{"_id":"6989","oa":1,"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. "}],"date_created":"2019-11-04T16:46:11Z","page":"164-170","month":"08","publisher":"Canadian Conference on Computational Geometry","author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"full_name":"Akitaya, Hugo A","last_name":"Akitaya","first_name":"Hugo A"},{"first_name":"Kenneth C","full_name":"Cheung, Kenneth C","last_name":"Cheung"},{"first_name":"Erik D","last_name":"Demaine","full_name":"Demaine, Erik D"},{"first_name":"Martin L","last_name":"Demaine","full_name":"Demaine, 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","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"first_name":"Maarten","full_name":"Löffler, Maarten","last_name":"Löffler"},{"last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"},{"first_name":"Klara","full_name":"Mundilova, Klara","last_name":"Mundilova"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","quality_controlled":"1","day":"01","article_processing_charge":"No","external_id":{"arxiv":["1910.09917"]},"department":[{"_id":"HeEd"}],"conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"title":"Folding polyominoes with holes into a cube","language":[{"iso":"eng"}],"oa_version":"Published Version","publication_status":"published","date_updated":"2023-08-04T10:57:42Z","related_material":{"record":[{"relation":"extended_version","id":"8317","status":"public"}]},"scopus_import":"1","status":"public","acknowledgement":"This research was performed in part at the 33rd BellairsWinter  Workshop  on  Computational  Geometry.    Wethank all other participants for a fruitful atmosphere.","year":"2019","type":"conference","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","main_file_link":[{"url":"https://cccg.ca/proceedings/2019/proceedings.pdf","open_access":"1"}],"citation":{"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.","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.","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.","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."},"date_published":"2019-08-01T00:00:00Z"}