Editing 24-cell (section)

=== As a configuration ===
This [[Regular 4-polytope#As configurations|configuration matrix]]{{Sfn|Coxeter|1973|p=12|loc=§1.8. Configurations}} represents the 24-cell. The rows and columns correspond to vertices, edges, faces, and cells. The diagonal numbers say how many of each element occur in the whole 24-cell. The non-diagonal numbers say how many of the column's element occur in or at the row's element.

<math display="block">\begin{bmatrix}\begin{matrix}24 & 8 & 12 & 6 \\ 2 & 96 & 3 & 3 \\ 3 & 3 & 96 & 2 \\ 6 & 12 & 8 & 24 \end{matrix}\end{bmatrix}</math>

Since the 24-cell is self-dual, its matrix is identical to its 180 degree rotation.