Combinatorics of sections of polytopes and Coxeter groups in Lobachevsky spaces
نویسنده
چکیده
Coxeter classified all discrete isometry groups generated by reflections that act on a Euclidean space or on a sphere of an arbitrary dimension (see [1]). His fundamental work became classical long ago. Lobachevsky spaces (classical hyperbolic spaces) are as symmetric as Euclidean spaces and spheres. However, discrete isometry groups generated by reflections, with fundamental polytopes of finite volume (see [2]), are not classified for Lobachevsky spaces. In 1985, M.N. Prokhorov and myself proved the following theorem.
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