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.
|Title of host publication||Proc. $31^th$ Annual Canadian Conference on Computational Geometry CCCG 2019|
|Place of Publication||Edmonton, Alberta, Canada|
|Number of pages||7|
|Publication status||Published - 2019|
- Information, Communication & Computing
, Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., [Unknown], SP. F., ... Schmidt, C. (2019). Folding Polyominoes with Holes into a Cube
. In Proc. $31^th$ Annual Canadian Conference on Computational Geometry CCCG 2019
(pp. 164-170). Edmonton, Alberta, Canada.