Snub cube

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

<math>\xi = \frac{1}{3}\left(\sqrt[3]{17+\sqrt{297}} - \sqrt[3]{-17+\sqrt{297}} - 1\right)<math>

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