written by Rene K. Mueller, Copyright (c) 2007, last updated Fri, February 25, 2022
Geodesic Cuboctahedron
Cuboctahedron
Cuboctahedron
Uniform Polyhedron: U7
Archimedean Solid: A1
Wythoff symbol: 2|3 4
Symmetry Group: octahedral
Vertex Configuration: {3, 4, 3, 4}
Dual: rhombic dodecahedron
V: s3 * 5/3 * √2
A: s2 * (6 + 2 * √3)
rinner: s * 3/4
router: s
Vertices/Connectors: 12 (4-way)
Faces: 14
8 x 3-sided
6 x 4-sided
Edges/Struts:
A x 24: 1.00000
Geodesic Cuboctahedron L1
Geodesic Cuboctahedron L1
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 Cuboctahedron Dome L1
Geodesic Cuboctahedron Dome L1
Geodesic Cuboctahedron Dome L1
Vertices/Connectors: 12
9 x 4-way
3 x 6-way
Faces: 16 (3-sided)
Cuboctahedron Dome L1 Construction Map
Edges/Struts:
A x 12: 0.76537
B x 15: 1.00000
total 27 struts (2 kinds)
strut variance 30.7%
Geodesic Cuboctahedron L2
Geodesic Cuboctahedron L2
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 Cuboctahedron Dome L2
Geodesic Cuboctahedron Dome L2
Geodesic Cuboctahedron Dome L2
Vertices/Connectors: 39
15 x 4-way
24 x 6-way
Faces: 64 (3-sided)
Cuboctahedron Dome L2 Construction Map
Edges/Struts:
A x 24: 0.39018
B x 24: 0.42291
C x 30: 0.51764
D x 12: 0.54120
E x 12: 0.57735
total 102 struts (5 kinds)
strut variance 47.9%
With a straight hemisphere line it is suitable, yet, the top for a skylight is a triangle, which means it's horizontal and water (rain) cannot flow down, so likely a slight tilt is required.
It provides three square windows on the side.
Geodesic Cuboctahedron Dome L2 Model (Closeup)
I made following model with 4mm thick and 40cm long bamboo, and 6mm/4mm clear PVC pipe as connector. A quick check how to optimize the struts:
12 x (A + E) = 1.0
12 x (A + D)
24 x (B + C)
6 x C
total 54 laths
Geodesic Cuboctahedron Dome L2 Model (46cm diameter)
(A+E) = 1.0, therefore
A = 0.403, B = 0.436, C = 0.534, D = 0.559, E = 0.596
(Alath+Elath) = ~20cm (using 27 x 40cm bamboo equal 54 x 20cm bamboo)
I first calculated A+E (instead of Alath+Elath) which made the struts 0.5cm longer A and B, for C, D and E the error was neglectable, but the resulting dome looked strange, until I realized those 0.75cm do really matter at that scale of the model.
So I recommend considering the distance the connector itself requires as well, even you are doing a model at 20cm scale or so, it matters.
