Geodesic
Spherical simplices generating discrete reflection groups
Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 585-598

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $P$ be a simplex in $\mathbb S^n$, and $G_P$ the group generated by reflections with respect to the faces of $P$. This paper considers the question of the conditions ensuring that $G_P$ is discrete. The main result is a description of all indecomposable spherical simplices generating discrete reflection groups. 
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     author = {A. A. Felikson},
     title = {Spherical simplices generating discrete reflection groups},
     journal = {Sbornik. Mathematics},
     pages = {585--598},
     publisher = {mathdoc},
     volume = {195},
     number = {4},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_4_a4/}
}
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A. A. Felikson. Spherical simplices generating discrete reflection groups. Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 585-598. http://geodesic.mathdoc.fr/item/SM_2004_195_4_a4/