Von Dyck group

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This article defines a family of groups whose members are parametrized by tuples of natural numbers. In other words, for every tuple of natural numbers, there is a unique corresponding group (upto isomorphism) in that family

Definition

For natural numbers $l,m,n$, the von Dyck group $D(l,m,n)$ is defined by the following presentation:

$<a,b,c|a^l=b^m=c^n=abc=1>$

This is a subgroup of index two in the triangle group, but some people use the term triangle group for the von Dyck group.