  We investigate subgroups of SL (n,Z) which preserve an open nondegenerate
convex cone in real n-space and admit in that cone as fundamental domain a
polyhedral cone of which some faces are allowed to lie on the boundary.
Examples are arithmetic groups acting on selfdual cones, Weyl groups of certain
Kac-Moody algebras and do occur in algebraic geometry as the automorphism
groups of projective manifolds acting on their ample cones.
