Folding Polyominoes with Holes into a Cube
Oswin Aichholzer, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine,, Martin L. Demaine, S\'andor P. Fekete, Linda Kleist, Irina Kostitsyna,, Maarten L\"offler, Zuzana Mas\'arov\'a, Klara Mundilova, Christiane Schmidt
TL;DR
This paper investigates the conditions under which polyominoes with holes can be folded into a cube, providing new sufficient and necessary criteria that extend previous work on hole-free shapes.
Contribution
It introduces new sufficient conditions for folding polyominoes with holes into a cube and identifies specific cases where folding is impossible.
Findings
All but five simple holes guarantee foldability into a cube.
Established sufficient conditions for polyominoes with multiple holes.
Identified cases where cube folding is impossible.
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.
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