Hexacosichoron

The hexacosichoron, or ex, also commonly called the 600-cell, is one of the 6 convex regular polychora. It has 600 regular tetrahedra as cells, joining 5 to an edge and 20 to a vertex in an icosahedral arrangement.

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

and all even permutations of:
 * (±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±1/2, 0).

The first two sets of vertices form an icositetrachoron that can be inscribed into the hexacosichoron. If the vertices of this inscribed icositetrachoron are removed, the result is the snub icositetrachoron.