Paper by Erik D. Demaine

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, and Christiane Schmidt, “Folding Polyominoes with Holes into a Cube”, Computational Geometry: Theory and Applications, volume 93, February 2021, Article 101700.

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.

This paper is also available from ScienceDirect and as arXiv:1910.09917.

The paper is 26 pages.

The paper is available in PDF (765k).
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Related papers:
CubeFoldingHoles_CCCG2019 (Folding Polyominoes with Holes into a Cube)
CubeFolding_CCCG2020 (Folding Small Polyominoes into a Unit Cube)
PolyformFolding_IJCGA (Folding Polyominoes into (Poly)Cubes)

Related webpages:
Cube Folding Font
Cube Folding Puzzles (Erik Demaine and Martin Demaine)

See also other papers by Erik Demaine.
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Last updated May 5, 2021 by Erik Demaine.