Paper by Erik D. Demaine

Reference:

Marshall Bern, Erik D. Demaine, David Eppstein, and Eric Kuo, “Ununfoldable Polyhedra”, Technical Report CS-99-04, Department of Computer Science, University of Waterloo, August 1999.

BibTeX

@TechReport{UnunfoldableTR,
  AUTHOR        = {Marshall Bern and Erik D. Demaine and David Eppstein and
                   Eric Kuo},
  TITLE         = {Ununfoldable Polyhedra},
  INSTITUTION   = {Department of Computer Science, University of Waterloo},
  INSTITUTIONURL = {http://www.cs.uwaterloo.ca/},
  NUMBER        = {CS-99-04},
  NUMBERURL     = {http://www.cs.uwaterloo.ca/cs-archive/CS-1999/CS-1999.shtml#04},
  MONTH         = {August},
  YEAR          = 1999,

  LENGTH        = {13 pages},
  PAPERS        = {Ununfoldable; CCCG99b; CGC99},
  COMMENTS      = {This paper is published in
                   <A HREF="../CCCG99b/">CCCG'99</A>. <BR>
                   It is also available as
                   <A HREF="http://arXiv.org/abs/cs.CG/9908003v1">
                   arXiv:cs.CG/9908003v1</A> of the
                   <A HREF="http://arXiv.org/archive/cs/intro.html">
                   Computing Research Repository (CoRR)</A>.},
}

Abstract:

A well-studied problem is that of unfolding a convex polyhedron into a simple planar polygon. In this paper, we study the limits of unfoldability. We give an example of a polyhedron with convex faces that cannot be unfolded by cutting along its edges. We further show that such a polyhedron can indeed be unfolded if cuts are allowed to cross faces. Finally, we prove that “open” polyhedra with convex faces may not be unfoldable no matter how they are cut.

Comments:

This paper is published in CCCG'99.
It is also available as arXiv:cs.CG/9908003v1 of the Computing Research Repository (CoRR).

Length:

The paper is 13 pages.

Availability:

The paper is available in PostScript (236k).

See information on file formats.

[Google Scholar search]

Related papers:

Ununfoldable (Ununfoldable Polyhedra with Convex Faces)

CCCG99b (Ununfoldable Polyhedra)

CGC99 (Ununfoldable Polyhedra with Triangular Faces)