Geodesic
Coxeter decompositions of hyperbolic tetrahedra
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 263-275 
A. A. Felikson. Coxeter decompositions of hyperbolic tetrahedra. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 263-275. http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a16/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we classify all Coxeter decompositions of hyperbolic tetrahedra. Using this classification one can find all Coxeter subgroups of the group generated by reflections with respect to the faces of the tetrahedra. The indices of such subgroups easily follow from the classification also.

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

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

[3] Felikson A., Coxeter decompositions of spherical tetrahedra, Preprint, Bielefeld, No 99-053

[4] Felikson A., Coxeter decompositions of hyperbolic piramids and triangular prisms, Preprint, Bielefeld, No 00-006