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Some Polycubes Have No Edge-Unzipping

07/19/2019

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by Joseph O'Rourke, et al.

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It is unknown whether or not every polycube has an edge-unfolding. A polycube is an object constructed by gluing cubes face-to-face. An edge-unfolding cuts edges on the surface and unfolds it to a net, a non-overlapping polygon in the plane. Here we explore the more restricted edge-unzippings where the cut edges form a path. We construct a polycube that has no edge-unzipping.

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