  The McKay correspondence has had much success in studying resolutions of
3-fold quotient singularities through a wide range of tools coming from
geometry, combinatorics, and representation theory. We develop a computational
perspective in this setting primarily realised through a web application to
explore mutations of quivers with potential and crepant triangulations. We use
this to study flops between different crepant resolutions of Gorenstein toric
quotient singularities and find many situations in which the mutations of a
quiver with potential classifies them. The application also implements key
constructions of the McKay correspondence, including the Craw--Reid procedure
and the process of associating a quiver to a toric resolution.
