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.