Schläfli symbol

Summary

The Schläfli symbol is a short notation $\set{p, q, r, \dots}$ for a regular polytope. The first entry gives the polygons that form the two-dimensional faces. Each further entry says how many of the previous pieces meet around a face of lower dimension. The symbol determines the regular polytope up to similarity, and reversing it gives the dual polytope. It is the main bookkeeping tool in the classification of regular polytopes.