Zipper unfolding of domes and prismoids
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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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2015
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| Online Access: | http://hdl.handle.net/1721.1/100407 https://orcid.org/0000-0003-3803-5703 |
| _version_ | 1826201779221561344 |
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| author | Demaine, Erik D. Demaine, Martin L. Uehara, Ryuhei |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Demaine, Erik D. Demaine, Martin L. Uehara, Ryuhei |
| author_sort | Demaine, Erik D. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:56:38Z |
| format | Article |
| id | mit-1721.1/100407 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:56:38Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | mit-1721.1/1004072022-10-01T07:10:13Z Zipper unfolding of domes and prismoids Demaine, Erik D. Demaine, Martin L. Uehara, Ryuhei Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Demaine, Erik D. Demaine, Martin L. 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) 2015-12-17T12:17:46Z 2015-12-17T12:17:46Z 2013-08 Article http://purl.org/eprint/type/ConferencePaper http://hdl.handle.net/1721.1/100407 Demaine, Erik D., Martin L. Demaine, and Ryuhei Uehara. "Zipper unfolding of domes and prismoids." 25th Canadian Conference on Computational Geometry (August 2013). https://orcid.org/0000-0003-3803-5703 en_US http://www.cccg.ca/proceedings/2013/ Proceedings of the 25th Canadian Conference on Computational Geometry Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf MIT web domain |
| spellingShingle | Demaine, Erik D. Demaine, Martin L. Uehara, Ryuhei Zipper unfolding of domes and prismoids |
| title | Zipper unfolding of domes and prismoids |
| title_full | Zipper unfolding of domes and prismoids |
| title_fullStr | Zipper unfolding of domes and prismoids |
| title_full_unstemmed | Zipper unfolding of domes and prismoids |
| title_short | Zipper unfolding of domes and prismoids |
| title_sort | zipper unfolding of domes and prismoids |
| url | http://hdl.handle.net/1721.1/100407 https://orcid.org/0000-0003-3803-5703 |
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