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

Authors

Joseph O'Rourke, Smith CollegeFollow

Document Type

Article

Publication Date

1-2003

Publication Title

Computational Geometry

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.

Keywords

Polyhedron, Polytope, Development, Unfolding

Volume

24

Issue

1

First Page

3

Last Page

10

DOI

dx.doi.org/10.1016/S0925-7721(02)00044-5

ISSN

0925-7721

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Comments

Author’s submitted manuscript.

Licensed CC-BY-NC-ND at the request of the publisher.

Recommended Citation

O'Rourke, Joseph, "On the Development of the Intersection of a Plane With a Polytope" (2003). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/69