Folding polyominoes with holes into a cube
When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube fold...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/129567 |
| _version_ | 1811089932406489088 |
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| author | Demaine, Erik D Demaine, Martin L Mundilova, Klara |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Demaine, Erik D Demaine, Martin L Mundilova, Klara |
| author_sort | Demaine, Erik D |
| collection | MIT |
| description | When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability. |
| first_indexed | 2024-09-23T14:27:20Z |
| format | Article |
| id | mit-1721.1/129567 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:27:20Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1295672022-09-29T09:33:12Z Folding polyominoes with holes into a cube Demaine, Erik D Demaine, Martin L Mundilova, Klara Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability. 2021-01-26T15:49:21Z 2021-01-26T15:49:21Z 2021-02 2020-12-09T15:54:35Z Article http://purl.org/eprint/type/JournalArticle 0925-7721 https://hdl.handle.net/1721.1/129567 Aichholzer, Oswin et al. “Folding polyominoes with holes into a cube.” Computational Geometry: Theory and Applications, 93 (Feruary 2021): 101700 © 2021 The Author(s) en 10.1016/j.comgeo.2020.101700 Computational Geometry: Theory and Applications Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Demaine, Erik D Demaine, Martin L Mundilova, Klara Folding polyominoes with holes into a cube |
| title | Folding polyominoes with holes into a cube |
| title_full | Folding polyominoes with holes into a cube |
| title_fullStr | Folding polyominoes with holes into a cube |
| title_full_unstemmed | Folding polyominoes with holes into a cube |
| title_short | Folding polyominoes with holes into a cube |
| title_sort | folding polyominoes with holes into a cube |
| url | https://hdl.handle.net/1721.1/129567 |
| work_keys_str_mv | AT demaineerikd foldingpolyominoeswithholesintoacube AT demainemartinl foldingpolyominoeswithholesintoacube AT mundilovaklara foldingpolyominoeswithholesintoacube |