Great cube

The great cube or compound of three square dihedra is a degenerate regular polyhedron compound, being the compound of three square dihedra. It has 6 square faces and 6 fissary vertices.

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

When embedded in Euclidean 3-space all 6 of its faces pass through the center of the polyhedron.

Vertex coordinates
Coordinates for the vertices of a great cube of edge length 1 centered at the origin are given by all permutations of:
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0\right).$$