Georgian Mathematical Journal 13 (2006), No. 2, 285--290
Copyright Heldermann Verlag 2006
On Decompositions of a Cube into Cubes and Simplexes
Alexander Kharazishvili
(1) A. Razmadze Mathematical Institute, 1 M. Aleksidze Street, Tbilisi 0193, Georgia
(2) I. Vekua Inst. of Applied Mathematics, I. Javakhishvili State University, 2 University Street, Tbilisi 0143, Georgia
kharaz2@yahoo.com
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.
Keywords: Cube, simplex, finite decomposition, decomposability number, convex polyhedron, primitive extension, primitive polyhedron.
MSC: 52A15, 52B05, 52B10
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