How to get a 600-cell
We can visualize the 600-cell (that is one of the six regular polytopes in dimension 4) in this way. We take a 24-cell, another of the six polytopes, made of 24 octahedra, and we imagine to inscribe each octahedron in an icosahedron, which is divided in 20 tetrahedra. In this way, we position 480 tetrahedra; the other 120 can be thought as disposed around the vertices of the 24-cell, at groups of five around each vertex.
immagine di Gian Marco Todesco