[{"author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"first_name":"Hugo A.","full_name":"Akitaya, Hugo A.","last_name":"Akitaya"},{"full_name":"Cheung, Kenneth C.","last_name":"Cheung","first_name":"Kenneth C."},{"full_name":"Demaine, Erik D.","last_name":"Demaine","first_name":"Erik D."},{"first_name":"Martin L.","full_name":"Demaine, Martin L.","last_name":"Demaine"},{"first_name":"Sándor P.","full_name":"Fekete, Sándor P.","last_name":"Fekete"},{"first_name":"Linda","full_name":"Kleist, Linda","last_name":"Kleist"},{"last_name":"Kostitsyna","full_name":"Kostitsyna, Irina","first_name":"Irina"},{"last_name":"Löffler","full_name":"Löffler, Maarten","first_name":"Maarten"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová","full_name":"Masárová, Zuzana"},{"last_name":"Mundilova","full_name":"Mundilova, Klara","first_name":"Klara"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"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."}],"publication_status":"published","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).","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.","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>","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>.","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.","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>"},"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.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"}],"oa_version":"Preprint","quality_controlled":"1","_id":"8317","publication_identifier":{"issn":["09257721"]},"date_updated":"2023-08-04T10:57:42Z","volume":93,"oa":1,"article_processing_charge":"No","arxiv":1,"external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"title":"Folding polyominoes with holes into a cube","year":"2021","doi":"10.1016/j.comgeo.2020.101700","related_material":{"record":[{"status":"public","relation":"shorter_version","id":"6989"}]},"isi":1,"article_number":"101700","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"status":"public","intvolume":"        93","type":"journal_article","day":"01","publication":"Computational Geometry: Theory and Applications","language":[{"iso":"eng"}],"publisher":"Elsevier","scopus_import":"1","date_published":"2021-02-01T00:00:00Z","article_type":"original","month":"02","date_created":"2020-08-30T22:01:09Z","department":[{"_id":"HeEd"}]},{"page":"28 - 31","publication":"Computational Geometry: Theory and Applications","type":"journal_article","day":"01","status":"public","intvolume":"        66","department":[{"_id":"UlWa"}],"date_created":"2018-12-11T11:48:32Z","date_published":"2017-01-01T00:00:00Z","month":"01","language":[{"iso":"eng"}],"publisher":"Elsevier","date_updated":"2023-09-27T12:15:16Z","volume":66,"publist_id":"6861","oa":1,"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"oa_version":"Submitted Version","quality_controlled":"1","_id":"793","publication_identifier":{"issn":["09257721"]},"publication_status":"published","citation":{"short":"R. Fulek, H. Mojarrad, M. Naszódi, J. Solymosi, S. Stich, M. Szedlák, Computational Geometry: Theory and Applications 66 (2017) 28–31.","ista":"Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. 2017. On the existence of ordinary triangles. Computational Geometry: Theory and Applications. 66, 28–31.","ama":"Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. On the existence of ordinary triangles. <i>Computational Geometry: Theory and Applications</i>. 2017;66:28-31. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">10.1016/j.comgeo.2017.07.002</a>","mla":"Fulek, Radoslav, et al. “On the Existence of Ordinary Triangles.” <i>Computational Geometry: Theory and Applications</i>, vol. 66, Elsevier, 2017, pp. 28–31, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">10.1016/j.comgeo.2017.07.002</a>.","chicago":"Fulek, Radoslav, Hossein Mojarrad, Márton Naszódi, József Solymosi, Sebastian Stich, and May Szedlák. “On the Existence of Ordinary Triangles.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">https://doi.org/10.1016/j.comgeo.2017.07.002</a>.","ieee":"R. Fulek, H. Mojarrad, M. Naszódi, J. Solymosi, S. Stich, and M. Szedlák, “On the existence of ordinary triangles,” <i>Computational Geometry: Theory and Applications</i>, vol. 66. Elsevier, pp. 28–31, 2017.","apa":"Fulek, R., Mojarrad, H., Naszódi, M., Solymosi, J., Stich, S., &#38; Szedlák, M. (2017). On the existence of ordinary triangles. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">https://doi.org/10.1016/j.comgeo.2017.07.002</a>"},"author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","first_name":"Radoslav","full_name":"Fulek, Radoslav","last_name":"Fulek","orcid":"0000-0001-8485-1774"},{"last_name":"Mojarrad","full_name":"Mojarrad, Hossein","first_name":"Hossein"},{"first_name":"Márton","full_name":"Naszódi, Márton","last_name":"Naszódi"},{"full_name":"Solymosi, József","last_name":"Solymosi","first_name":"József"},{"first_name":"Sebastian","last_name":"Stich","full_name":"Stich, Sebastian"},{"last_name":"Szedlák","full_name":"Szedlák, May","first_name":"May"}],"abstract":[{"text":"Let P be a finite point set in the plane. A cordinary triangle in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P . Motivated by a question of Erdös, and answering a question of de Zeeuw, we prove that there exists a constant c &gt; 0such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(| P |). ","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1701.08183","open_access":"1"}],"isi":1,"ec_funded":1,"year":"2017","doi":"10.1016/j.comgeo.2017.07.002","external_id":{"isi":["000412039700003"]},"title":"On the existence of ordinary triangles"}]