## 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

### Keywords:

non-normal regular partitions; Lobachevskij space
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