Stellated cube

The stellated cube or compound of three square hosohedra is a degenerate regular polyhedron compound, being the compound of three square hosohedra. It has 12 digonal faces that form 6 stellated squares due to pairs falling in the same plane.

It can be formed as a degenerate stellation of the cube, by extending the edges to infinity.

Its quotient prismatic equivalent is the hexateron, which is five-dimensional.

Vertex coordinates
Coordinates for the vertices of a stellated cube of edge length 1 centered at the origin are given by all permutations of:
 * $$\left(±\frac12,\,0,\,0\right).$$