Great cubicuboctahedron | |
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Type | Uniform star polyhedron |
Elements | F = 20, E = 48 V = 24 (χ = −4) |
Faces by sides | 8{3}+6{4}+6{8/3} |
Coxeter diagram | ![]() ![]() ![]() ![]() |
Wythoff symbol | 3 4 | 4/3 4 3/2 | 4 |
Symmetry group | Oh, [4,3], *432 |
Index references | U14, C50, W77 |
Dual polyhedron | Great hexacronic icositetrahedron |
Vertex figure | ![]() 3.8/3.4.8/3 |
Bowers acronym | Gocco |
In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48 edges, and 24 vertices.[1] Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron. The prefix great serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions.[2]