conference paper
Folding polyominoes with holes into a cube
published
yes
Oswin
Aichholzer
author
Hugo A
Akitaya
author
Kenneth C
Cheung
author
Erik D
Demaine
author
Martin L
Demaine
author
Sandor P
Fekete
author
Linda
Kleist
author
Irina
Kostitsyna
author
Maarten
Löffler
author
Zuzana
Masárová
author 45CFE238-F248-11E8-B48F-1D18A9856A870000-0002-6660-1322
Klara
Mundilova
author
Christiane
Schmidt
author
HeEd
department
CCCG: Canadian Conference in Computational Geometry
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.
Canadian Conference on Computational Geometry2019Edmonton, Canada
eng
Proceedings of the 31st Canadian Conference on Computational Geometry
1910.09917
164-170
Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Canadian Conference on Computational Geometry, 2019, pp. 164–70.
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, in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–170.
Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry; 2019:164-170.
Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” In <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, 164–70. Canadian Conference on Computational Geometry, 2019.
Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry 164–170.
O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” in <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Edmonton, Canada, 2019, pp. 164–170.
Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i> (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.
69892019-11-04T16:46:11Z2019-11-14T08:43:44Z