How to cage an egg

SummaryThis paper proves that given a convex polyhedronP ⊂ ℝ3 and a smooth strictly convex bodyK ⊂ ℝ3, there is some convex polyhedronQ combinatorically equivalent toP whichmidscribes K; that is, all the edges ofQ are tangent toK. Furthermore, with some stronger smoothness conditions on ∂K, the space of all suchQ is a six dimensional differentiable manifold.