2025/10/21 by Florian Lehner, Lehner, Florian, Shirley, Benjamin
Engineering · Mathematics · #Advanced Materials and Mechanics #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2510.18197
openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We study the problem of whether rectangular polyominoes with holes are cube-foldable, that is, whether they can be folded into a cube, if creases are only allowed along grid lines. It is known that holes of sufficient size guarantee that this is the case. Smaller holes which by themselves do not make a rectangular polyomino cube-foldable can sometimes be combined to create cube-foldable polyominoes. We investigate minimal sets of holes which guarantee cube-foldability. We show that if all holes are of the same type, the these minimal sets have size at most 4, and if we allow different types of holes, then there is no upper bound on the size.