Small cubicuboctahedron
In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.
| Small cubicuboctahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 20, E = 48 V = 24 (χ = −4) |
| Faces by sides | 8{3}+6{4}+6{8} |
| Coxeter diagram | |
| Wythoff symbol | 3/2 4 | 4 3 4/3 | 4 |
| Symmetry group | Oh, [4,3], *432 |
| Index references | U13, C38, W69 |
| Dual polyhedron | Small hexacronic icositetrahedron |
| Vertex figure | 4.8.3/2.8 |
| Bowers acronym | Socco |
The small cubicuboctahedron is a faceting of the rhombicuboctahedron. Its square faces and its octagonal faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron. The small suffix serves to distinguish it from the great cubicuboctahedron, which also has faces in the aforementioned directions.
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