Geometric Relations
The snub cube can be generated by taking the six faces of the cube, pulling them outward so they no longer touch, then giving them each a small rotation on their centers (all clockwise or all counter-clockwise) until the spaces between can be filled with equilateral triangles.
Cube |
Rhombicuboctahedron (Expanded cube) |
Snub cube |
It can also be constructed as an alternation of a nonuniform omnitruncated cube, deleting every other vertex and creating new triangles at the deleted vertices. A properly proportioned (nonuniform) great rhombicuboctahedron will create equilateral triangles at the deleted vertices. Depending on which set of vertices are alternated, the resulting snub cube can have a clockwise or counterclockwise twist.
A "improved" snub cube, with a slightly smaller square face and slightly larger triangular faces compared to Archimedes' uniform snub cube, is useful as a spherical design.
Read more about this topic: Snub Cube
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