Some Polycubes Have No Edge Zipper Unfolding
arXiv:1907.08433
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.
11 pages, 10 figures, 9 references. Updated to match the version that will appear in the Canad. Conf. Comput. Geom., Aug. 2020