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On the Development of the Intersection of a Plane with a Polytope

Joseph O'Rourke
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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 self-intersection. The key tool used is a generalization of Cauchy's arm lemma to permit nonconvex ``openings'' of a planar convex chain.

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Joseph O'Rourke. 2006-08-03. On the Development of the Intersection of a Plane with a Polytope. https://arxiv.org/abs/cs/0006035

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