Rhombisnub dishexahedron

The rhombisnub dishexahedron, risdoh, or compound of six cubes is a uniform polyhedron compound. It consists of 48 squares (six pairs of which fall into coincident planes and combine into stellated octagons), with three faces joining at a vertex.

This compound has rotational freedom, represented by an angle θ. At θ = 0°, all six cubes coincide. We rotate these cubes around their 4-fold axes of symmetry (2 each), seeing them as square prisms (thus their bases combine). At θ = 45° pairs of cubes coincide and the resulting compound is the rhombihexahedron.

Vertex coordinates
The vertices of a rhombisnub dishexahedron of edge length 1 and rotation angle θ are given by all permutations of:
 * $$\left(±\frac{\cos(\theta)+\sin(\theta)}{2},\,±\frac{\cos(\theta)-\sin(\theta)}{2},\,±\frac12\right).$$