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Geodesic Polyhedra

written by Rene K. Mueller, Copyright (c) 2007, last updated Fri, February 25, 2022

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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Creative Commons (CC) BY-SA-NC 2005-2017, developed, designed and written by René K. Müller
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