Retroantiprismatosnub disicositetrachoron

The retroantiprismatosnub disicositetrachoron, or rappisdi, is a nonconvex uniform polychoron that consists of 96 regular octahedra, 24 icosahedra, and 24 great icosahedra. 6 octahedra, 3 icosahedra, and 3 great icosahedra join at each vertex.

This polychoron has the same symmetry as the snub disicositetrachoron, with the octahedra acting as triangular antifrusta. It can be thought as a partial faceting of the small stellated hecatonicosachoron.

Vertex coordinates
The vertices of a retroantiprismatosnub disicositetrachoron of edge length 1, centered at the origin, are given by all even permutations of:


 * $$\left(±\frac{1+\sqrt{5}}{4},\,±\frac{\sqrt{5}-1}{4},\,±\frac{1}{2},\,0\right).$$

Related polychora
The retroantiprismatosnub disicositetrachoron shares its vertices and edges with the small retrohemiantiprismatosnub prismatodisicositetrachoron and great retrohemiantiprismatosnub prismatodisicositetrachoron.