[{"corr_author":"1","citation":{"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>.","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.","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>.","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>"},"department":[{"_id":"HeEd"}],"project":[{"name":"Mathematics, Computer Science","call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"publication":"Computational Geometry: Theory and Applications","external_id":{"arxiv":["1910.09917"],"isi":["000579185100004"]},"intvolume":"        93","date_updated":"2026-06-18T19:14:36Z","title":"Folding polyominoes with holes into a cube","doi":"10.1016/j.comgeo.2020.101700","date_created":"2020-08-30T22:01:09Z","status":"public","arxiv":1,"volume":93,"publisher":"Elsevier","article_number":"101700","related_material":{"record":[{"relation":"shorter_version","id":"6989","status":"public"}]},"language":[{"iso":"eng"}],"day":"01","article_type":"original","scopus_import":"1","article_processing_charge":"No","main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"publication_identifier":{"issn":["0925-7721"],"eissn":["1879-081X"]},"isi":1,"oa":1,"year":"2021","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.","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","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Akitaya, Hugo A.","first_name":"Hugo A.","last_name":"Akitaya"},{"full_name":"Cheung, Kenneth C.","first_name":"Kenneth C.","last_name":"Cheung"},{"full_name":"Demaine, Erik D.","first_name":"Erik D.","last_name":"Demaine"},{"full_name":"Demaine, Martin L.","first_name":"Martin L.","last_name":"Demaine"},{"full_name":"Fekete, Sándor P.","last_name":"Fekete","first_name":"Sándor P."},{"first_name":"Linda","last_name":"Kleist","full_name":"Kleist, Linda"},{"full_name":"Kostitsyna, Irina","first_name":"Irina","last_name":"Kostitsyna"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"last_name":"Masárová","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"full_name":"Schmidt, Christiane","first_name":"Christiane","last_name":"Schmidt"}],"publication_status":"published","month":"02","oa_version":"Preprint","quality_controlled":"1","type":"journal_article","date_published":"2021-02-01T00:00:00Z","_id":"8317","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd"},{"date_created":"2018-12-11T12:06:12Z","oa_version":"None","OA_type":"free access","publication_status":"published","month":"11","status":"public","volume":41,"type":"journal_article","publisher":"Elsevier","extern":"1","language":[{"iso":"eng"}],"day":"01","_id":"3971","date_published":"2008-11-01T00:00:00Z","article_type":"original","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"No","citation":{"ieee":"H. Edelsbrunner, J. Harer, A. Mascarenhas, V. Pascucci, and J. Snoeyink, “Time-varying Reeb graphs for continuous space-time data,” <i>Computational Geometry: Theory and Applications</i>, vol. 41, no. 3. Elsevier, pp. 149–166, 2008.","short":"H. Edelsbrunner, J. Harer, A. Mascarenhas, V. Pascucci, J. Snoeyink, Computational Geometry: Theory and Applications 41 (2008) 149–166.","ista":"Edelsbrunner H, Harer J, Mascarenhas A, Pascucci V, Snoeyink J. 2008. Time-varying Reeb graphs for continuous space-time data. Computational Geometry: Theory and Applications. 41(3), 149–166.","chicago":"Edelsbrunner, Herbert, John Harer, Ajith Mascarenhas, Valerio Pascucci, and Jack Snoeyink. “Time-Varying Reeb Graphs for Continuous Space-Time Data.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2008. <a href=\"https://doi.org/10.1016/j.comgeo.2007.11.001\">https://doi.org/10.1016/j.comgeo.2007.11.001</a>.","mla":"Edelsbrunner, Herbert, et al. “Time-Varying Reeb Graphs for Continuous Space-Time Data.” <i>Computational Geometry: Theory and Applications</i>, vol. 41, no. 3, Elsevier, 2008, pp. 149–66, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2007.11.001\">10.1016/j.comgeo.2007.11.001</a>.","ama":"Edelsbrunner H, Harer J, Mascarenhas A, Pascucci V, Snoeyink J. Time-varying Reeb graphs for continuous space-time data. <i>Computational Geometry: Theory and Applications</i>. 2008;41(3):149-166. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2007.11.001\">10.1016/j.comgeo.2007.11.001</a>","apa":"Edelsbrunner, H., Harer, J., Mascarenhas, A., Pascucci, V., &#38; Snoeyink, J. (2008). Time-varying Reeb graphs for continuous space-time data. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2007.11.001\">https://doi.org/10.1016/j.comgeo.2007.11.001</a>"},"publication_identifier":{"eissn":["1879-081X"],"issn":["0925-7721"]},"publication":"Computational Geometry: Theory and Applications","intvolume":"        41","publist_id":"2158","year":"2008","abstract":[{"text":"The Reeb graph is a useful tool in visualizing real-valued data obtained from computational simulations of physical processes. We characterize the evolution of the Reeb graph of a time-varying continuous function defined in three-dimensional space. We show how to maintain the Reeb graph over time and compress the entire sequence of Reeb graphs into a single, partially persistent data structure, and augment this data structure with Betti numbers to describe the topology of level sets and with path seeds to assist in the fast extraction of level sets for visualization.","lang":"eng"}],"issue":"3","doi":"10.1016/j.comgeo.2007.11.001","title":"Time-varying Reeb graphs for continuous space-time data","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Harer, John","last_name":"Harer","first_name":"John"},{"full_name":"Mascarenhas, Ajith","last_name":"Mascarenhas","first_name":"Ajith"},{"last_name":"Pascucci","first_name":"Valerio","full_name":"Pascucci, Valerio"},{"full_name":"Snoeyink, Jack","last_name":"Snoeyink","first_name":"Jack"}],"date_updated":"2026-05-29T09:15:13Z","page":"149 - 166"}]