A characterization of convex hyperbolic polyhedra and of convex   polyhedra inscribed in the sphere
  We describe a characterization of convex polyhedra in $\h^3$ in terms of their dihedral angles, developed by Rivin. We also describe some geometric and combinatorial consequences of that theory. One of these consequences is a combinatorial characterization of convex polyhedra in $\E^3$ all of whose vertices lie on the unit sphere. That resolves a problem posed by Jakob Steiner in 1832. 
Craig D. Hodgson, Igor Rivin, Warren D. Smith