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|Bowers style acronym||Groh|
|Faces||12 squares, 6 octagrams|
|Vertex figure||Butterfly, edge lengths √2 and √2–√2 |
|Measures (edge length 1)|
|Dihedral angles||8/3–4 #1: 90°|
|8/3–4 #2: 45°|
|Number of external pieces||366|
|Level of complexity||56|
|Army||Tic, edge length|
|Convex core||Rhombic dodecahedron|
|Abstract & topological properties|
|Symmetry||B3, order 48|
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"