Coxeter decompositions of hyperbolic simplices

Details Coxeter decompositions of hyperbolic simplices Coxeter decompositions of hyperbolic simplices

2002-10-04

arxiv.org/abs/math/0210067v2

Mathematics

Metric Geometry

31 pages, 4 figures, 5 tables. New references added, errors corrected

Scientific paper

Let X be a space of constant curvature and P be a convex polyhedron in X. A Coxeter decomposition of the polyhedron P is a decomposition of P into finitely many Coxeter polyhedra, such that any two polyhedra having a common facet are symmetric with respect to this facet. In this paper we classify Coxeter decompositions of simplices in hyperbolic space of dimension greater than 3. The problem is close to the classification of the finite index subgroups in the discrete hyperbolic reflection groups.

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