Paper by Erik D. Demaine

Erik D. Demaine, Martin L. Demaine, David Eppstein, and Joseph O'Rourke, “Some Polycubes Have No Edge-Unzipping”, in Proceedings of the 32nd Canadian Conference in Computational Geometry (CCCG 2020), Saskatchewan, Saskatoon, Canada, August 5–7, 2020.

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.

Joseph O'Rourke's presentation is available on YouTube.

The paper is available in PDF (1658k).
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Last updated March 15, 2021 by Erik Demaine.