  Consider a group $G$ acting nicely on a simply-connected simplicial complex
$X$. Numerous classical methods exist for using this group action to produce a
presentation for $G$. For the case that $X/G$ is 2-connected, we give a new
method that has the novelty that one does not have to identify a fundamental
domain for the action. Indeed, the resulting presentation is canonical in the
sense that no arbitrary choices need to be made. It can be viewed as a
nonabelian analogue of a simple result in the study of equivariant homology.
