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. 
@article{MZM_2004_75_6_a8,
     author = {P. V. Tumarkin},
     title = {Hyperbolic {Coxeter} $N${-Polytopes} with $n+2$ {Facets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {909--916},
     publisher = {mathdoc},
     volume = {75},
     number = {6},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a8/}
}
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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/