English

Folding Polyominoes with Holes into a Cube

Computational Geometry 2020-07-03 v3

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 \emph{simple} holes guarantee foldability.

Keywords

Cite

@article{arxiv.1910.09917,
  title  = {Folding Polyominoes with Holes into a Cube},
  author = {Oswin Aichholzer and Hugo A. Akitaya and Kenneth C. Cheung and Erik D. Demaine and Martin L. Demaine and Sándor P. Fekete and Linda Kleist and Irina Kostitsyna and Maarten Löffler and Zuzana Masárová and Klara Mundilova and Christiane Schmidt},
  journal= {arXiv preprint arXiv:1910.09917},
  year   = {2020}
}

Comments

24 pages, 21 figures

R2 v1 2026-06-23T11:51:08.045Z