• DOI:10.1016/J.COMGEO.2020.101700
Corpus ID: 199529411

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}
}

O. Aichholzer, Hugo A. Akitaya, +9 authors Christiane Schmidt

Published 2019

Computer Science, Mathematics

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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.