Polyominoes Folding into Four and Five Distinct Boxes

We present new results on polyomino nets that fold into four or five distinct boxes. With the help of AI, we first found examples with areas 532 and 2128, respectively. We analyze these examples and reduce their areas to 178 and 358, respectively. We also generalize the construction of the five-box net and show that infinitely many polyomino nets fold into five distinct boxes.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-03
DOI
https://doi.org/10.48550/arxiv.2611.04246
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

Polyominoes Folding into Four and Five Distinct Boxes

Erik D. Demaine, Michael Tardibuono, Ryuhei Uehara, Reed Silverstein et al.
arXiv (Cornell University)
Advanced Combinatorial Mathematics
preprint

Polyominoes Folding into Four and Five Distinct Boxes

Erik D. Demaine, Michael Tardibuono, Ryuhei Uehara, Reed Silverstein, Conner Silverstein, Toshihiro Shirakawa
preprint en

Abstract

We present new results on polyomino nets that fold into four or five distinct boxes. With the help of AI, we first found examples with areas 532 and 2128, respectively. We analyze these examples and reduce their areas to 178 and 358, respectively. We also generalize the construction of the five-box net and show that infinitely many polyomino nets fold into five distinct boxes.

arXiv (Cornell University)
Advanced Combinatorial Mathematics
DOIOpen Access PDFOpenAlex
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Polyominoes Folding into Four and Five Distinct Boxes — Erik D. Demaine, Michael Tardibuono, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS