Geodesic
Hyperbolic Coxeter $N$-Polytopes with $n+2$ Facets
Matematičeskie zametki, Tome 75 (2004) no. 6, pp. 909-916.

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In this paper, we classify all the hyperbolic noncompact Coxeter polytopes of finite volume whose combinatorial type is either that of a pyramid over a product of two simplices or a product of two simplices of dimension greater than one. Combined with the results of Kaplinskaja (1974) and Esselmann (1996), this completes the classification of hyperbolic Coxeter $N$-polytopes of finite volume with $n+2$ facets. 
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P. V. Tumarkin. Hyperbolic Coxeter $N$-Polytopes with $n+2$ Facets. Matematičeskie zametki, Tome 75 (2004) no. 6, pp. 909-916. http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a8/

[1] Andreev E. M., “O vypuklykh mnogogrannikakh v prostranstvakh Lobachevskogo”, Matem. sb., 81:3 (1970), 445–478 | MR | Zbl

[2] Andreev E. M., “O vypuklykh mnogogrannikakh konechnogo ob'ema v prostranstve Lobachevskogo”, Matem. sb., 83:2 (1970), 256–260 | MR | Zbl

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

[4] Vinberg E. B., “Diskretnye gruppy, porozhdennye otrazheniyami, v prostranstvakh Lobachevskogo”, Matem. sb., 72(114):3 (1967), 471–488 | MR | Zbl

[5] Kaplinskaya I. M., “O diskretnykh gruppakh, porozhdennykh otrazheniyami v granyakh simplitsialnykh prizm v prostranstvakh Lobachevskogo”, Matem. zametki, 15:1 (1974), 159–164 | MR

[6] Esselmann F., “The classification of compact hyperbolic Coxeter $d$-polytopes with $d+2$ facets”, Comm. Math. Helv., 71 (1996), 229–242 | DOI | MR | Zbl

[7] Grünbaum B., Convex Polytopes, John Wiley Sons, New York, 1967 | Zbl

[8] Emelichev V. A., Kovalev M. M., Kravtsov M. K., Mnogogranniki, grafy, optimizatsiya, Nauka, M., 1981

[9] Vinberg E. B., “Giperbolicheskie gruppy otrazhenii”, UMN, 40:1 (1985), 29–64

[10] Vinberg E. B., “Otsutstvie kristallograficheskikh grupp otrazhenii v prostranstvakh Lobachevskogo bolshoi razmernosti”, Tr. MMO, 47, URSS, M., 1984, 68–102 | Zbl

[11] Tumarkin P., Hyperbolic Coxeter $n$-polytopes with $n+2$ facets, , 2003 E-print math.MG/0301133