Zipper Unfoldings of Polyhedral Complexes
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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.
Date issued
2010-08Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
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