Great cubicuboctahedron
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Great cubicuboctahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Gocco |
Coxeter diagram | x4/3x3o4*a () |
Elements | |
Faces | 8 triangles, 6 squares, 6 octagrams |
Edges | 24+24 |
Vertices | 24 |
Vertex figure | Isosceles trapezoid, edge lengths 1, √2–√2, √2, √2–√2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 8/3–3: |
8/3–4: 90° | |
Central density | 4 |
Number of external pieces | 62 |
Level of complexity | 13 |
Related polytopes | |
Army | Tic, edge length |
Regiment | Gocco |
Dual | Great hexacronic icositetrahedron |
Conjugate | Small cubicuboctahedron |
Convex core | Cube |
Abstract & topological properties | |
Flag count | 192 |
Euler characteristic | -4 |
Orientable | Yes |
Genus | 3 |
Properties | |
Symmetry | B_{3}, order 48 |
Flag orbits | 4 |
Convex | No |
Nature | Tame |
The great cubicuboctahedron, or gocco, is a uniform polyhedron. It consists of 8 triangles, 6 squares, and 6 octagrams. One triangle, one square, and two octagrams meet at each vertex. It also has 12 square pseudofaces.
Vertex coordinates[edit | edit source]
A great cubicuboctahedron of edge length 1 has vertex coordinates given by all permutations of:
Related polyhedra[edit | edit source]
The great cubicuboctahedron is the colonel of a three-member regiment that also includes the quasirhombicuboctahedron and the great rhombihexahedron.
The rhombiquasihyperhombicosicosahedron is a uniform polyhedron compound composed of 5 great 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 links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#45).
- Klitzing, Richard. "gocco".
- Wikipedia contributors. "Great cubicuboctahedron".
- McCooey, David. "Great Cubicuboctahedron"