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# Geodesic Polyhedra

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

## Geodesic Icosidodecahedron

### Icosidodecahedron

 Icosidodecahedron
• Uniform Polyhedron: U24
• Archimedean Solid: A4
• Wythoff symbol: 2|3 5
• Symmetry Group: icosahedral
• Vertex Configuration: {3, 5, 3, 5}
• Dual: rhombic triacontahedron
• V: s3 / 6 * (45 + 17 * √5)
• A: s2 * (5 * √3 + 3 * √5 * √(5 + 2 * √5))
• rinner: s / 8 * (5 + 3 * √5)
• router: s * (1 + √5) / 2
• Vertices/Connectors: 30 (4-way)
• Faces: 32
• 20 x 3-sided
• 12 x 5-sided
• Edges/Struts:
• A x 60: 0.61803

### Geodesic Icosidodecahedron L1

 Geodesic Icosidodecahedron L1
• Vertices/Connectors: 42
• 12 x 5-way
• 30 x 6-way
• Faces: 80 (3-sided)
• Edges/Struts:
• A x 60: 0.54653
• B x 60: 0.61803
• total 120 struts (2 kinds)
• strut variance 13.0%

### Geodesic Icosidodecahedron Dome L1

 Geodesic Icosidodecahedron Dome L1
 Geodesic Icosidodecahedron Dome L1
• Vertices/Connectors: 26
• 10 x 4-way
• 6 x 5-way
• 10 x 6-way
• Faces: 40 (3-sided)
•  Icosidodecahedron Dome L1 Construction Map
• Edges/Struts:
• A x 30: 0.54653
• B x 35: 0.61803
• total 65 struts (2 kinds)
• strut variance 13.0%

d= A= x 30, B= x 35,
After triangulating it's the same as the Icosahedron 2V or L2. It's a bit of redundancy to list it anyway.

### Geodesic Icosidodecahedron L2

 Geodesic Icosidodecahedron L2
• Vertices/Connectors: 162
• 12 x 5-way
• 150 x 6-way
• Faces: 320 (3-sided)
• Edges/Struts:
• A x 120: 0.27590
• B x 120: 0.28547
• C x 120: 0.31287
• D x 60: 0.32124
• E x 60: 0.32492
• total 480 struts (5 kinds)
• strut variance 17.8%

### Geodesic Icosidodecahedron Dome L2

 Geodesic Icosidodecahedron Dome L2
 Geodesic Icosidodecahedron Dome L2
• Vertices/Connectors: 91
• 20 x 4-way
• 6 x 5-way
• 65 x 6-way
• Faces: 160 (3-sided)
•  Icosidodecahedron Dome L2 Construction Map
• Edges/Struts:
• A x 60: 0.27590
• B x 60: 0.28547
• C x 70: 0.31287
• D x 30: 0.32124
• E x 30: 0.32492
• total 250 struts (5 kinds)
• strut variance 17.8%

d= A= x 60, B= x 60, C= x 70, D= x 30, E= x 30,
The L2 is the same as a Icosahedron with 4V or L3.

### Geodesic Icosidodecahedron L2T

 Geodesic Icosidodecahedron L2T
• Vertices/Connectors: 242
• 120 x 4-way
• 80 x 6-way
• 12 x 10-way
• 30 x 12-way
• Faces: 480 (3-sided)
• Edges/Struts:
• A x 60: 0.15841
• B x 120: 0.17931
• C x 60: 0.18843
• D x 120: 0.27590
• E x 60: 0.30389
• F x 120: 0.31287
• G x 120: 0.34893
• H x 60: 0.36284
• total 720 struts (8 kinds)
• strut variance 129.7%

### Geodesic Icosidodecahedron Dome L2T

 Geodesic Icosidodecahedron Dome L2T
 Geodesic Icosidodecahedron Dome L2T
• Vertices/Connectors: 131
• 10 x 3-way
• 55 x 4-way
• 40 x 6-way
• 10 x 7-way
• 6 x 10-way
• 10 x 12-way
• Faces: 240 (3-sided)
•  Icosidodecahedron Dome L2T Construction Map
• Edges/Struts:
• A x 30: 0.15841
• B x 60: 0.17931
• C x 30: 0.18843
• D x 60: 0.27590
• E x 30: 0.30389
• F x 70: 0.31287
• G x 60: 0.34893
• H x 30: 0.36284
• total 370 struts (8 kinds)
• strut variance 129.7%

d= A= x 30, B= x 60, C= x 30, D= x 60, E= x 30, F= x 70, G= x 60, H= x 30,
Very beautiful construct, the same would have been achieved to triaconize a 2V or L2 Icosahedron (2V.2VT)

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