Octahedron atop cube

Octahedron atop cube, or octacube, is a convex segmentochoron (designated K-4.15 on Richard Klitzing's list). As the name suggests, it consists of a cube and an octahedron as bases, connected by 6 square pyramids and 8+12 tetrahedra.

It is also commonly referred to as a cubic or octahedral antiprism, as the two bases are a pair of dual polyhedra.

Vertex coordinates
The vertices of an octahedron atop cube segmentochoron of edge length 1 are given by:
 * (±$\sqrt{2}$/2, 0, 0, $\sqrt{(4+√2)/7}$/2) and all permutations of first 3 coordinates
 * (±1/2, ±1/2, ±1/2, 0)