Geometry and Topology of 3D Voronoi Partitions

Abstract

A new algorithm to determine Voronoi partitions of space using periodic boundary conditions has been implemented in GAMGI free software package. This algorithm was used to study the topological and geometric properties of Voronoi polyhedra obtained for Poisson and Laguerre seeding distributions. The Random Sequential Adsorption (RSA) method was used to generate a Laguerre seeding distribution with a volume fraction of spheres φ ≈ 0.36. The resulting normalised cell volume distributions were compared with the gamma and lognormal density functions using χ2 goodness of fit testing, and in both cases the gamma function provides a better description. The Lewis and Aboav empirical relations approximately apply to both partitions, with least square correlation factors R2 equal to 0.98 for the Lewis law and 0.95 for the Aboav law.