Hexagrammatic disnub octahedron

The hexagrammatic disnub octahedron, hidso, or compound of eight octahedra is a uniform polyhedron compound. It consists of 16+64 triangles (all of which form coplanar pairs, forming 8+24 hexagrams), with 4 triangles joining at each vertex.

It is a special case of the more general disnub octahedron, with a rotation angle of $$\arccos\left(\frac{3\sqrt5-1}{8}\right) \approx 44.47751^\circ$$.

Its quotient prismatic equivalent is the triangular antiprismatic octaexoorthowedge, which is ten-dimensional.

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