ABSTRACT: A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in O+(3,1), with fundamental domain a geodesic simple in H3 (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. This is joint work with Jean F. Lafont (Ohio State University).