Geometry
Vertices and cells of a 120-cell
Recently I needed the vertices and cells of a regular 4D polychoron — the120-cell. After investing some effort, I have computed the vertex positions and cell indices. They did not fulfill the original purpose, however someone might still find them 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 |
A negative index means you should take the negative of the given value. The list of vertices:vertices.txt.
The cells are 120 dodecahedra, each consisting of 20 vertices that share the same hyperplane. Indices:cells.txt.
If you need a 600-cell, you can obtain it 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):neighbours.txt.
Hope this helps someone :)