Snub cube
Click on picture for large version. Click here for spinning version.
Click on picture for large version. Click here for spinning version.
Type	Archimedean
Faces	32 triangles 6 squares
Edges	60
Vertices	24
Vertex configuration	3,3,3,3,4
Symmetry group	octahedral (O)
Dual polyhedron	pentagonal icositetrahedron
Properties	convex, semi-regular (vertex-uniform), chiral

The snub cube, or snub cuboctahedron, is an Archimedean solid, usually regarded as a truncated polyhedron derived by truncating either a cube or an octahedron.

The snub cube has 38 faces, of which 6 are squares and the other 32 are equilateral triangles. It has 60 edges and 24 vertices. In three-dimensional space, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. In higher-dimensional spaces, these are congruent.

Canonical coordinates for a snub cube are all the even permutations of (±1, ±ξ, ±1/ξ) with an even number of plus signs, along with all the odd permutations with an odd number of plus signs, where ξ is the real solution to ξ³+ξ²+ξ=1, which can be written

or approximately 0.543689. Taking the even permutations with an odd number of plus signs, and the odd permutations with an even number of plus signs gives a different snub cube, the mirror image.

The snub cube should not be confused with the truncated cube.

See also

• snub dodecahedron

External links

• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra