 
Summary: J. Phys. A: Math. Gen. 31 (1998) 85778593. Printed in the UK PII: S03054470(98)919904
Dynamical partitions of space in any dimension
Tomaso Aste
AAS, Sal. Spianata Castelletto 16, 16124 Genova, Italy
and LDFC, Institut de Physique, Universitīe Louis Pasteur, 67084 Strasbourg, France
Received 23 February 1998, in final form 20 May 1998
Abstract. Topologically stable cellular partitions of Ddimensional spaces are studied. A
complete statistical description of the average structural properties of such partitions is given
in terms of a sequence of D
2  1 (or D1
2 ) variables for D even (or odd). These variables
are the average coordination numbers of the 2kdimensional polytopes (2k < D) which make
up the cellular structure. A procedure to produce Ddimensional space partitions through cell
division and cellcoalescence 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 VoronoĻi partitions and sphere packings in high dimensions.
1. Introduction
We study the topologically stable division of any dimensional space by cells. Such
systems have minimal incidence numbers. Configurations with higher incidence numbers
