| Abstract: | This paper gives distributional properties of geometrical characteristics 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 two neighbouring faces, the angle between two edges emanating from the ‘typical’ vertex, the distance of two neighbouring Poisson points, the angle between two edges emanating from the ‘typical’ vertex of the Poisson Voronoi tessellation and some others. These density functions are given partly explicitely and partly in integral form. |
