On non-normal partitions of Lobachevskij space. (Russian) Zbl 0739.51016

Balkan, V. V.

Mat. Issled. 119, 29-38 (1990).

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.

Reviewer: E.Jucovic (Košice)

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