Some Polycubes Have No Edge Zipper Unfolding

Published 19 Jul 2019 in cs.CG and cs.DM | (1907.08433v3)

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.

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