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# Geodesic Polyhedra

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

## Geodesic Truncated Icosahedron

### Truncated Icosahedron

 Truncated Icosahedron
• Uniform Polyhedron: U25
• Archimedean Solid: A11
• Wythoff symbol: 2 5|3
• Symmetry Group: icosahedral
• Vertex Configuration: {6, 6, 5}
• Dual: pentakis dodecahedron
• V: s3 / 4 * (125 + 43 * √5)
• A: s2 * 3 * (10 * √3 + √5 * √(5 + 2 * √5))
• rinner: s * 9/872 * (21 + √5) * √(58 + 18 * √5)
• router: s / 4 * √(58 + 18 * √5)
• Vertices/Connectors: 60 (3-way)
• Faces: 32
• 12 x 5-sided
• 20 x 6-sided
• Edges/Struts:
• A x 90: 0.40355

### Geodesic Truncated Icosahedron L1

 Geodesic Truncated Icosahedron L1
• Vertices/Connectors: 92
• 12 x 5-way
• 80 x 6-way
• Faces: 180 (3-sided)
• Edges/Struts:
• A x 60: 0.34862
• B x 90: 0.40355
• C x 120: 0.41241
• total 270 struts (3 kinds)
• strut variance 18.1%

### Geodesic Truncated Icosahedron Dome L1

 Geodesic Truncated Icosahedron Dome L1
 Geodesic Truncated Icosahedron Dome L1
• Vertices/Connectors: 46
• 15 x 4-way
• 6 x 5-way
• 25 x 6-way
• Faces: 75 (3-sided)
•  Truncated Icosahedron Dome L1 Construction Map
• Edges/Struts:
• A x 30: 0.34862
• B x 40: 0.40355
• C x 50: 0.41241
• total 120 struts (3 kinds)
• strut variance 18.1%

d= A= x 30, B= x 40, C= x 50,
The L1 seems like having two straight hemisphere lines, at 3/7 and 4/7 approximately, looks like a Icosahedron 3V.

### Geodesic Truncated Icosahedron L2

 Geodesic Truncated Icosahedron L2
• Vertices/Connectors: 362
• 12 x 5-way
• 350 x 6-way
• Faces: 720 (3-sided)
• Edges/Struts:
• A x 120: 0.17498
• B x 120: 0.17741
• C x 180: 0.20282
• D x 60: 0.20491
• E x 120: 0.20621
• F x 240: 0.20732
• G x 240: 0.21063
• total 1080 struts (7 kinds)
• strut variance 20.6%

### Geodesic Truncated Icosahedron Dome L2

 Geodesic Truncated Icosahedron Dome L2
 Geodesic Truncated Icosahedron Dome L2
• Vertices/Connectors: 196
• 30 x 4-way
• 6 x 5-way
• 160 x 6-way
• Faces: 360 (3-sided)
•  Truncated Icosahedron Dome L2 Construction Map
• Edges/Struts:
• A x 60: 0.17498
• B x 60: 0.17741
• C x 90: 0.20282
• D x 30: 0.20491
• E x 65: 0.20621
• F x 120: 0.20732
• G x 130: 0.21063
• total 555 struts (7 kinds)
• strut variance 20.6%

d= A= x 60, B= x 60, C= x 90, D= x 30, E= x 65, F= x 120, G= x 130,

### Geodesic Truncated Icosahedron L2T

 Geodesic Truncated Icosahedron L2T
• Vertices/Connectors: 542
• 270 x 4-way
• 180 x 6-way
• 12 x 10-way
• 80 x 12-way
• Faces: 1080 (3-sided)
• Edges/Struts:
• A x 60: 0.09684
• B x 120: 0.11337
• C x 240: 0.12015
• D x 120: 0.12264
• E x 120: 0.17498
• F x 60: 0.19033
• G x 180: 0.20282
• H x 240: 0.20732
• I x 120: 0.22432
• J x 240: 0.23636
• K x 120: 0.24155
• total 1620 struts (11 kinds)
• strut variance 149.5%

### Geodesic Truncated Icosahedron Dome L2T

 Geodesic Truncated Icosahedron Dome L2T
 Geodesic Truncated Icosahedron Dome L2T
• Vertices/Connectors: 289
• 12 x 3-way
• 141 x 4-way
• 88 x 6-way
• 8 x 7-way
• 4 x 10-way
• 36 x 12-way
• Faces: 540 (3-sided)
•  Truncated Icosahedron Dome L2T Construction Map
• Edges/Struts:
• A x 32: 0.09684
• B x 60: 0.11337
• C x 120: 0.12015
• D x 64: 0.12264
• E x 64: 0.17498
• F x 32: 0.19033
• G x 92: 0.20282
• H x 120: 0.20732
• I x 60: 0.22432
• J x 120: 0.23636
• K x 64: 0.24155
• total 828 struts (11 kinds)
• strut variance 149.5%

d= A= x 32, B= x 60, C= x 120, D= x 64, E= x 64, F= x 32, G= x 92, H= x 120, I= x 60, J= x 120, K= x 64,

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