Physical Sciences and Mathematics Commons^™

On The Development Of The Intersection Of A Plane With A Polytope, Joseph O'Rourke

Computer Science: Faculty Publications

Define a “slice” curve as the intersection of a plane with the surface of a polytope, i.e., a convex polyhedron in three dimensions. We prove that a slice curve develops on a plane without self-intersection. The key tool used is a generalization of Cauchy's arm lemma to permit nonconvex “openings” of a planar convex chain.