Small rhombihexahedron

Small rhombihexahedron
File:Small rhombihexahedron.png
Type	Uniform star polyhedron
Elements	F = 18, E = 48 V = 24 (χ = −6)
Faces by sides	12{4}+6{8}
Coxeter diagram	Template:CDD (with extra double-covered triangles) Template:CDD (with extra double-covered squares)
Wythoff symbol
Symmetry group	O_h, [4,3], *432
Index references	U₁₈, C₆₀, W₈₆
Dual polyhedron	Small rhombihexacron
Vertex figure	File:Small rhombihexahedron vertfig.png 4.8.4/3.8/7
Bowers acronym	Sroh

3D model of a 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.

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).

File:Small rhombicuboctahedron.png Rhombicuboctahedron	File:Small cubicuboctahedron.png Small cubicuboctahedron	File:Small rhombihexahedron.png Small rhombihexahedron	File:Stellated truncated hexahedron.png Stellated truncated hexahedron

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