THE GEOMETRY OF CROOKED PLANES

Crooked planes are polyhedra used to construct fundamental polyhedra for discrete groups of Lorentz isometries acting properly on Minkowski (2+1)-space. This paper explores intersections of crooked planes. Criteria for the disjointness of crooked planes are developed. These criteria are applied to derive sufficient conditions for affine deformations of a discrete subgroup of SO(2, 1) to act properly on Minkowski space.