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.
The goal of this paper is to give a conjectural census of complex hyperbolic sporadic triangle groups. We prove that only finitely many of these sporadic groups are lattices. We also give a conjectural list of all lattices among sporadic groups, and for each group in the list we give a conjectural group presentation, as well as a list of cusps and… (More)