[{"scopus_import":"1","month":"08","_id":"6989","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","title":"Folding polyominoes with holes into a cube","page":"164-170","oa":1,"quality_controlled":"1","acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational  Geometry. We thank all other participants for a fruitful atmosphere.","external_id":{"arxiv":["1910.09917"]},"date_created":"2019-11-04T16:46:11Z","day":"01","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"arxiv":1,"type":"conference","date_updated":"2026-06-18T19:14:37Z","publisher":"Canadian Conference on Computational Geometry","article_processing_charge":"No","related_material":{"record":[{"relation":"extended_version","status":"public","id":"8317"}]},"abstract":[{"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. ","lang":"eng"}],"conference":{"start_date":"2019-08-08","location":"Edmonton, Canada","end_date":"2019-08-10","name":"CCCG: Canadian Conference in Computational Geometry"},"ddc":["500"],"oa_version":"Published Version","date_published":"2019-08-01T00:00:00Z","year":"2019","status":"public","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://sites.ualberta.ca/~cccg2019/cccg2019_proceedings.pdf"}],"citation":{"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.","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.","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.","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.","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.","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.","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."},"author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"first_name":"Hugo A","last_name":"Akitaya","full_name":"Akitaya, Hugo A"},{"full_name":"Cheung, Kenneth C","last_name":"Cheung","first_name":"Kenneth C"},{"first_name":"Erik D","full_name":"Demaine, Erik D","last_name":"Demaine"},{"full_name":"Demaine, Martin L","last_name":"Demaine","first_name":"Martin L"},{"last_name":"Fekete","full_name":"Fekete, Sandor P","first_name":"Sandor P"},{"first_name":"Linda","full_name":"Kleist, Linda","last_name":"Kleist"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mundilova","full_name":"Mundilova, Klara","first_name":"Klara"},{"first_name":"Christiane","full_name":"Schmidt, Christiane","last_name":"Schmidt"}]}]