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Some Polycubes Have No Edge Zipper Unfolding

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arxiv 1907.08433 v3 pith:7765CSVQ submitted 2019-07-19 cs.CG cs.DM

Erik D. Demaine , Martin L. Demaine , David Eppstein , Joseph O'Rourke This is my paper · ORCID
classification cs.CGcs.DM
keywords edgeunfoldingcubesedgespolycubepolycubeszipperalong
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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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Cited by 1 Pith paper

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  1. Unfolding Polyhedra

    cs.CG 2019-08 accept novelty 2.0 of 10

    A survey classifying four cut types against five polyhedron classes, producing a table of solved, open, and impossible unfolding problems.

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