Disnubahedron

The disnubahedron, dis, or compound of twelve tetrahedra is a uniform polyhedron compound. It consists of 48 triangles, with three faces joining at a vertex.

This compound has rotational freedom. In fact it can be formed from the rhombisnub dishexahedron by replacing each cube with the inscribed stella octangula.

Vertex coordinates
The vertices of a disnubahedron of edge length 1 and rotation angle θ are given by all permutations of:
 * $$\left(±\frac{\cos(\theta)+\sin(\theta)}{2\sqrt2},\,±\frac{\cos(\theta)-\sin(\theta)}{2\sqrt2},\,±\frac{\sqrt2}{4}\right).$$