THE POISSON VORONOI TESSELLATION - III - MILES FORMULA

This paper gives distributional properties of geometrical characterist ics of a Voronoi tessellation generated by a stationary Poisson point process. The considerations are based on a well-known formula given by [10] describing size and shape of a cell of the Delaunay tessellation and on the close connection between Delaunay and Voronoi tessellation . Several results are given for the two-dimensional case, but the main part is the investigation of the three-dimensional case. They include the density functions of the angles perpendicular to the ''typical'' edge, spanned by two neighbouring Poisson points and that spanned by t wo neighbouring faces, the angle between two edges emanating from the ''typical'' vertex, the distance of two neighbouring Poisson points, t he angle between two edges emanating from the ''typical'' vertex of th e Poisson Voronoi tessellation and some others. These density function s are given partly explicitely and partly in integral form.