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We construct a sequence of convex polyhedra on n vertices with the property that, as n -> infinity, the fraction of its edge unfoldings that avoid overlap approaches 0, and so the fraction that overlap approaches 1. Nevertheless, each does have (several) nonoverlapping edge unfoldings.


Author’s submitted manuscript.

Another version of this paper appeared in the Proceedings of the 20th Annual Canadian Conference on Computational Geometry August 13–15, 2008 McGill University, Montréal, Québec.



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