Rhombihexahedron

Not to be confused with the small rhombihexahedron or great rhombihexahedron. The rhombihexahedron, rah, or compound of three cubes is a uniform polyhedron compound. It consists of 6+12 squares, with three faces joining at a vertex.

A complete double cover of this compound is a special case of the general rhombisnub dishexahedron.

The cube components each have square prismatic symmetry. In fact this compound can be constructed by starting with three fully coincident cubes and rotating one 45º along each of the 4-fold symmetry axes.

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

Vertex coordinates
The vertices of a rhombihexahedron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{\sqrt2}{2},\,±\frac12,\,0\right).$$