On the classification of hyperbolic Coxeter polyhedra

In this talk, we discuss the classification of hyperbolic Coxeter polyhedral, that is, hyperbolic polyhedra whose dihedral angles are integer submultiples of \pi. We give an overview of the main classification results and discuss the few known examples in higher dimensions. We present a method to construct hyperbolic Coxeter polyhedra with mutually intersecting facets and non-zero dihedral angles. We provide a new Coxeter polyhedron in dimension 9 and complete the classification of hyperbolic Coxeter polyhedra with mutually intersecting facets and dihedral angles \pi/2, \pi/3 and \pi/6.