Coxeter Decompositions of Bounded Hyperbolic Pyramids and Triangular Prisms

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.

Euclidean simplices generating discrete reflection groups

Let P be a convex polytope in the spherical space S, in the Euclidean space E, or in the hyperbolic space H. Consider the group GP generated by reflections in the facets of P . We call GP a reflection group generated by P . The problem we consider in this paper is to list polytopes generating discrete reflection groups. The answer is known only for some combinatorial types of polytopes. Already...

Coxeter polytopes with a unique pair of non-intersecting facets

We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d + 3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88–91] and the second author [...

Coxeter decompositions of hyperbolic simplices

Stable and Compatible Polynomial Extensions in Three Dimensions and Applications to the p and h-p Finite Element Method

Polynomial extensions play a vital role in the analysis of the p and h-p FEM and the spectral element method. We construct explicitly polynomial extensions on standard elements: cubes, triangular prisms and pyramids, which together with the extension on tetrahedrons are used by the p and h-p FEM in three dimensions. These extensions are proved to be stable and compatible with FEM subspaces on t...