Finitely Generated Groups

Abstract

We recall that a side s of a convex fundamental polygon P is a segment of the form $\tilde P \cap g(\tilde P)$ (except that this set may be considered as two sides when g is elliptic and of order two). By an edge of P we mean a maximal geodesic segment in ∂P. We must distinguish carefully between sides and edges and to convince the reader of the necessity of this, we begin with an example in which one edge contains infinitely many sides.