Cuboctatruncated cuboctahedron
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Cuboctatruncated cuboctahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Cotco |
Coxeter diagram | x4/3x3x4*a () |
Elements | |
Faces | 8 hexagons, 6 octagons, 6 octagrams |
Edges | 24+24+24 |
Vertices | 48 |
Vertex figure | Scalene triangle, edge lengths √3, √2+√2, √2–√2 |
Measures (edge length 1) | |
Circumradius | |
Volume | 10 |
Dihedral angles | 8/3–6: |
8/3–8: 90° | |
8–6: | |
Central density | 4 |
Number of external pieces | 62 |
Level of complexity | 15 |
Related polytopes | |
Army | Semi-uniform Girco, edge lengths (of octagons) and 1 (ditrigon-rectangle) |
Regiment | Cotco |
Dual | Tetradyakis hexahedron |
Conjugate | Cuboctatruncated cuboctahedron |
Convex core | Cube |
Abstract & topological properties | |
Flag count | 288 |
Euler characteristic | -4 |
Orientable | Yes |
Genus | 3 |
Properties | |
Symmetry | B_{3}, order 48 |
Flag orbits | 6 |
Convex | No |
Nature | Tame |
The cuboctatruncated cuboctahedron or cotco, also called the cubitruncated cuboctahedron, is a uniform polyhedron. It consists of 8 hexagons, 6 octagons, and 6 octagrams, with one of each type of face meeting per vertex.
Vertex coordinates[edit | edit source]
A cuboctatruncated cuboctahedron of edge length 1 has vertex coordinates given by all permutations of:
Related polyhedra[edit | edit source]
Oddly, it has the same circumradius as the rhombidodecadodecahedron.
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 links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 5: Omnitruncates" (#62).
- Klitzing, Richard. "cotco".
- Wikipedia contributors. "Cubitruncated cuboctahedron".
- McCooey, David. "Cubitruncated Cuboctahedron"