2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130469The rich theory of Coxeter groups is used to provide an algebraic construction of finite volume hyperbolic n-manifolds. Combinatorial properties of finite images of these groups can be used to compute the volumes of the resulting manifolds. Three examples, in 4,5 and 6-dimensions, are given, each of very small volume, and in one case of smallest possible volume.No major changes, just some minor improvements and correctionsGeometric TopologyGroup Theorytext