--- _id: '8317' 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. article_number: '101700' article_processing_charge: No article_type: original author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Hugo A. full_name: Akitaya, Hugo A. last_name: Akitaya - first_name: Kenneth C. full_name: Cheung, Kenneth C. last_name: Cheung - first_name: Erik D. full_name: Demaine, Erik D. last_name: Demaine - 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 - first_name: Irina full_name: Kostitsyna, Irina last_name: Kostitsyna - first_name: Maarten full_name: Löffler, Maarten last_name: Löffler - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Klara full_name: Mundilova, Klara last_name: Mundilova - first_name: Christiane full_name: Schmidt, Christiane last_name: Schmidt citation: ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700' 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. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700' 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.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700.' ieee: 'O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 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.' mla: 'Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.' 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).' date_created: 2020-08-30T22:01:09Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-08-04T10:57:42Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2020.101700 external_id: arxiv: - '1910.09917' isi: - '000579185100004' intvolume: ' 93' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.09917v3 month: '02' oa: 1 oa_version: Preprint project: - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: 'Computational Geometry: Theory and Applications' publication_identifier: issn: - '09257721' publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '6989' relation: shorter_version status: public scopus_import: '1' status: public title: Folding polyominoes with holes into a cube type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 93 year: '2021' ...