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:
 * (±(cos(θ)+sin(θ))$\sqrt{6}$/4, ±(cos(θ)–sin(θ))$\sqrt{6}$/4, ±$\sqrt{2}$/4)