Hexagrammatic disnub tetrahedron

The hexagrammatic disnub tetrahedron, hidsit, or pyritohedral compound of four octahedra 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 $$\arccos\left(\frac{3\sqrt5-1}{8}\right) \approx 44.47751^\circ$$.

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

Its quotient prismatic equivalent is the triangular antiprismatic pyritotetrahedroorthowedge, which is six-dimensional.

Vertex coordinates
The vertices of a hexagrammatic disnub tetrahedron of edge length 1 are given by all even permutations of:
 * $$\left(\pm\frac{\sqrt2}{4},\,\pm\frac{\sqrt2+\sqrt{10}}{8},\,\pm\frac{\sqrt{10}-\sqrt2}{8}\right).$$