Zipper unfolding of domes and prismoids
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Demaine_Zipper unfolding.pdf
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1.13 MB
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Author(s)
Demaine, Erik D.
Demaine, Martin L.
Uehara, Ryuhei
Date Issued
August 2013
Journal
Proceedings of the 25th Canadian Conference on Computational Geometry
Citation
Demaine, Erik D., Martin L. Demaine, and Ryuhei Uehara. "Zipper unfolding of domes and prismoids." 25th Canadian Conference on Computational Geometry (August 2013).
Version
Author's final manuscript
Abstract
We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. First we consider domes, which are simple convex polyhedra. We find a family of domes whose graphs are Hamiltonian, yet any Hamiltonian unfolding causes overlap, making the domes Hamiltonian-ununfoldable. Second we turn to prismoids, which are another family of simple convex polyhedra. We show that any nested prismoid is Hamiltonian-unfoldable, and that for general prismoids, Hamiltonian unfoldability can be tested in polynomial time.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://www.cccg.ca/proceedings/2013/
