We construct a sequence of convex polyhedra on n vertices with the property that, as n, the fraction of its edge unfoldings that avoid overlap approaches 0, and so the frac
We define a notion of local overlaps in polyhedron unfoldings. We use this concept to construct convex polyhedra for which certain classes of edge unfoldings contain overlaps, the...
We prove that an infinite class of convex polyhedra, produced by restricted vertex truncations, always unfold without overlap. The class includes the “domes,” providing a sim...
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the ...
Marshall W. Bern, Erik D. Demaine, David Eppstein,...
This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restri...