D x 12: 0.48701
    • E x 14: 0.60581
    • F x 24: 0.66092
    • total 114 struts (6 kinds)
    • strut variance 126.4%

d= A= x 12, B= x 24, C= x 28, D= x 12, E= x 14, F= x 24,
The L2 looks good to explore this form as well, straight hemisphere line makes it a good 4/8 dome.


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