On the Development of the Intersection of a Plane with a Polytope
Abstract
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 selfintersection. The key tool used is a generalization of Cauchy's arm lemma to permit nonconvex ``openings'' of a planar convex chain.
 Publication:

arXiv eprints
 Pub Date:
 June 2000
 arXiv:
 arXiv:cs/0006035
 Bibcode:
 2000cs........6035O
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics;
 F.2.2
 EPrint:
 11 pages, 8 figures. Earlier version replaced after I discovered Schur's 1921 theorem, whose proof can be followed to establish the key generalization of Cauchy's arm lemma, my Theorem 1. Paper revised accordingly. New (2006) version corrects two errors in the proofs found by Raghavan Dhandapani