Line arrangements in H3

If M = H-3/G is a hyperbolic manifold and.. M is a simple closed geodesic, then. lifts to a collection of lines in H-3 acted upon by G. In this paper we show that such a collection of lines cannot contain a particular type of subset ( called a bad triple) unless G has orientation-reversing elements. This fact allows us to extend certain lower bounds on hyperbolic volume to the non-orientable case.