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.
Polyhedron, Polytope, Development, Unfolding
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O'Rourke, Joseph, "On the Development of the Intersection of a Plane With a Polytope" (2003). Faculty Publications. Paper 69.