What polyominoes fold into a cube? This seemingly simple question is still
an unsolved mathematical problem. These puzzles illustrate some of the cases
we (only recently) understand.
These cube folding puzzles are based on the following sources:
- Martin Gardner, “Paper cutting”, in New Mathematical Diversions, Revised, Mathematical Association of America, 1995.
- Jill Bigley Dunham and Gwyneth R. Whieldon, “Enumeration of solutions to Gardner's paper cutting and folding problem”, in The Mathematics of Various Entertaining Subjects, volume 2, 2018, pages 108–124.
- Oswin Aichholzer, Michael Biro, Erik D. Demaine, Martin L. Demaine, David Eppstein, Sándor P. Fekete, Adam Hesterberg, Irina Kostitsyna, and Christiane Schmidt, “Folding polyominoes into (poly)cubes”, International Journal of Computational Geometry and Applications, 28(3):197–226, 2018.
- Oswin Aichholzer, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor 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, August 2019.
This edition of the puzzles was prepared for MoMath for a Cube Conundrums workshop in The Six Series.
To try these puzzles, print the
11-page PDF of puzzles, cut out each puzzle you'd
like to try, cut along the indicated slits (doubled bold lines), and
cut out any gray squares with a scissors icon.
