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On the fundamental polyhedron for a discrete group of motions of the Lobachevskij space. (Russian) Zbl 0736.51014
The author proves that the class of the normal regular partitions related to a given discrete group of motion is in general infinite in the hyperbolic 3-space. It is shown that there is an at least countable infinite set of groups with the following property. Each of them have countable infinite topologically different stereohedra and partitions. A continuous three-parametric deformation is allowable on each of these stereohedra. The analogous theorem for the 4-dimensional hyperbolic space is proved, too.
MSC:
51M20 Polyhedra and polytopes; regular figures, division of spaces
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
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