Folding Polyominoes with Holes into a Cube

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

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

Abstract

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. $31^th$ Annual Canadian Conference on Computational Geometry CCCG 2019
Place of PublicationEdmonton, Alberta, Canada
Pages164-170
Number of pages7
Publication statusPublished - 2019

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Fields of Expertise

  • Information, Communication & Computing

Cite this

Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., [Unknown], SP. F., ... Schmidt, C. (2019). Folding Polyominoes with Holes into a Cube. In Proc. $31^th$ Annual Canadian Conference on Computational Geometry CCCG 2019 (pp. 164-170). Edmonton, Alberta, Canada.