{"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","publisher":"Canadian Conference on Computational Geometry","abstract":[{"lang":"eng","text":"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 hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. "}],"related_material":{"record":[{"status":"public","id":"8317","relation":"extended_version"}]},"article_processing_charge":"No","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"conference":{"location":"Edmonton, Canada","name":"CCCG: Canadian Conference in Computational Geometry","end_date":"2019-08-10","start_date":"2019-08-08"},"publication_status":"published","citation":{"ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry; 2019:164-170.","ieee":"O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” in <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Edmonton, Canada, 2019, pp. 164–170.","chicago":"Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” In <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, 164–70. Canadian Conference on Computational Geometry, 2019.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i> (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–170.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Canadian Conference on Computational Geometry, 2019, pp. 164–70.","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 164–170."},"scopus_import":"1","acknowledgement":"This research was performed in part at the 33rd BellairsWinter  Workshop  on  Computational  Geometry.    Wethank all other participants for a fruitful atmosphere.","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"first_name":"Hugo A","full_name":"Akitaya, Hugo A","last_name":"Akitaya"},{"full_name":"Cheung, Kenneth C","last_name":"Cheung","first_name":"Kenneth C"},{"full_name":"Demaine, Erik D","last_name":"Demaine","first_name":"Erik D"},{"full_name":"Demaine, Martin L","last_name":"Demaine","first_name":"Martin L"},{"first_name":"Sandor P","last_name":"Fekete","full_name":"Fekete, Sandor P"},{"full_name":"Kleist, Linda","last_name":"Kleist","first_name":"Linda"},{"first_name":"Irina","full_name":"Kostitsyna, Irina","last_name":"Kostitsyna"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"last_name":"Masárová","full_name":"Masárová, Zuzana","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322"},{"last_name":"Mundilova","full_name":"Mundilova, Klara","first_name":"Klara"},{"full_name":"Schmidt, Christiane","last_name":"Schmidt","first_name":"Christiane"}],"date_published":"2019-08-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://cccg.ca/proceedings/2019/proceedings.pdf"}],"year":"2019","day":"01","type":"conference","status":"public","date_created":"2019-11-04T16:46:11Z","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","page":"164-170","month":"08","date_updated":"2023-08-04T10:57:42Z","_id":"6989","title":"Folding polyominoes with holes into a cube","quality_controlled":"1","external_id":{"arxiv":["1910.09917"]},"department":[{"_id":"HeEd"}]}