An algorithm for classification of fundamental polygons for a plane discontinuous group
An algorithm and the computer program for complete enumeration of combinatorial equivalence classes of fundamental polygons for any fixed plane discontinuous group is given. This result is due to Delone for the Euclidean plane but for hyperbolic plane it is a long standing problem. \par Some nontrivial bounds on the number of vertices and edges of the fundamental polygon of the plane discontinuous group in the term of its Macbeath signature is given. \par For some concrete groups a full lists of its fundamental polygons are obtained. For the entire collection see [Zbl 1400.52002].
scientific article; zbMATH DE number 7049370