2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226383A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in the isometry group of hyperbolic 3-space, with fundamental domain a geodesic simplex (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examples. We provide a complete computation of the lower algebraic K-theory of the integral group ring of all the hyperbolic 3-simplex reflection groups.33 pages, 2 figures, 7 tablesK-Theory and HomologyGeometric Topologytext