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.

Removing one set of an inscribed icositetrachoron's vertices on the snub disicositetrachoron yields a bi-icositetradiminished hexacosichoron, while removing two sets yields a tri-icositetradiminished hexacosichoron

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+$\sqrt{5}$)/4, ±1/2, 0).