Let S be a sphere of unit radius in three dimensional Euclidean space, R^3. Given a
positive real number e, does there always exist a convex polyhedron P in R^3 such that:
(1) S is a subset of P (2) The boundary of P is homeomorphic to the boundary of S (3) The
volume of P does not exceed the volume of S by more than e? It is not required that S be
tangent to any of the faces of P.



A question about convex polyhedra
For small $\epsilon$ let $Q$ be the convex symmetric hull of a finite $\epsilon$ net for the boundary of $S$ and let $P=(1+\epsilon) Q$. 


