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 = 0º, 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 = 45º 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:
 * (±(cos(θ)+sin(θ))/2, ±(cos(θ)–sin(θ))/2, ±1/2)