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

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

2000-06-26

arxiv.org/abs/cs/0006035v4

Computer Science

Computational Geometry

11 pages, 8 figures. Earlier version replaced after I discovered Schur's 1921 theorem, whose proof can be followed to establis

Scientific paper

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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