Paper by Martin L. Demaine

Reference:

Kingston Yao Czajkowski, Erik D. Demaine, Martin L. Demaine, Kim Eppling, Robby Kraft, Klara Mundilova, and Levi Smith, “Folding Small Polyominoes into a Unit Cube”, in Proceedings of the 32nd Canadian Conference in Computational Geometry (CCCG 2020), Saskatchewan, Saskatoon, Canada, August 5–7, 2020.

Abstract:

We demonstrate that a 3 × 3 square can fold into a unit cube using horizontal, vertical, and diagonal creases on the 6 × 6 half-grid. Together with previous results, this result implies that all tree-shaped polyominoes with at least nine squares fold into a unit cube. We also make partial progress on the analogous problem for septominoes and octominoes by showing a half-grid folding of the U septomino and 2 × 4 rectangle into a unit cube.

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