Recently I needed the vertices and cells of a regular 4D polychoron - the 120-cell. After investing some effort, I have computed the vertex positions and cell indices. They did not fulfill the original purpose, however, still, someone might find those useful. The vertex table contains indices to values that are repeated, here is the key:
| v0= | 0 |
| v1= | 1 |
| v2= | sqrt(5) |
| v3= | (1+v2)/2 |
| v4= | 1/(v3*v3) |
| v5= | v3*v3 |
| v6= | 1/v3 |
| v7= | 2 |
Negative index means you should take negative of the given value. So, here is the list of vertices: vertices.txt
The cells are 120 dodecahedra, each consisting of 20 vertices that share the same hyperplane. Here are the indices: cells.txt
If you need a 600-cell, you can obtain it easily by taking the dual: each cell becomes a vertex, each vertex becomes a cell. You may also need the list of adjacent vertices for each vertex (which also works as a list of edges). Here it is: neighbours.txt
Hope this helps someone :)