Local Overlaps In Special Unfoldings Of Convex Polyhedra - Lucier, Brendan (Canadian Conference on Computational Geometry 2006 and Computational Geometry: Theory and Applications 2009, 2007)
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, thereby negatively resolving some open conjectures. In particular, we construct a convex polyhedron for which every shortest path unfolding contains an overlap. We also present a convex polyhedron for which every steepest edge unfolding contains an overlap. We conclude by analyzing a broad class of unfoldings and again find a convex polyhedron for which they all contain overlaps.