Zipper Unfoldability of Domes and Prismoids

• Demaine, Erik D.

• Demaine, Martin L.

• Uehara, Ryuhei

Abstract

We study Hamiltonian unfolding-cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap, which could be implemented by a single zipper-of two classes of polyhedra. First we consider domes, which are simple convex polyhedra. We find a series 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.

identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/11621

Journal

• Proceedings of the 25th Canadian Conference on Computational Geometry (CCCG 2013)

  Proceedings of the 25th Canadian Conference on Computational Geometry (CCCG 2013) 43-48, 2013-08

  CCCG

Keywords

• edge unfolding
• zipper unfolding
• paper folding
• dome
• prismoid

Details

• CRID: 1050574047097902208
• NII Article ID: 120006675377
• Web Site: http://hdl.handle.net/10119/11621
• Text Lang: en
• Article Type: conference paper
• Data Source:
  • IRDB
  • CiNii Articles