Edge-Unfolding Nested Polyhedral Bands

Authors

Greg Aloupis, Université McGill
Erik D. Demaine, MIT Computer Science & Artificial Intelligence Laboratory
Stefan Langerman, Université Libre de Bruxelles
Pat Morin, Carleton University
Joseph O'Rourke, Smith CollegeFollow
Ileana Streinu, Smith CollegeFollow
Godfried Toussaint, Université McGill

Document Type

Conference Proceeding

Publication Date

1-1-2008

Publication Title

Computational Geometry: Theory and Applications

Abstract

A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the other in the projection orthogonal to the parallel planes, then the band is nested. We prove that all nested bands can be unfolded, by cutting along exactly one edge and folding continuously to place all faces of the band into a plane, without intersection. © 2007 Elsevier B.V.

Keywords

Folding, Polyhedra, Slice curves

Volume

39

Issue

1

First Page

30

Last Page

42

DOI

10.1016/j.comgeo.2007.05.009

ISSN

09257721

Rights

© the authors

Comments

Author submitted manuscript

Recommended Citation

Aloupis, Greg; Demaine, Erik D.; Langerman, Stefan; Morin, Pat; O'Rourke, Joseph; Streinu, Ileana; and Toussaint, Godfried, "Edge-Unfolding Nested Polyhedral Bands" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/192