| Great rhombihexahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 18, E = 48 V = 24 (χ = −6) |
| Faces by sides | 12{4}+6{8/3} |
| Coxeter diagram |      (with extra double-covered triangles) (with extra double-covered squares)
|
| Wythoff symbol | 2 4/3 (3/2 4/2) | |
| Symmetry group | Oh, [4,3], *432 |
| Index references | U21, C82, W103 |
| Dual polyhedron | Great rhombihexacron |
| Vertex figure |  4.8/3.4/3.8/5 |
| Bowers acronym | Groh |
In geometry, the great rhombihexahedron (or great rhombicube) is a nonconvex uniform polyhedron, indexed as U21. It has 18 faces (12 squares and 6 octagrams), 48 edges, and 24 vertices.[1] Its dual is the great rhombihexacron.[2] Its vertex figure is a crossed quadrilateral.
- ^ Maeder, Roman. "21: great rhombihexahedron". MathConsult.
- ^ Weisstein, Eric W. "Great Rhombihexahedron". MathWorld.