Snub hexecontatetrasnub-snub disoctachoron

The snub hexecontatetrasnub-snub disoctachoron, or siggissido, is a nonconvex uniform polychoron that consists of 8 icosahedra, 8 great icosahedra, 64+96 regular octahedra, and 192 tetrahedra. 1 icosahedron, 1 great icosahedron, 4+6 octahedra, and 8 tetrahedra join at each vertex.

This polychoron has pyritohexadecachoric symmetry, with the icosahedra and great icosahedra acting as snub tetrahedra. It can be thought as a kind of sub-symmetrical faceting of the small stellated hecatonicosachoron.

It was discovered on January 28, 2021, by Polytope Discord user _Geometer. Following the discovery of six uniforms the previous year its discovery led to the find of several hundred additional uniforms in the same regiment.

Vertex coordinates
The vertices of a snub hexecontatetrasnub-snub disoctachoron of edge length 1, centered at the origin, are given by all even permutations of:

$$\biggl(\pm\frac{1+\sqrt{5}}{4},\pm\frac{\sqrt{5}-1}{4},\pm\frac{1}{2},0\biggr).$$