Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, September 01, 2011, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Joseph O'Rourke (Smith College, Northampton, MA, USA)

New Methods for Unfolding Convex Polyhedra

The surface of a convex polyhedron can be cut open and flattened to the plane as a simple polygon. In particular, the unfolding does not self-overlap. So the polygon may be cut out of paper and folded to the convex polyhedron.

It is most natural to restrict the cuts to follow the edges of the polyhedron. It remains an open problem to settle whether or not every convex polyhedron can be cut open to a "net" along edges. Without the edge restriction, there are several methods known to cut open any convex polyhedron to a polygon. I will describe two: one old one, based on an idea of Alexandrov from the 1940's, and a new generalization I obtained in joint work with Jin-ichi Itoh and Costin Vilcu.

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