ABSTRACT
The ordinary Schla¨fli symbol, {p, q} in Coxeter’s version (Schla¨fli wrote (p, q) and Hoppe (p|q)), denotes the Platonic solid whose faces are regular p-gons and whose vertex figures are regular q-gons. In this chapter, we describe a generalization we call the “generalized Schla¨fli symbol of Dress and Delaney” that works for all topologically spherical polyhedra (and as we shall see later, also in higher dimensions). Andreas Dress, who really coined the symbol, called it the “Delaney Symbol” because he got the idea from a paper of M. Delaney. Our changed name reflects the fact that the version we present here visibly generalizes the Schla¨fli symbol.
