Poincaré Theorem on Kleinian groups (groups acting discontinously on Euclidean or hyperbolic spaces or on spheres) provides a method to obtain a presentation of a Kleinian group from a fundamental polyhedra.
I know the proof in Maskit book (Kleinian groups) but I would like to know other proofs. I also know other proofs for Fuchsian groups (dimension 2) which does not generalize to higher dimension (e.g. Beardon's book, The geometry of discrete groups).
I have two motivations: 1) Maskit proof also proves Poincaré Polyhedra Theorem, which states the necessary and sufficient conditions for a polyhedra to be fundamental polyhedra of some Kleinian group. I have the filling that a direct proof of the "presentation theorem" should be possible and simpler than proving the "Polyhedra Theorem".
2) Does Poincaré Theorem generalizes to direct product of hyperbolic spaces?