Folding Polyominoes with Holes into a Cube

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

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


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 publicationProc. 31th Annual Canadian Conference on Computational Geometry CCCG 2019
Place of PublicationEdmonton, Alberta, Canada
Number of pages7
Publication statusPublished - 2019

Fields of Expertise

  • Information, Communication & Computing


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