The poisson-voronoi tessellation: relationships for edges

In a unifed approach, this paper presents distributional properties ofa Voronoi tesselation.- o generated by a homogeneous Poisson point process in the Euclidean space of arbitrary dimension. Probability density functions and moments are given for characteristics of the 'typical' edge in lower-dimensional section hyperplanes (edge lengths, adjacent angles). We investigate relationships between edges and their neighbours, called Poison points or centres; namely angular distributions, distances, and positions of neighbours relative to the edge. The approach is analytical, and the results are given partly explicitly and partly as integral expressions, which are suitable for the numerical calculations also presented.