Geodesic
Coxeter decompositions of hyperbolic simplexes
Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1867-1888 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Coxeter decomposition of a polyhedron in a hyperbolic space $\mathbb H^n$ is a decomposition of it into finitely many Coxeter polyhedra such that any two tiles having a common facet are symmetric with respect to it. The classification of Coxeter decompositions is closely related to the problem of the classification of finite-index subgroups generated by reflections in discrete hyperbolic groups generated by reflections. All Coxeter decompositions of simplexes in the hyperbolic spaces $\mathbb H^n$ with $n>3$ are described in this paper. 
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     title = {Coxeter decompositions of hyperbolic simplexes},
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     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_12_a5/}
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A. A. Felikson. Coxeter decompositions of hyperbolic simplexes. Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1867-1888. http://geodesic.mathdoc.fr/item/SM_2002_193_12_a5/

[1] Klimenko E., Sakuma M., “Two-generator discrete subgroups of $\operatorname{Isom}(\mathbb H^2)$ containing orientation-reversing elements”, Geom. Dedicata, 72 (1998), 247–282 | DOI | MR | Zbl

[2] Knapp A. W., “Doubly generated Fuchsian groups”, Michigan Math. J., 15 (1968), 289–304 | DOI | MR | Zbl

[3] Matelski J. P., “The classification of discrete 2-generator subgroups of $\operatorname{PSL}_2(\mathbb R)$”, Israel J. Math., 42 (1982), 309–317 | DOI | MR | Zbl

[4] Mostow G. D., “On discontinuous action of monodromy groups on the complex $n$-ball”, J. Amer. Math. Soc., 1:3 (1988), 555–586 | DOI | MR | Zbl

[5] Felikson A., “Coxeter decompositions of hyperbolic polygons”, European J. Combin., 19 (1998), 801–817 | DOI | MR | Zbl

[6] Felikson A., Coxeter decompositions of hyperbolic tetrahedra, Preprint No 98-083, Bielefeld | MR

[7] Andreev E. M., “O peresechenii ploskostei granei mnogogrannikov s ostrymi uglami”, Matem. zametki, 8:4 (1970), 521–527 | MR | Zbl

[8] Johnson N. W., Kellerhals R., Ratcliffe J. G., Tschantz S. T., “The size of a hyperbolic Coxeter simplex”, Transform. Groups, 4:4 (1999), 329–353 | DOI | MR | Zbl

[9] Felikson A., Coxeter decompositions of hyperbolic simplices, http://arXiv.org/abs/math.MG/0210067

[10] Felikson A., “Koksterovskie razbieniya sfericheskikh simpleksov s nerazrezannymi dvugrannymi uglami”, UMN, 57:2 (2002), 201–202 | MR | Zbl

[11] Dynkin E. B., “Poluprostye podalgebry poluprostykh algebr Li”, Matem. sb., 30:2 (1952), 349–462 | MR | Zbl