Hyperbolic Coxeter Pyramids

Coxeter Decompositions of Bounded Hyperbolic Pyramids and Triangular Prisms

Coxeter decompositions of hyperbolic simplices where studied in math.MG/0212010 and math.MG/0210067. In this paper we use the methods of these works to classify Coxeter decompositions of bounded convex pyramids and triangular prisms in the hyperbolic space IH.

Essential Hyperbolic Coxeter Polytopes

We introduce a notion of essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We determine a potentially large combinatorial class of polytopes containing, in particular, all the compact hyperbolic Coxeter polytopes of dimens...

On hyperbolic Coxeter n-cubes

Beside simplices, n-cubes form an important class of simple polyhedra. Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter n-cubes are not classified. In this work, we first show that there are no Coxeter n-cubes in H for n ≥ 10. Then, we show that the ideal ones exist only for n = 2 and 3, and provide a classification. The methods used are of combinatorial and algebraic nature, using prope...

Coxeter decompositions of hyperbolic simplices

Coxeter Decompositions of Hyperbolic Tetrahedra

In this paper, we classify Coxeter decompositions of hyperbolic tetrahedra, i.e. simplices in the hyperbolic space IH. The paper together with [2] completes the classification of Coxeter decompositions of hyperbolic simplices.