Small snubahedron

The small snubahedron, sis, or compound of six tetrahedra with rotational freedom is a uniform polyhedron compound. It consists of 24 triangles, with three faces joining at a vertex.

This compound has rotational freedom, represented by an angle θ. At θ = 0°, all six tetrahedra coincide. We rotate these tetrahedra around their 2-fold axes of symmetry (2 each), seeing them as digonal antiprisms. At θ = 45° the compound has double symmetry resulting in the snubahedron.

This compound can be formed by taking one of the tetrahedra inscribed in each cube of the rhombisnub dishexahedron.

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