A method for constructing the fundamental region of a discontinuous group of linear transformations
J. I. Hutchinson · Transactions of the American Mathematical Society · 1907
Two methods at present exist for the construction of the fundamental region of a discontinuous group.t The one applies only to groups which are capable of extension by reflection and consists in constructing first the region for the extended group (which can be done by a direct process) and then combining two such regions that are adjacent. The other method uses the process of the continuous reduction of a quadratic form. It is, however, tedious in application, and this fact appears to place a narrow restriction on its range of practical effectiveness. In the following pages I propose a much more simple and effective method, applicable to groups which leave a given Hermitian form invariant.