Paper by Erik D. Demaine

Reference:

Zachary Abel, Erik D. Demaine, and Martin L. Demaine, “A Topologically Convex Vertex-Ununfoldable Polyhedron”, in Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011), Toronto, Ontario, Canada, August 10–12, 2011, to appear.

BibTeX

@InProceedings{VertexUnunfoldable_CCCG2011,
  AUTHOR        = {Zachary Abel and Erik D. Demaine and Martin L. Demaine},
  TITLE         = {A Topologically Convex Vertex-Ununfoldable Polyhedron},
  BOOKTITLE     = {Proceedings of the 23rd Canadian Conference on
                   Computational Geometry (CCCG 2011)},
  bookurl       = {http://2011.cccg.ca/},
  ADDRESS       = {Toronto, Ontario, Canada},
  MONTH         = {August 10--12},
  YEAR          = 2011,
  PAGES         = {to appear},

  withstudent   = 1,
  unrefereed    = 1,
  dblp          = {https://dblp.org/rec/conf/cccg/AbelDD11},
  ee            = {http://www.cccg.ca/proceedings/2011/papers/paper85.pdf},
}

Abstract:

We construct a polyhedron that is topologically convex (i.e., has the graph of a convex polyhedron) yet has no vertex unfolding: no matter how we cut along the edges and keep faces attached at vertices to form a connected (hinged) surface, the surface necessarily unfolds with overlap.

Availability:

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