Small rhombihexahedron
# Small rhombihexahedron

Small rhombihexahedron :

| Type | Uniform star polyhedron |
| - | - |
| Elements | F = 18, E = 48 V = 24 (χ = −6) |
| Faces by sides | 12{4}+6{8} |
| Coxeter diagram | (with extra double-covered triangles) (with extra double-covered squares) |
| Wythoff symbol | 2 4 (3/2 4/2) | |
| Symmetry group | $O_h,$ [4,3], *432 |
| Index references | $U_{18},$ $C_{60},$ $W_{86}$ |
| Dual polyhedron | Small rhombihexacron |
| Vertex figure | 4.8.4/3.8/7 |
| Bowers acronym | Sroh |

In geometry, the small rhombihexahedron (or small rhombicube) is a nonconvex uniform polyhedron, indexed as $U_{18}.$ It has 18 faces (12 squares and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is an antiparallelogram.

## Related polyhedra

This polyhedron shares the vertex arrangement with the stellated truncated hexahedron. It additionally shares its edge arrangement with the convex rhombicuboctahedron (having 12 square faces in common) and with the small cubicuboctahedron (having the octagonal faces in common).

| Rhombicuboctahedron | Small cubicuboctahedron | Small rhombihexahedron | Stellated truncated hexahedron |
| - | - | - | - |

It may be constructed as the exclusive or (blend) of three octagonal prisms.

