We describe an experimental method for studying the combinatorics of Dirichlet domains in the complex hyperbolic plane based on numerical and graphical techniques. We apply our techniques to the complex reflection groups that appear in Mostow's seminal paper on the subject and list a number of corrections to the combinatorics of the Dirichlet domains.
"Dirichlet Domains for the Mostow Lattices." Experiment. Math. 14 (4) 467 - 490, 2005.