Great snub cube

The great snub cube, gassic, or compound of three square antiprisms is a uniform polyhedron compound. It consists of 24 triangles and 6 squares, with one square and three triangles joining at a vertex.

Its quotient prismatic equivalents are the small square antiprismatic triothowedge, great square antiprismatic triorthowedge, and the transitional square antiprismatic triorthowedge, which are five-dimensional.

Vertex coordinates
The vertices of a great snub cube of edge length 1 are given by all even sign changes and even permutations, plus all odd sign changes and odd permutations, of:
 * $$\left(\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{2-\sqrt2}{8}},\,\frac{\sqrt[4]{8}}{4}\right).$$

Related polyhedra
This compound is chiral. The compound of the two enantiomorphs is the great disnub cube.