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Geodesic Polyhedra

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

Geodesic Dodecahedron

Dodecahedron

 Dodecahedron
• Uniform Polyhedron: U23
• Platonic Solid
• Platonic Element: Ether
• Wythoff symbol: 3|2 5
• Symmetry Group: icosahedral
• Vertex Configuration: {5, 5, 5}
• Dual: icosahedron
• V: s3 / 4 * (15 + 7 * √5)
• A: s2 * 12 / 4 * √(25 + 10 * √5)
• rinner: s / 20 * √(250 + 110 * √5)
• router: s / 4 * (√15 + √3)
• Vertices/Connectors: 20 (3-way)
• Faces: 12 (5-sided)
• Edges/Struts:
• A x 30: 0.71364

Geodesic Dodecahedron L1

 Geodesic Dodecahedron L1
• Vertices/Connectors: 32
• 12 x 5-way
• 20 x 6-way
• Faces: 60 (3-sided)
• Edges/Struts:
• A x 60: 0.64085
• B x 30: 0.71364
• total 90 struts (2 kinds)
• strut variance 11.4%

Geodesic Dodecahedron L2

 Geodesic Dodecahedron L2
• Vertices/Connectors: 122
• 12 x 5-way
• 110 x 6-way
• Faces: 240 (3-sided)
• Edges/Struts:
• A x 120: 0.32474
• B x 120: 0.34034
• C x 60: 0.36284
• D x 60: 0.37668
• total 360 struts (4 kinds)
• strut variance 16.0%
Looks very symmertrical, L1 & L2 - yet, no straight hemisphere line.

Geodesic Dodecahedron L2T

 Geodesic Dodecahedron L2T
• Vertices/Connectors: 182
• 90 x 4-way
• 60 x 6-way
• 12 x 10-way
• 20 x 12-way
• Faces: 360 (3-sided)
• Edges/Struts:
• A x 60: 0.19071
• B x 120: 0.21151
• C x 120: 0.32474
• D x 60: 0.36059
• E x 60: 0.36284
• F x 120: 0.40698
• total 540 struts (6 kinds)
• strut variance 113.1%

Geodesic Dodecahedron Dome L2T

 Geodesic Dodecahedron Dome L2T
 Geodesic Dodecahedron Dome L2T
• Vertices/Connectors: 101
• 8 x 3-way
• 45 x 4-way
• 32 x 6-way
• 4 x 7-way
• 4 x 10-way
• 8 x 12-way
• Faces: 180 (3-sided)
•  Dodecahedron Dome L2T Construction Map
• Edges/Struts:
• A x 32: 0.19071
• B x 60: 0.21151
• C x 64: 0.32473
• D x 32: 0.36059
• E x 32: 0.36284
• F x 60: 0.40698
• total 280 struts (6 kinds)
• strut variance 113.1%

d= A= x 32, B= x 60, C= x 64, D= x 32, E= x 32, F= x 60,

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Creative Commons (CC) BY, SA, NC 2005-2017, developed, designed and written by René K. Müller,
Graphics & illustrations made with Inkscape, Tgif, Gimp, PovRay, GD.pm