{"title":"Folding polyominoes with holes into a cube","article_number":"101700","date_created":"2020-08-30T22:01:09Z","publisher":"Elsevier","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"month":"02","publication_status":"published","language":[{"iso":"eng"}],"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. 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.","citation":{"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.","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>.","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.","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>.","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).","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>"},"project":[{"call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"year":"2021","related_material":{"record":[{"relation":"shorter_version","status":"public","id":"6989"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"doi":"10.1016/j.comgeo.2020.101700","date_updated":"2023-08-04T10:57:42Z","publication_identifier":{"issn":["09257721"]},"date_published":"2021-02-01T00:00:00Z","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."}],"oa":1,"article_processing_charge":"No","author":[{"last_name":"Aichholzer","full_name":"Aichholzer, Oswin","first_name":"Oswin"},{"full_name":"Akitaya, Hugo A.","first_name":"Hugo A.","last_name":"Akitaya"},{"first_name":"Kenneth C.","full_name":"Cheung, Kenneth C.","last_name":"Cheung"},{"first_name":"Erik D.","full_name":"Demaine, Erik D.","last_name":"Demaine"},{"full_name":"Demaine, Martin L.","first_name":"Martin L.","last_name":"Demaine"},{"full_name":"Fekete, Sándor P.","first_name":"Sándor P.","last_name":"Fekete"},{"full_name":"Kleist, Linda","first_name":"Linda","last_name":"Kleist"},{"full_name":"Kostitsyna, Irina","first_name":"Irina","last_name":"Kostitsyna"},{"full_name":"Löffler, Maarten","first_name":"Maarten","last_name":"Löffler"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","last_name":"Masárová","first_name":"Zuzana","full_name":"Masárová, Zuzana"},{"last_name":"Mundilova","first_name":"Klara","full_name":"Mundilova, Klara"},{"last_name":"Schmidt","full_name":"Schmidt, Christiane","first_name":"Christiane"}],"intvolume":"        93","oa_version":"Preprint","day":"01","isi":1,"scopus_import":"1","type":"journal_article","_id":"8317","external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"publication":"Computational Geometry: Theory and Applications","status":"public","article_type":"original","volume":93}