Line Arrangements in H3

If$M = \mathbb{H}^3/G $is a hyperbolic manifold and$\gamma \subset M$is a simple closed geodesic, then γ lifts to a collection of lines in H3acted 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-orient able case.