On the dilated facets of a Poisson-Voronoi tessellation

Abstract

In this paper, the parallel set ΞR of the facets {(d-1)-faces) of a stationary Poisson-Voronoi tessellation in R2 and R3 is investigated. An analytical formula for the spherical contact distribution function of the tessellation allows for the derivation of formulae for the volume density and the specific surface area of ΞR. The densities of the remaining intrinsic volumes are studied by simulation. The results are used for fitting a dilated Poisson-Voronoi tessellation to the microstructure of a closed-cell foam.