Paper by Erik D. Demaine

Reference:

Marshall Bern, Erik D. Demaine, David Eppstein, and Eric Kuo, “Ununfoldable Polyhedra”, in Proceedings of the 11th Canadian Conference on Computational Geometry (CCCG'99), Vancouver, British Columbia, Canada, August 15–18, 1999, pages 13–16.

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 also available from the electronic proceedings as http://www.cs.ubc.ca/conferences/CCCG/elec_proc/fp38.ps.gz.
It is also available as version 1 of arXiv:cs.CG/9908003 of the Computing Research Repository (CoRR).

Updates:

We have solved some of the open problems mentioned in this paper; see the CGTA paper.

Length:

The paper is 13 pages.

Availability:

The paper is available in PostScript (236k).

See information on file formats.

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Related papers:

Ununfoldable (Ununfoldable Polyhedra with Convex Faces)

CGC99 (Ununfoldable Polyhedra with Triangular Faces)