Folding Polyominoes with Holes into a Cube

  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 Zuzana Mas{\'a}rov{\'a} and K. Mundilova and Christiane Schmidt},
  • O. Aichholzer, Hugo A. Akitaya, +9 authors Christiane Schmidt
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • 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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    • 2019