Inventiones mathematicae

, Volume 107, Issue 1, pp 543–560

How to cage an egg

  • Oded Schramm

DOI: 10.1007/BF01231901

Cite this article as:
Schramm, O. Invent Math (1992) 107: 543. doi:10.1007/BF01231901


This 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.

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Oded Schramm
    • 1
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA