Geodesic
The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension
Izvestiya. Mathematics, Tome 28 (1987) no. 2, pp. 401-411 
M. N. Prokhorov. The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension. Izvestiya. Mathematics, Tome 28 (1987) no. 2, pp. 401-411. http://geodesic.mathdoc.fr/item/IM2_1987_28_2_a6/
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     title = {The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in {Lobachevskii} space of large dimension},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The following theorem is proved: There are no discrete groups generated by reflections with fundamental polyhedron of finite volume in Lobachevskii space of dimension $995$. Bibliography: 8 titles.

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[2] Vinberg E. B., “Diskretnye gruppy, porozhdennye otrazheniyami v prostranstvakh Lobachevskogo”, Matem. sb., 72 (1967), 471–488 | MR | Zbl

[3] Vinberg E. B., “Ob unimodulyarnykh tselochislennykh kvadratichnykh formakh”, Funkts. analiz i ego prilozh., 6 (1972), 25–32 | MR

[4] Vinberg E. B., “Otsutstvie kristallograficheskikh grupp otrazhenii v prostranstvakh Lobachevskogo bolshoi razmernosti”, Tr. Mosk. matem. o-va, 47, 1984, 68–102 | MR | Zbl

[5] Nikulin V. V., “O klassifikatsii arifmeticheskikh grupp, porozhdennykh otrazheniyami, v prostranstvakh Lobachevskogo”, Izv. AN SSSR. Ser. matem., 45:1 (1981), 113–142 | MR | Zbl

[6] Nikulin V. V., “O faktor-gruppakh grupp avtomorfizmov giperbolicheskikh form po podgruppam, porozhdennym 2-otrazheniyami. Algebro-geometricheskie prilozheniya”, Sovremennye problemy matematiki, 18, VINITI, 1981, 3–114 | MR

[7] Khovanskii L. G., “Giperploskie secheniya mnogogrannikov, toricheskie mnogoobraziya i diskretnye gruppy v prostranstve Lobachevskogo”, Funkts. analiz i ego prilozh., 20:1 (1986), 50–61 | MR

[8] Lannér F., “On complexes with transitive groups of automorphism”, Comm. Sém. Math. Univ. Lund., 11 (1950), 1–71 | MR