{"date_published":"2021-02-01T00:00:00Z","publication_identifier":{"issn":["09257721"]},"month":"02","publication_status":"published","date_created":"2020-08-30T22:01:09Z","related_material":{"record":[{"id":"6989","relation":"shorter_version","status":"public"}]},"year":"2021","citation":{"ieee":"O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” <i>Computational Geometry: Theory and Applications</i>, vol. 93. Elsevier, 2021.","chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. <i>Computational Geometry: Theory and Applications</i>. 2021;93. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>","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, Computational Geometry: Theory and Applications 93 (2021).","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Computational Geometry: Theory and Applications</i>, vol. 93, 101700, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>","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. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700."},"project":[{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF"}],"oa_version":"Preprint","volume":93,"_id":"8317","arxiv":1,"author":[{"last_name":"Aichholzer","full_name":"Aichholzer, Oswin","first_name":"Oswin"},{"first_name":"Hugo A.","last_name":"Akitaya","full_name":"Akitaya, Hugo A."},{"first_name":"Kenneth C.","last_name":"Cheung","full_name":"Cheung, Kenneth C."},{"last_name":"Demaine","full_name":"Demaine, Erik D.","first_name":"Erik D."},{"first_name":"Martin L.","full_name":"Demaine, Martin L.","last_name":"Demaine"},{"first_name":"Sándor P.","last_name":"Fekete","full_name":"Fekete, Sándor P."},{"last_name":"Kleist","full_name":"Kleist, Linda","first_name":"Linda"},{"full_name":"Kostitsyna, Irina","last_name":"Kostitsyna","first_name":"Irina"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322"},{"full_name":"Mundilova, Klara","last_name":"Mundilova","first_name":"Klara"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"department":[{"_id":"HeEd"}],"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 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."}],"article_type":"original","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. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","article_number":"101700","title":"Folding polyominoes with holes into a cube","main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"publication":"Computational Geometry: Theory and Applications","scopus_import":"1","corr_author":"1","date_updated":"2025-06-26T12:36:56Z","article_processing_charge":"No","oa":1,"quality_controlled":"1","intvolume":"        93","doi":"10.1016/j.comgeo.2020.101700","day":"01","language":[{"iso":"eng"}],"publisher":"Elsevier","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1910.09917"],"isi":["000579185100004"]},"type":"journal_article","isi":1,"status":"public"}