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.

Cube, Folding, Non-simple polyomino, Origami folding, Polyomino with holes
Computational Geometry
School of Computer Science

Aichholzer, O. (Oswin), Akitaya, H.A. (Hugo A.), Cheung, K.C. (Kenneth C.), Demaine, E.D. (Erik D.), Demaine, M.L. (Martin L.), Fekete, S.P. (Sándor P.), … Schmidt, C. (Christiane). (2021). Folding polyominoes with holes into a cube. Computational Geometry, 93. doi:10.1016/j.comgeo.2020.101700