Edge-unfolding nested polyhedral bands

Greg Aloupis, Erik D. Demaine, Stefan Langerman, Pat Morin, Joseph O'Rourke, Ileana Streinu, Godfried Toussaint

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)30-42
Number of pages13
JournalComputational Geometry: Theory and Applications
Volume39
Issue number1
DOIs
StatePublished - Jan 1 2008

Fingerprint

Unfolding
Intersection
Polyhedron
Convex polyhedron
Convex polygon
Orthogonal Projection
Folding
Polygon
Face

Keywords

  • Folding
  • Polyhedra
  • Slice curves

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

Aloupis, G., Demaine, E. D., Langerman, S., Morin, P., O'Rourke, J., Streinu, I., & Toussaint, G. (2008). Edge-unfolding nested polyhedral bands. Computational Geometry: Theory and Applications, 39(1), 30-42. https://doi.org/10.1016/j.comgeo.2007.05.009

Edge-unfolding nested polyhedral bands. / Aloupis, Greg; Demaine, Erik D.; Langerman, Stefan; Morin, Pat; O'Rourke, Joseph; Streinu, Ileana; Toussaint, Godfried.

In: Computational Geometry: Theory and Applications, Vol. 39, No. 1, 01.01.2008, p. 30-42.

Research output: Contribution to journalArticle

Aloupis, G, Demaine, ED, Langerman, S, Morin, P, O'Rourke, J, Streinu, I & Toussaint, G 2008, 'Edge-unfolding nested polyhedral bands', Computational Geometry: Theory and Applications, vol. 39, no. 1, pp. 30-42. https://doi.org/10.1016/j.comgeo.2007.05.009
Aloupis G, Demaine ED, Langerman S, Morin P, O'Rourke J, Streinu I et al. Edge-unfolding nested polyhedral bands. Computational Geometry: Theory and Applications. 2008 Jan 1;39(1):30-42. https://doi.org/10.1016/j.comgeo.2007.05.009
Aloupis, Greg ; Demaine, Erik D. ; Langerman, Stefan ; Morin, Pat ; O'Rourke, Joseph ; Streinu, Ileana ; Toussaint, Godfried. / Edge-unfolding nested polyhedral bands. In: Computational Geometry: Theory and Applications. 2008 ; Vol. 39, No. 1. pp. 30-42.
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