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# Geodesic Polyhedra

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

## Geodesic Octahedron

### Octahedron

 Octahedron
• Uniform Polyhedron: U5
• Platonic Solid
• Platonic Element: Air
• Wythoff symbol: 4|2 3
• Symmetry Group: octahedral
• Vertex Configuration: {3, 3, 3, 3}
• Dual: cube
• V: s3 / 3 * √2
• A: s2 * 8 / 4 * √3
• rinner: s / 6 * √6
• router: s / 2 * √2
• Vertices/Connectors: 6 (4-way)
• Faces: 8 (3-sided)
• Edges/Struts:
• A x 12: 1.41421
Octahedron looks very suitable for a dome construction, straight hemisphere line.

The L1 is the same as the original aka L0, since there are just triangles, so jump direct on the L2.

### Geodesic Octahedron L2

 Geodesic Octahedron L2
• Vertices/Connectors: 18
• 6 x 4-way
• 12 x 6-way
• Faces: 32 (3-sided)
• Edges/Struts:
• A x 24: 0.76537
• B x 24: 1.00000
• total 48 struts (2 kinds)
• strut variance 30.7%

### Geodesic Octahedron Dome L2

 Geodesic Octahedron Dome L2
 Geodesic Octahedron Dome L2
• Vertices/Connectors: 13
• 4 x 3-way
• 5 x 4-way
• 4 x 6-way
• Faces: 16 (3-sided)
•  Octahedron Dome L2 Construction Map
• Edges/Struts:
• A x 16: 0.76537
• B x 12: 1.00000
• total 28 struts (2 kinds)
• strut variance 30.7%

d= A= x 16, B= x 12,

### Geodesic Octahedron L3

 Geodesic Octahedron L3
• Vertices/Connectors: 66
• 6 x 4-way
• 60 x 6-way
• Faces: 128 (3-sided)
• Edges/Struts:
• A x 48: 0.39018
• B x 48: 0.42291
• C x 48: 0.51764
• D x 24: 0.54120
• E x 24: 0.57735
• total 192 struts (5 kinds)
• strut variance 47.9%

### Geodesic Octahedron Dome L3

 Geodesic Octahedron Dome L3
 Geodesic Octahedron Dome L3
• Vertices/Connectors: 41
• 4 x 3-way
• 13 x 4-way
• 24 x 6-way
• Faces: 64 (3-sided)
•  Octahedron Dome L3 Construction Map
• Edges/Struts:
• A x 32: 0.39018
• B x 24: 0.42291
• C x 24: 0.51764
• D x 12: 0.54120
• E x 12: 0.57735
• total 104 struts (5 kinds)
• strut variance 47.9%

d= A= x 32, B= x 24, C= x 24, D= x 12, E= x 12,
The L3 has even a square skylight, but likely it needs to be composed by triangles so the rain flows down from the top. I likely build a L3 as a model to explore the details.

### Geodesic Octahedron L2T

 Geodesic Octahedron L2T
• Vertices/Connectors: 26
• 12 x 4-way
• 8 x 6-way
• 6 x 8-way
• Faces: 48 (3-sided)
• Edges/Struts:
• A x 24: 0.60581
• B x 24: 0.76537
• C x 24: 0.91940
• total 72 struts (3 kinds)
• strut variance 51.7%

### Geodesic Octahedron Dome L2T

 Geodesic Octahedron Dome L2T
 Geodesic Octahedron Dome L2T
• Vertices/Connectors: 17
• 4 x 3-way
• 4 x 4-way
• 4 x 5-way
• 4 x 6-way
• 1 x 8-way
• Faces: 24 (3-sided)
•  Octahedron Dome L2T Construction Map
• Edges/Struts:
• A x 12: 0.60581
• B x 16: 0.76537
• C x 12: 0.91940
• total 40 struts (3 kinds)
• strut variance 51.7%

d= A= x 12, B= x 16, C= x 12,

### Geodesic Octahedron L3T

 Geodesic Octahedron L3T
• Vertices/Connectors: 146
• 72 x 4-way
• 48 x 6-way
• 12 x 8-way
• 8 x 12-way
• 6 x 16-way
• Faces: 288 (3-sided)
• Edges/Struts:
• A x 48: 0.19241
• B x 48: 0.24650
• C x 48: 0.27801
• D x 48: 0.30653
• E x 48: 0.34535
• F x 48: 0.39018
• G x 48: 0.46472
• H x 48: 0.47313
• I x 48: 0.54543
• total 432 struts (9 kinds)
• strut variance 183.9%

### Geodesic Octahedron Dome L3T

 Geodesic Octahedron Dome L3T
 Geodesic Octahedron Dome L3T
• Vertices/Connectors: 81
• 8 x 3-way
• 32 x 4-way
• 4 x 5-way
• 24 x 6-way
• 4 x 8-way
• 4 x 9-way
• 4 x 12-way
• 1 x 16-way
• Faces: 144 (3-sided)
•  Octahedron Dome L3T Construction Map
• Edges/Struts:
• A x 24: 0.19241
• B x 24: 0.24650
• C x 24: 0.27801
• D x 24: 0.30653
• E x 24: 0.34535
• F x 32: 0.39018
• G x 24: 0.46472
• H x 24: 0.47313
• I x 24: 0.54543
• total 224 struts (9 kinds)
• strut variance 183.9%

d= A= x 24, B= x 24, C= x 24, D= x 24, E= x 24, F= x 32, G= x 24, H= x 24, I= x 24,

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