Euclidean simplices generating discrete reflection groups

Let $P$ be a convex polytope in the Euclidean space \E^n. Consider the group $G_P$ generated by reflections in the facets of $P$. We say that $P$ {\it generates a reflection group $G_P$}. In the present paper, we list all Euclidean simplices generating discrete reflection groups.Comment: 20 pages; MPIM preprin

Coxeter Decompositions of Hyperbolic Tetrahedra

We classify Coxeter decompositions of hyperbolic tetrahedra, i.e. simplices in the hyperbolic space H^3. The paper completes the classification of Coxeter decompositions of hyperbolic simplices.Comment: 14 pages, 4 figures, 3 table