Paper by Martin L. Demaine

Reference:

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.

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.

Length:

The paper is 6 pages.

Availability:

The paper is available in PostScript (3211k), gzipped PostScript (956k), and PDF (979k).

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Related papers:

Zippers_CCCG2010 (Zipper Unfoldings of Polyhedral Complexes)

Related webpages:

Zipper Unfolding