Geodesic
On convex polyhedra in Lobachevskii spaces
Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 413-440 
E. M. Andreev. On convex polyhedra in Lobachevskii spaces. Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 413-440. http://geodesic.mathdoc.fr/item/SM_1970_10_3_a7/
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     author = {E. M. Andreev},
     title = {On~convex polyhedra in {Lobachevskii} spaces},
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     volume = {10},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_10_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is concerned with the investigation of properties of convex polyhedra in Lobachevskii spaces; it gives a complete description of convex bounded polyhedra with dihedral angles not exceeding $90^\circ$, in a three-dimensional Lobachevskii space. This in turn permits a description of the discrete groups generated by reflections acting in the three-dimensional Lobachevskii space with a compact fundamental region. Figures: 6. Bibliography: 6 titles.

[1] A. D. Aleksandrov, Vypuklye mnogogranniki, Gostekhizdat, Moskva–Leningrad, 1950 | MR

[2] E. B. Vinberg, “Diskretnye gruppy, porozhdennye otrazheniyami, v prostranstvakh Lobachevskogo”, Matem. sb., 72(114) (1967), 471–478 | MR

[3] L. A. Lyusternik, Vypuklye figury i mnogogranniki, Gostekhizdat, Moskva, 1956 | MR

[4] Fan Tszi, “O sistemakh lineinykh neravenstv”, Lineinye neravenstva i smezhnye voprosy, 1959, 214–262, IL, Moskva

[5] H. S. Coxeter, “Discrete groups generated by reflections”, Ann. Math., 35:3 (19341), 588–621 | DOI | MR | Zbl

[6] F. Lanner, “On complexes with transitive groups of automorfisms”, Comm. Sem. Math., 11 (1950) | MR | Zbl