Affine unfoldings of convex polyhedra

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 Dürer’s unfoldability problem, which answers a question of Croft, Falconer and Guy. Among other techniques, the proof employs a topological characterization of embeddings among the planar immersions of the disk.