Distributional properties of the three-dimensional Poisson Delaunay cell

This paper gives distributional properties of geometrical characteristics of the Delaunay tessellation generated by a stationary Poisson point process in R(3). The considerations are based on a well-known formula given by Miles which describes the size and shape of the ''typical'' three-dimensional Poisson Delaunay cell. The results are the probability density functions for its volume, the area, and the perimeter of one of its faces, the angle spanned in a face by two of its edges, and the length of an edge. These probability density functions are given in integral form. Formulas for higher moments of these characteristics are given explicitly.