Small cubicuboctahedron
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.
Small cubicuboctahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Socco |
Coxeter diagram | x4/3o3x4*a () |
Elements | |
Faces | 8 triangles, 6 squares, 6 octagons |
Edges | 24+24 |
Vertices | 24 |
Vertex figure | Crossed isosceles trapezoid, edge lengths 1, √2+√2, √2, √2+√2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 8–4: 90° |
8–3: | |
Central density | 2 |
Number of external pieces | 62 |
Level of complexity | 9 |
Related polytopes | |
Army | Sirco |
Regiment | Sirco |
Dual | Small hexacronic icositetrahedron |
Conjugate | Great cubicuboctahedron |
Convex core | Cube |
Abstract & topological properties | |
Flag count | 192 |
Euler characteristic | –4 |
Orientable | Yes |
Genus | 3 |
Properties | |
Symmetry | B_{3}, order 48 |
Convex | No |
Nature | Tame |
It is a faceting of the small rhombicuboctahedron, using its 6 squares and 8 triangles, along with 6 new octagons.
Vertex coordinatesEdit
Its vertices are the same as those of its regiment colonel, the rhombicuboctahedron.
RepresentationsEdit
A small cubicuboctahedron has the following Coxeter diagrams:
- x4/3o3x4*a
- x4o3ß ( , as holosnub)
Related polyhedraEdit
The rhombihyperhombicosicosahedron is a uniform polyhedron compound composed of 5 small cubicuboctahedra.
Name | OBSA | CD diagram | Picture |
---|---|---|---|
(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 linksEdit
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#37).
- Klitzing, Richard. "socco".
- Wikipedia Contributors. "Small cubicuboctahedron".
- McCooey, David. "Small Cubicuboctahedron"