Ma. Fortes, APPLICABILITY OF THE LEWIS AND ABOAV-WEAIRE LAWS TO 2D AND 3D CELLULAR STRUCTURES BASED ON POISSON PARTITIONS, Journal of physics. A, mathematical and general, 28(4), 1995, pp. 1055-1068
Two- and three-dimensional networks of a columnar type are described,
which result from partitions based on Poisson point distributions. The
metric and topological properties of such laminated Poisson networks
are derived and the applicability of the Lewis and Aboav-Weaire laws t
o them is tested. The 2D Poisson network contains cells with i greater
than or equal to 4 (i is the number of sides) and both laws are obeye
d. The 3D Poisson networks are of various types and have F greater tha
n or equal to 6 (F is the number of faces in a cell) and ($) over bar
F = 14. In one particular type of 3D Poisson network the two laws are
again exactly obeyed. In another type, the laws show large deviations
at low F but are asymptotically obeyed when F tends to infinite.