Alexander Kharazishvili

On Decompositions of a Cube into Cubes and Simplexes

Some combinatorial results concerning finite decompositions (dissections) of a k-dimensional cube into cubes (respectively, simplexes) of the same dimension are presented in the paper. In connection with such decompositions, the notion of a decomposability number is introduced and the problem of description of all these numbers is discussed.

Cube, simplex, finite decomposition, decomposability number, convex polyhedron, primitive extension, primitive polyhedron.

MSC 2000: 52A15, 52B05, 52B10