Affine unfoldings of convex polyhedra

Ghomi, Mohammad¹

¹ School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332, USA

Geometry & topology, Tome 18 (2014) no. 5, pp. 3055-3090.

Résumé

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.

Détail

DOI : 10.2140/gt.2014.18.3055

Classification : 52B05, 57N35, 05C10, 57M10
Keywords: convex polyhedron, unfolding, development, spanning tree, edge graph, isometric embedding, immersion, covering spaces, Dürer's problem

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