  Let $M$ be a compact oriented 3-manifold with non-empty boundary consisting
of surfaces of genii $>1$ such that the interior of $M$ is hyperbolizable. We
show that for each spherical cone-metric $d$ on $\partial M$ such that all
cone-angles are greater than $2\pi$ and the lengths of all closed geodesics
that are contractible in $M$ are greater than $2\pi$ there exists a unique
strictly polyhedral hyperbolic metric on $M$ such that $d$ is the induced dual
metric on $\partial M$.
