Paper by Erik D. Demaine

Reference:

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”, in Proceedings of the 31st Canadian Conference in Computational Geometry (CCCG 2019), Edmonton, Alberta, Canada, August 8–10, 2019, pages 164–170.

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 hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability.

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Related papers:

CubeFoldingHoles_CGTA (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)