Paper by Erik D. Demaine

Reference:

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

BibTeX

@InProceedings{PolycubeZipper_CCCG2020,
  AUTHOR        = {Erik D. Demaine and Martin L. Demaine and David Eppstein and Joseph O'Rourke},
  TITLE         = {Some Polycubes Have No Edge Zipper Unfolding},
  BOOKTITLE     = {Proceedings of the 32nd Canadian Conference in Computational Geometry (CCCG 2020)},
  bookurl       = {http://vga.usask.ca/cccg2020/},
  ADDRESS       = {Saskatchewan, Saskatoon, Canada},
  MONTH         = {August 5--7},
  YEAR          = 2020,

  unrefereed    = 1,
  dblp          = {https://dblp.org/rec/conf/cccg/DemaineDEO20},
  comments      = {This paper is available as <A HREF="https://arXiv.org/abs/1907.08433">arXiv:1907.08433</A>. Joseph O'Rourke's presentation is available on <A HREF="https://youtu.be/Tes2L-HyBKc">YouTube</A>.},
}

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.

Comments:

This paper is available as arXiv:1907.08433. Joseph O'Rourke's presentation is available on YouTube.

Availability:

The paper is available in PDF (1658k).

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