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Topologically stable cellular partitions of D dimensional spaces are studied.A complete statistical description of the average structural properties of suchpartition is given in term of a sequence of D/2-1 (or (D-1)/2) variables for Deven (or odd). These variables are the average coordination numbers of the2k-dimensional polytopes (2k < D) which make the cellular structure. Aprocedure to built D dimensional space partitions trough cell-division andcell-coalescence transformations is presented. Classes of structures which areinvariant under these transformations are found and the average properties ofsuch structures are illustrated. Homogeneous partitions are constructed andcompared with the known structures obtained by Voronoi partitions and spherepackings in high dimensions.Comment: LaTeX 5 eps figures, submetted to J. Phys.

Dynamical partitions of space in any dimension