  A 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.
