Title: Unfolding Orthogonal Polyhedra
Speaker: Robin Flatland
Abstract:
An unfolding of a polyhedron is a set of cuts that can be applied to its
surface so that it can be unfolded flat as a single piece without
overlap. Applications of polyhedra unfolding arise in manufacturing
processes that construct three-dimensional objects by bending sheet
metal. It is a long unsolved problem to determine whether every
polyhedron may be unfolded. In this talk, the focus is on recent
progress in unfolding orthogonal polyhedra, a class of polyhedra whose
faces all meet at right angles. An algorithm will be presented that
proves every orthogonal polyhedron of genus zero may be unfolded. For a
polyhedron of $n$ vertices, portions of the unfolding are rectangular
strips which, in the worst case, may need to be as thin as \epsilon = 1
/ 2^{\Omega(n)}.