[{"related_material":{"record":[{"status":"public","relation":"shorter_version","id":"6989"}]},"article_number":"101700","main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"isi":1,"title":"Folding polyominoes with holes into a cube","external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"year":"2021","doi":"10.1016/j.comgeo.2020.101700","_id":"8317","publication_identifier":{"issn":["09257721"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","oa_version":"Preprint","quality_controlled":"1","project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"arxiv":1,"volume":93,"date_updated":"2023-08-04T10:57:42Z","oa":1,"article_processing_charge":"No","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 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.","lang":"eng"}],"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."},{"last_name":"Demaine","full_name":"Demaine, Erik D.","first_name":"Erik D."},{"full_name":"Demaine, Martin L.","last_name":"Demaine","first_name":"Martin L."},{"first_name":"Sándor P.","full_name":"Fekete, Sándor P.","last_name":"Fekete"},{"full_name":"Kleist, Linda","last_name":"Kleist","first_name":"Linda"},{"full_name":"Kostitsyna, Irina","last_name":"Kostitsyna","first_name":"Irina"},{"first_name":"Maarten","full_name":"Löffler, Maarten","last_name":"Löffler"},{"full_name":"Masárová, Zuzana","last_name":"Masárová","orcid":"0000-0002-6660-1322","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Klara","full_name":"Mundilova, Klara","last_name":"Mundilova"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"publication_status":"published","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>","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>.","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>.","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).","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."},"date_created":"2020-08-30T22:01:09Z","department":[{"_id":"HeEd"}],"publisher":"Elsevier","scopus_import":"1","language":[{"iso":"eng"}],"month":"02","date_published":"2021-02-01T00:00:00Z","article_type":"original","publication":"Computational Geometry: Theory and Applications","intvolume":"        93","status":"public","day":"01","type":"journal_article"},{"date_published":"2017-01-01T00:00:00Z","month":"01","language":[{"iso":"eng"}],"publisher":"Elsevier","department":[{"_id":"UlWa"}],"date_created":"2018-12-11T11:48:32Z","type":"journal_article","day":"01","status":"public","intvolume":"        66","page":"28 - 31","publication":"Computational Geometry: Theory and Applications","ec_funded":1,"year":"2017","doi":"10.1016/j.comgeo.2017.07.002","title":"On the existence of ordinary triangles","external_id":{"isi":["000412039700003"]},"main_file_link":[{"url":"https://arxiv.org/abs/1701.08183","open_access":"1"}],"isi":1,"publication_status":"published","citation":{"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>.","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.","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>","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.","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>."},"author":[{"first_name":"Radoslav","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hossein","full_name":"Mojarrad, Hossein","last_name":"Mojarrad"},{"first_name":"Márton","last_name":"Naszódi","full_name":"Naszódi, Márton"},{"first_name":"József","full_name":"Solymosi, József","last_name":"Solymosi"},{"first_name":"Sebastian","last_name":"Stich","full_name":"Stich, Sebastian"},{"first_name":"May","last_name":"Szedlák","full_name":"Szedlák, 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"}],"volume":66,"date_updated":"2023-09-27T12:15:16Z","publist_id":"6861","oa":1,"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"oa_version":"Submitted Version","_id":"793","publication_identifier":{"issn":["09257721"]}}]