Great rhombihexahedron
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| Great rhombihexahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Groh |
| Elements | |
| Faces | 12 squares, 6 octagrams |
| Edges | 24+24 |
| Vertices | 24 |
| Vertex figure | Butterfly, edge lengths √2 and √2–√2  |
| Measures (edge length 1) | |
| Circumradius | |
| Dihedral angles | 8/3–4 #1: 90° |
| 8/3–4 #2: 45° | |
| Central density | odd |
| Number of external pieces | 366 |
| Level of complexity | 56 |
| Related polytopes | |
| Army | Tic, edge length |
| Regiment | Gocco |
| Dual | Great rhombihexacron |
| Conjugate | Small rhombihexahedron |
| Convex core | Rhombic dodecahedron |
| Abstract & topological properties | |
| Flag count | 192 |
| Euler characteristic | -6 |
| Orientable | No |
| Genus | 8 |
| Properties | |
| Symmetry | B3, order 48 |
| Convex | No |
| Nature | Tame |
The great rhombihexahedron, or groh, is a uniform polyhedron. It consists of 12 squares and 6 octagrams. Two squares and two octagrams meet at each vertex. It also has 8 triangular pseudofaces and 6 square pseudofaces.
It is a faceting of the great cubicuboctahedron, using its 6 octagrams along with 12 squares of the quasirhombicuboctahedron.
It can be constructed as a blend of three orthogonal octagrammic prisms, with 6 pairs of coinciding square faces blending out.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the great cubicuboctahedron.
Related polyhedra[edit | edit source]
The rhombisnub quasihyperhombihedron is a uniform polyhedron compound composed of 5 great rhombihexahedra.
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#47).
- Klitzing, Richard. "groh".
- Wikipedia Contributors. "Great rhombihexahedron".
- McCooey, David. "Great Rhombihexahedron"