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%
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%
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.
