Snub disicositetrachoron

The snub disicositetrachoron, or sadi, also commonly called the snub 24-cell, is a convex uniform polychoron that consists of 24+96 regular tetrahedra and 24 regular icosahedra. 5 tetrahedra and 3 icosahedra join at each vertex, forming a tridiminished icosahedron as the vertex figure.

It can be constructed by alternating the vertices of a truncated icositetrachoron and then adjusting for equal edge lengths. Alternatively, it can be thought of as a diminishing of the regular hexacosichoron, where 24 vertices corresponding to the vertices of an inscribed icositetrachoron are removed.

Vertex coordinates
The vertices of a snub disicositetrachoron of edge length 1, centered at the origin, are given by all even permutations of:
 * (±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{2}$)/4, ±1/2, 0).