Zipper unfolding of domes and prismoids
Author(s)Demaine, Erik D.; Demaine, Martin L.; Uehara, Ryuhei
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 25th Canadian Conference on Computational Geometry
Demaine, Erik D., Martin L. Demaine, and Ryuhei Uehara. "Zipper unfolding of domes and prismoids." 25th Canadian Conference on Computational Geometry (August 2013).
Author's final manuscript