A class of hyperbolic Coxeter groups (Q1062274)

Let \(P^ n\) be the real projective n-space equipped with a quadric Q inducing hyperbolic geometry in its interior. The author generalizes the notion of an orthoscheme to so called complete orthoschemes and claims that a list given by him contains all complete orthoschemes in \((P^ n,Q)\) whose dihedral angles are either natural or of type \(\circ\overset{^\infty}\diagrbar\circ\theta_\rho\circ\diagrbar\circ\). The result yields the classification of a certain type of hyperbolic Coxeter groups with finite covolume.