English

Some Polycubes Have No Edge Zipper Unfolding

Computational Geometry 2022-05-24 v3 Discrete Mathematics

Abstract

It is unknown whether every polycube (polyhedron constructed by gluing cubes face-to-face) has an edge unfolding, that is, cuts along edges of the cubes that unfolds the polycube to a single nonoverlapping polygon in the plane. Here we construct polycubes that have no *edge zipper unfolding* where the cut edges are further restricted to form a path.

Keywords

Cite

@article{arxiv.1907.08433,
  title  = {Some Polycubes Have No Edge Zipper Unfolding},
  author = {Erik D. Demaine and Martin L. Demaine and David Eppstein and Joseph O'Rourke},
  journal= {arXiv preprint arXiv:1907.08433},
  year   = {2022}
}

Comments

11 pages, 10 figures, 9 references. Updated to match the version that will appear in the Canad. Conf. Comput. Geom., Aug. 2020

R2 v1 2026-06-23T10:25:06.840Z