Small rhombihexahedron

In geometry, the small rhombihexahedron (or small rhombicube) is a nonconvex uniform polyhedron, indexed as U₁₈. It has 18 faces (12 squares and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is an antiparallelogram.

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	Oh, [4,3], *432
Index references	U18, C60, W86
Dual polyhedron	Small rhombihexacron
Vertex figure	4.8.4/3.8/7
Bowers acronym	Sroh

3D model of a small rhombihexahedron

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.

External links

• Weisstein, Eric W., "Small rhombihexahedron" ("Uniform polyhedron") at MathWorld.