2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103851If a (cusped) surface S admits an ideal triangulation T with no shears, we show an efficient algorithm to give S as a quotient of hypebolic plane by a subgroup of PSL(2, Z). The algorithm runs in time O(n log n), where n is the number of triangles in the triangulation T. The algorithm generalizes to producing fundamental groups of general surfaces and geometric manifolds of higher dimension.6 pages, 2 figuresGeometric TopologyCombinatorics57M15; 57M50; 57M05; 68w40; 11F06text