# Snub cube

Snub cube
Snub cube, anticlockwise twistSnub cube, clockwise twist
Click on pictures for large 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.

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. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other.

## Canonical coordinates

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 ξ32+ξ=1, which can be written

$\displaystyle \xi = \frac{1}{3}\left(\sqrt[3]{17+\sqrt{297}} - \sqrt[3]{-17+\sqrt{297}} - 1\right)$

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.

## 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 give them all a small rotation on their centers (all clockwise or all counter-clockwise) until the space between can be filled by triangles.

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