  We show that the Volume Conjecture for polyhedra implies a weak version of
the Stoker Conjecture; in turn we prove that this weak version of the Stoker
conjecture implies the Stoker conjecture. The main tool used is an extension of
a result of Montcouquiol and Weiss, saying that dihedral angles are local
coordinates for compact polyhedra with angles $\leq \pi$.
