A Class of Convex Polyhedra with Few Edge Unfoldings

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https://scholarworks.smith.edu/csc_facpubs/41; http://repository.cmu.edu/compsci/1129; http://www.cccg.ca/proceedings/2008/
Miller, Gary L.; Phillips, Todd; Sheehy, Donald
Computer Sciences; Geometry and Topology; Mathematics
conference paper description
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.