ABSTRACT
Suppose that P is a finite-volume polyhedron in H3 each of whose dihedral angles is an integer submultiple of π. Then the group Λ(P ) generated by reflections in the faces of P is a discrete subgroup of Isom(H3). If one restricts attention to the subgroup Γ(P ) consisting of orientationpreserving elements of Λ(P ), one naturally obtains a discrete subgroup of PSL(2,C) ∼= Isom+(H3). This very classical family of finite-covolume Kleinian groups is known as the family of polyhedral reflection groups.
