Affine unfoldings of convex polyhedra
arXiv:1305.3231 · doi:10.2140/gt.2014.18.3055
Abstract
We show that every convex polyhedron admits a simple edge unfolding after an affine transformation. In particular there exists no combinatorial obstruction to a positive resolution of Durer's unfoldability problem, which answers a question of Croft, Falconer, and Guy. Among other techniques, the proof employs a topological characterization for embeddings among the planar immersions of the disk.
32 pages, 21 figures; Minor changes including an index of notation; Accepted for publication in Geometry and Toplogy