| Great rhombihexahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 18, E = 48 V = 24 (χ = −6) |
| Faces by sides | 12{4}+6{8/3} |
| Wythoff symbol | 2 4/3 (3/2 4/2) | |
| Symmetry group | Oh, [4,3], *432 |
| Index references | U21, C82, W103 |
| Bowers acronym | Groh |
4.8/3.4/3.8/5 (Vertex figure) |
Great rhombihexacron (dual polyhedron) |
In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U21. Its dual is the great rhombihexacron.[1] Its vertex figure is a crossed quadrilateral.
It shares the vertex arrangement with the convex truncated cube. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having 12 square faces in common), and with the great cubicuboctahedron (having the octagrammic faces in common).
Truncated cube |
Nonconvex great rhombicuboctahedron |
Great cubicuboctahedron |
Great rhombihexahedron |
It may be constructed as the exclusive or of three octagrammic prisms.