[{"doi":"10.1016/j.comgeo.2020.101700","publication_identifier":{"issn":["0925-7721"],"eissn":["1879-081X"]},"date_updated":"2026-07-28T13:08:48Z","date_published":"2021-02-01T00:00:00Z","title":"Folding polyominoes with holes into a cube","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."}],"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.","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"publication":"Computational Geometry: Theory and Applications","publication_status":"published","oa":1,"language":[{"iso":"eng"}],"date_created":"2020-08-30T22:01:09Z","type":"journal_article","arxiv":1,"article_processing_charge":"No","_id":"8317","corr_author":"1","intvolume":"        93","related_material":{"record":[{"status":"public","relation":"shorter_version","id":"6989"}]},"scopus_import":"1","status":"public","publisher":"Elsevier","article_type":"original","day":"01","department":[{"_id":"HeEd"}],"month":"02","external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","volume":93,"citation":{"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>.","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.","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>","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>","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."},"isi":1,"project":[{"call_identifier":"FWF","grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"last_name":"Akitaya","first_name":"Hugo A.","full_name":"Akitaya, Hugo A."},{"first_name":"Kenneth C.","last_name":"Cheung","full_name":"Cheung, Kenneth C."},{"last_name":"Demaine","first_name":"Erik D.","full_name":"Demaine, Erik D."},{"full_name":"Demaine, Martin L.","last_name":"Demaine","first_name":"Martin L."},{"full_name":"Fekete, Sándor P.","first_name":"Sándor P.","last_name":"Fekete"},{"full_name":"Kleist, Linda","last_name":"Kleist","first_name":"Linda"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"full_name":"Schmidt, Christiane","first_name":"Christiane","last_name":"Schmidt"}],"quality_controlled":"1","year":"2021","article_number":"101700","oa_version":"Preprint"}]