Vinberg, Eh. B. Discrete reflection groups in Lobachevskij spaces of high dimension. (Russian) Zbl 0539.51005 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 132, 62-68 (1983). It is proved that in Lobachevskij space of dimension \(n\geq 62\) there exist no discrete reflection groups with a bounded fundamental polyhedron. The proof is based on recent results on combinatorics of simplicial convex polyhedra. A more careful analysis carried out in another work of the author [VINITI Dep. No.3417-82] enables one to prove the same for \(n\geq 30\). Cited in 1 ReviewCited in 1 Document MSC: 51F15 Reflection groups, reflection geometries 20H15 Other geometric groups, including crystallographic groups 51M10 Hyperbolic and elliptic geometries (general) and generalizations Keywords:bounded fundamental polyhedron; simplicial convex polyhedra PDFBibTeX XMLCite \textit{Eh. B. Vinberg}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 132, 62--68 (1983; Zbl 0539.51005) Full Text: EuDML