Zipper unfolding of domes and prismoids

• Main Authors: Demaine, Erik D. (Contributor), Demaine, Martin L. (Contributor), Uehara, Ryuhei (Author)
• Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: 2015-12-17T12:17:46Z.
• Subjects: Article
• Online Access: Get fulltext

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.
National Science Foundation (U.S.) (Origami Design for Integration of Self-assembling Systems for Engineering Innovation Grant EFRI-1240383)
National Science Foundation (U.S.) (Expedition Grant CCF-1138967)