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