Snub disoctahedron

The snub disoctahedron, siddo, or compound of two icosahedra is a uniform polyhedron compound. It consists of 40 triangles (8 pairs of which form hexagrams due to following in the same plane), with five faces joining at a vertex.

The icosahedra have pyritohedral symmetry, and can be seen as two forms of alternation of the semi-uniform truncated octahedron that is its convex hull.

Its quotient prismatic equivalent is the pyritohedral icosahedral antiprism, which is four-dimensional.

Vertex coordinates
The vertices of a snub disoctahedron of edge length 1 can be given by all permutations of:
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,0\right).$$