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Geodesic Polyhedra

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

Geodesic Truncated Cube

Truncated Cube

 Truncated Cube
• Uniform Polyhedron: U9
• Archimedean Solid: A9
• Wythoff symbol: 2 3|4
• Symmetry Group: octahedral
• Vertex Configuration: {8, 8, 3}
• Dual: triakis octahedron
• V: s3 / 3 * (21 + 14 * √2)
• A: s2 * 2 * (6 + 6 * √2 + √3)
• rinner: s / 17 * (5 + 2 * √2 * √(7 + 4 * √2))
• router: s / 2 * √(7 + 4 * √2)
• Vertices/Connectors: 24 (3-way)
• Faces: 14
• 8 x 3-sided
• 6 x 8-sided
• Edges/Struts:
• A x 36: 0.56217

Geodesic Truncated Cube L1

 Geodesic Truncated Cube L1
• Vertices/Connectors: 30
• 24 x 5-way
• 6 x 8-way
• Faces: 56 (3-sided)
• Edges/Struts:
• A x 36: 0.56217
• B x 48: 0.80175
• total 84 struts (2 kinds)
• strut variance 42.7%

Geodesic Truncated Cube L2

 Geodesic Truncated Cube L2
• Vertices/Connectors: 114
• 24 x 5-way
• 84 x 6-way
• 6 x 8-way
• Faces: 224 (3-sided)
• Edges/Struts:
• A x 72: 0.28396
• B x 24: 0.29289
• C x 48: 0.30682
• D x 96: 0.40955
• E x 96: 0.42500
• total 336 struts (5 kinds)
• strut variance 49.6%
I actually like this form, in particular the L1. The L2 doesn't provide a straight hemisphere line, unfortunately.

Geodesic Truncated Cube L2T

 Geodesic Truncated Cube L2T
• Vertices/Connectors: 170
• 84 x 4-way
• 56 x 6-way
• 24 x 10-way
• 6 x 16-way
• Faces: 336 (3-sided)
• Edges/Struts:
• A x 24: 0.16971
• B x 96: 0.20622
• C x 48: 0.26223
• D x 72: 0.28396
• E x 24: 0.32905
• F x 96: 0.38292
• G x 96: 0.40955
• H x 48: 0.51649
• total 504 struts (8 kinds)
• strut variance 203.5%

Geodesic Truncated Cube Dome L2T

 Geodesic Truncated Cube Dome L2T
 Geodesic Truncated Cube Dome L2T
• Vertices/Connectors: 95
• 6 x 3-way
• 47 x 4-way
• 28 x 6-way
• 2 x 9-way
• 10 x 10-way
• 2 x 16-way
• Faces: 168 (3-sided)
•  Truncated Cube Dome L2T Construction Map
• Edges/Struts:
• A x 14: 0.16971
• B x 48: 0.20622
• C x 26: 0.26223
• D x 38: 0.28396
• E x 14: 0.32905
• F x 48: 0.38292
• G x 48: 0.40955
• H x 26: 0.51649
• total 262 struts (8 kinds)
• strut variance 203.5%

d= A= x 14, B= x 48, C= x 26, D= x 38, E= x 14, F= x 48, G= x 48, H= x 26,

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