2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66023Let $P$ be a simplex in $S^n$ and $G_P$ be a group generated by the reflections with respect to the facets of $P$. We are interested in the case when the group $G_P$ is discrete. In this case we say that $G$ generates the discrete reflection group $G_P$. We develop the criteria for a simplex generating a discrete reflection group. We also describe all indecomposable spherical simplices generating discrete reflection groups.21 pages, 3 figures, 4 tablesMetric GeometryGroup Theorytext