Ununfoldable polyhedra.
M. Bern,
E. Demaine,
D. Eppstein,
E. Kuo,
A. Mantler, and
J. Snoeyink.
arXiv:cs.CG/9908003.
Tech. rep.
CS-99-04, Univ. of Waterloo, Dept. of Computer Science, Aug. 1999.
11th Canad. Conf. Comp. Geom., 1999, paper 38.
4th CGC
Worksh. Computational Geometry, Johns Hopkins Univ., 1999.
Comp. Geom. Theory & Applications 24 (2): 51–62, 2003,
doi:10.1016/S0925-7721(02)00091-3 (special
issue for 4th CGC Worksh.).
We prove the existence of polyhedra in which all faces are convex, but which can not be cut along edges and folded flat.
Note variations in different versions: the CCCG one was only Bern, Demain, Eppstein, and Kuo, and the WCG one had the title "Ununfoldable polyhedra with triangular faces". The journal version uses the title "Ununfoldable polyhedra with convex faces" and the combined results from both conference versions. This became the first in a sequence of papers on ununfoldable polyhedra; see also "Ununfoldable polyhedra with 6 vertices or 6 faces" and "Acutely triangulated, stacked, and very ununfoldable polyhedra".