Dynamical partitions of space in any dimension
Tomaso Aste · Journal of Physics A Mathematical and General · 1998
Topologically stable cellular partitions of D -dimensional spaces are studied. A complete statistical description of the average structural properties of such partitions is given in terms of a sequence of (or ) variables for D even (or odd). These variables are the average coordination numbers of the 2k -dimensional polytopes which make up the cellular structure. A procedure to produce D -dimensional space partitions through cell-division and cell-coalescence transformations is presented. Classes of structures which are invariant under these transformations are found and the average properties of such structures are illustrated. Homogeneous partitions are constructed and compared with the known structures obtained by Voronoï partitions and sphere packings in high dimensions.