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Small rhombihexahedron

Polyhedron with 18 faces From Wikipedia, the free encyclopedia

Small rhombihexahedron
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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
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TypeUniform star polyhedron
ElementsF = 18, E = 48
V = 24 (χ = 6)
Faces by sides12{4}+6{8}
Coxeter diagram (with extra double-covered triangles)
(with extra double-covered squares)
Wythoff symbol2 4 (3/2 4/2) |
Symmetry groupOh, [4,3], *432
Index referencesU18, C60, W86
Dual polyhedronSmall rhombihexacron
Vertex figureThumb
4.8.4/3.8/7
Bowers acronymSroh
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3D model of a small rhombihexahedron
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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).

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Rhombicuboctahedron
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Small cubicuboctahedron
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Small rhombihexahedron
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Stellated truncated hexahedron

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

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