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 gyroprismatic triothowedge, medial square gyroprismatic triorthowedge, great square gyroprismatic triorthowedge, small transitional square gyroprismatic triorthowedge, and great transitional square gyroprismatic 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.