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|Bowers style acronym||Socco|
|Coxeter diagram||x4/3o3x4*a ()|
|Faces||8 triangles, 6 squares, 6 octagons|
|Vertex figure||Crossed isosceles trapezoid, edge lengths 1, √2+√2, √2, √2+√2 |
|Measures (edge length 1)|
|Dihedral angles||8–4: 90°|
|Number of external pieces||62|
|Level of complexity||9|
|Dual||Small hexacronic icositetrahedron|
|Abstract & topological properties|
|Symmetry||B3, order 48|
The small cubicuboctahedron, or socco, is a uniform polyhedron. It consists of 8 triangles, 6 squares, and 6 octagons. One triangle, one square, and two octagons meet at each vertex. It also has 12 square pseudofaces.
It is a faceting of the small rhombicuboctahedron, using its 6 squares and 8 triangles, along with 6 new octagons.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the rhombicuboctahedron.
Representations[edit | edit source]
A small cubicuboctahedron has the following Coxeter diagrams:
- x4o3ß (, as holosnub)
Related polyhedra[edit | edit source]
The rhombihyperhombicosicosahedron is a uniform polyhedron compound composed of 5 small cubicuboctahedra.
|(degenerate, double cover of cube)||x4/3o3o4*a ()|
|Great cubicuboctahedron||gocco||x4/3x3o4*a ()|
|(degenerate, oct+6(4))||o4/3x3o4*a ()|
|(degenerate, double cover of cho)||o4/3x3x4*a ()|
|(degenerate, oct+6(4))||o4/3o3x4*a ()|
|Small cubicuboctahedron||socco||x4/3o3x4*a ()|
|Cuboctatruncated cuboctahedron||cotco||x4/3x3x4*a ()|
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#37).
- Klitzing, Richard. "socco".
- Wikipedia Contributors. "Small cubicuboctahedron".
- McCooey, David. "Small Cubicuboctahedron"