Folding polyominoes with holes into a cube

Oswin Aichholzer, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, Irina Kostitsyna, Maarten Löffler, Zuzana Masárová, Klara Mundilova, Christiane Schmidt

Research output: Contribution to journalArticlepeer-review


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 “basic” holes guarantee foldability.
Original languageEnglish
Article number101700
Pages (from-to)1-14
Number of pages14
JournalComputational Geometry
Publication statusPublished - 2021


  • Folding
  • Origami folding
  • Cube
  • Polyomino with holes
  • Non-simple polyomino

ASJC Scopus subject areas

  • Computational Mathematics
  • Control and Optimization
  • Geometry and Topology
  • Computer Science Applications
  • Computational Theory and Mathematics

Fields of Expertise

  • Information, Communication & Computing


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