Folding Polyominoes with Holes into a Cube
@article{Aichholzer2019FoldingPW, title={Folding Polyominoes with Holes into a Cube}, author={O. Aichholzer and Hugo A. Akitaya and Kenneth C. Cheung and E. Demaine and Martin L. Demaine and S{\'a}ndor P. Fekete and L. Kleist and I. Kostitsyna and M. L{\"o}ffler and Z. Mas{\'a}rov{\'a} and K. Mundilova and Christiane Schmidt}, journal={ArXiv}, year={2019}, volume={abs/1910.09917} }
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 \emph{simple} holes guarantee foldability.
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SHOWING 1-10 OF 27 REFERENCES
Universal Hinge Patterns for Folding Strips Efficiently into Any Grid Polyhedron
- Mathematics, Computer Science
- WADS
- 2017
- 3
- PDF
Universal hinge patterns for folding strips efficiently into any grid polyhedron
- Mathematics, Computer Science
- Comput. Geom.
- 2020
- 1
- PDF
Common Developments of Three Incongruent Orthogonal Boxes
- Mathematics, Computer Science
- Int. J. Comput. Geom. Appl.
- 2013
- 8
Common developments of three incongruent boxes of area 30
- Computer Science, Mathematics
- Comput. Geom.
- 2017
- 9
- PDF