Hexagrammatic disnub tetrahedron

The hexagrammatic disnub tetrahedron, hidsit, or compound of four octahedra with rotational freedom is a uniform polyhedron compound. It consists of 8+24 triangles (the set of 24 falling into coplanar pairs forming 12 hexagrams), with 4 triangles joining at each vertex.

It is a special case of the more general disnub tetrahedron, with a rotation angle of acos((3√5–1)/8) ≈ 44.47751º.

It can be formed by removing one component from the small icosicosahedron.

Vertex coordinates
The vertices of a hexagrammatic disnub tetrahedron of edge length 1 are given by all even permutations of:
 * (±$\sqrt{2}$/4, ±($\sqrt{6}$+$\sqrt{2}$)/8, ±($\sqrt{2}$–$\sqrt{2}$)/8)