PROPERTIES OF A 2-DIMENSIONAL POISSON-VORONOI TESSELATION - A MONTE-CARLO STUDY

On the basis of simulation of 2 x 10(6) polygons, the distribution of the topological parameter (number of sides) as well as the distributions of area, perimeter, and edge length of the two-dimensional (2D) Poisson-Voronoi polygons have been accurately determined. A two-parameter gamma distribution has been found to be a good fit to both the topological and the area distributions. For sample sizes less than 5000 polygons, the two-parameter lognormal distribution can also be used to accurately describe these distributions. The area, perimeter, and edge length distributions for polygons having a fixed number of edges have also been obtained. The 2D cross section of a three-dimensional Voronoi tesselation has also been studied. The side and area distributions for these cross sections have been found to be significantly different from those in the case of pure 2D Voronoi tesselation. For the former case, our results for the mean number of sides of the neighboring cells of an n-sided cell are in agreement with Aboav's rule as well as his experimental results for the 2D cross section of magnesium oxide grains.