Hexacosichoron

The hexacosichoron, also known as the 600-cell, is one of the six convex regular polychora. It consists of 600 tetrahedra that join 5 to an edge and 20 to a vertex.

Vertex coordinates
Coordinates for vertices of a hexacosichoron of side length 1 can be given by all permutations of:


 * (±(1+√5)/2, 0, 0, 0),
 * (±(1+√5)/4, ±(1+√5)/4, ±(1+√5)/4, ±(1+√5)/4),

and all even permutations of


 * (±(3+√5)/4, ±(1+√5)/4, ±1/2, 0).

The first two vertex sets define the vertices of an inscribed icositetrachoron.