Paper by Martin L. Demaine
- Erik D. Demaine, Martin L. Demaine, and Ryuhei Uehara, “Zipper Unfolding of Domes and Prismoids”, in Proceedings of the 25th Canadian Conference on Computational Geometry (CCCG 2013), Waterloo, Ontario, Canada, August 8–10, 2013, to appear.
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.
- The paper is 6 pages.
- The paper is available in PostScript (3211k), gzipped PostScript (956k), and PDF (979k).
- See information on file formats.
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- Related papers:
- Zippers_CCCG2010 (Zipper Unfoldings of Polyhedral Complexes)
- Related webpages:
- Zipper Unfolding
See also other papers by Martin Demaine.
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