Folding polyominoes with holes into a cube

Author(s)
Demaine, Erik D; Demaine, Martin L; Mundilova, Klara
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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 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.
Date issued
2021-02
URI
https://hdl.handle.net/1721.1/129567
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Journal
Computational Geometry: Theory and Applications
Publisher
Elsevier BV
Citation
Aichholzer, Oswin et al. “Folding polyominoes with holes into a cube.” Computational Geometry: Theory and Applications, 93 (Feruary 2021): 101700 © 2021 The Author(s)
Version: Original manuscript
ISSN
0925-7721
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