Zipper Unfoldings of Polyhedral Complexes
Name
Demaine_Zipper unfoldings.pdf
Size
2.72 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Demaine, Erik D.
Demaine, Martin L.
Lubiw, Anna
Shallit, Arlo
Shallit, Jonah L.
Date Issued
August 2010
Journal
Proceedings of the 22nd Canadian Conference on Computational Geometry, 2010, (CCCG 2010)
Publisher
University of Manitoba
Citation
Demaine, Erik D. et al. "Zipper Unfoldings of Polyhedral Complexes." 22nd Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg MB, August 9-11, 2010.
Version
Author's final manuscript
Abstract
We explore which polyhedra and polyhedral complexes
can be formed by folding up a planar polygonal region
and fastening it with one zipper. We call the reverse
process a zipper unfolding. A zipper unfolding of a
polyhedron is a path cut that unfolds the polyhedron
to a planar polygon; in the case of edge cuts, these are
Hamiltonian unfoldings as introduced by Shephard in
1975. We show that all Platonic and Archimedean solids
have Hamiltonian unfoldings.
We give examples of polyhedral complexes that are,
and are not, zipper [edge] unfoldable. The positive examples
include a polyhedral torus, and two tetrahedra
joined at an edge or at a face.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
http://www.cs.umanitoba.ca/~cccg2010/accepted.html
