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: s^{3} * 5/3 * √2

A: s^{2} * (6 + 2 * √3)

r_{inner}: s * 3/4

r_{outer}: 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

(A_{lath}+E_{lath}) = ~20cm (using 27 x 40cm bamboo equal 54 x 20cm bamboo)

I first calculated A+E (instead of A_{lath}+E_{lath}) 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.