Folding polyominoes with holes into a cube

Oswin Aichholzer, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, Irina Kostitsyna, Maarten Löffler, Zuzana Masárová, Klara Mundilova, Christiane Schmidt

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)


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 hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability.

Original languageEnglish
Title of host publicationProceedings of the 31th Annual Canadian Conference on Computational Geometry (CCCG 2019)
Number of pages7
Publication statusPublished - 1 Jan 2019
Event31st Canadian Conference on Computational Geometry, CCCG 2019 - Edmonton, Canada
Duration: 8 Aug 201910 Aug 2019


Conference31st Canadian Conference on Computational Geometry, CCCG 2019


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