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Snub (geometry)

The two snubbed Archimedean solids

Snub cube or
Snub cuboctahedron
Snub dodecahedron or
Snub icosidodecahedron
Two chiral copies of the snub cube, as alternated (red or green) vertices of the truncated cuboctahedron.
A snub cube can be constructed from a rhombicuboctahedron by rotating the 6 blue square faces until the 12 white square faces become pairs of equilateral triangle faces.

In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus simus) and snub dodecahedron (dodecaedron simum).[1]

In general, snubs have chiral symmetry with two forms: with clockwise or counterclockwise orientation. By Kepler's names, a snub can be seen as an expansion of a regular polyhedron: moving the faces apart, twisting them about their centers, adding new polygons centered on the original vertices, and adding pairs of triangles fitting between the original edges.

The terminology was generalized by Coxeter, with a slightly different definition, for a wider set of uniform polytopes.

  1. ^ Kepler, Harmonices Mundi, 1619

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