  A bar framework determined by a finite graph $G$ and configuration $\bf p$ in
$d$ space is universally rigid if it is rigid in any ${\mathbb R}^D \supset
{\mathbb R}^d$. We provide a characterization of universally rigidity for any
graph $G$ and any configuration ${\bf p}$ in terms of a sequence of affine
subsets of the space of configurations. This corresponds to a facial reduction
process for closed finite dimensional convex cones.
