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On non-normal partitions of Lobachevskij space. (Russian) Zbl 0739.51016
A partition \(P\) of the \(n\)-space \(S_ n\) into polytopes is regular if to any two polytopes there is a mapping of \(P\) carrying one polytope into any other. \(P\) is non-normal if in \(P\) there are couples of polytopes having \((n-1)\)-dimensional proper parts of the \((n-1)\)-faces in common.
Examples of infinite series of non-normal regular partitions of the 3-, 4- and 5-dimensional Lobachevskij space are presented.
MSC:
51M20 Polyhedra and polytopes; regular figures, division of spaces
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
51M10 Hyperbolic and elliptic geometries (general) and generalizations
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