Hyperbolic 3-space is the set H~3 = {(x_1,x_2,x_3)∈ R~3:x_3 >0} endowed with the complete Riemannian metric ds = |dx|/x_3 of constant curvature equal to -1. A Kleinian group G is a discrete nonelementary subgroup of Isom~+(H~3), where Isom~+(H~3) is the group of orientation preserving isometries. In this setting, nonelementary means that the group G is not virtually abelian. Finally a hyperbolic 3-orbifold Q is the orbit space of a Kleinian group G, Q = H~3/G. (1.1) The orbit space is a hyperbolic 3-manifold if the group G is torsion-free. For the general facts about hyperbolic geometry and Kleinian groups we refer the reader to the monographs, and [23].
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