We define a notion of local overlaps in polyhedron unfoldings. We use this concept to construct new examples of polyhedra that cannot be edge unfolded without overlap. In particular, we present a polyhedron with 16 triangular faces for which every unfolding contains a vertex with total face angle greater than 2\u0019. We also construct an ununfoldable polyhedron with 9 convex faces, improving upon the previously best known bound of 13.<\/p>\n","protected":false},"excerpt":{"rendered":"
We define a notion of local overlaps in polyhedron unfoldings. We use this concept to construct new examples of polyhedra that cannot be edge unfolded without overlap. In particular, we present a polyhedron with 16 triangular faces for which every unfolding contains a vertex with total face angle greater than 2\u0019. 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