These relations can be rewritten in the special form that defines the Coxeter groups, so the affine symmetric groups are Coxeter groups, with the s i as their Coxeter generating sets. Each Coxeter group may be represented by a Coxeter–Dynkin diagram, in which vertices correspond to generators and edges encode the relations between them. For n ≥ ≥ 3 , the Coxeter–Dynkin diagram of S ~ ~ n is the n -cycle (where the edges correspond to the relations between pairs of consecutive generators and the absence of an edge between other pairs of generators indicates that they commute), while for n = 2 it consists of two nodes joined by an edge labeled ∞ ∞ .