We review the model of the Voronoi Diagrams which allows to reproduce the large-scale structures of our
universe as given by the astronomical catalogs. The observed number of galaxies in a given solid angle with a chosen
flux/magnitude versus the redshift presents a maximum that is a function of the flux/magnitude ; it can be explained by a
detailed analysis of the standard luminosity function for galaxies as well by two new luminosity function for galaxies. The
current status of the research on the statistics of the Voronoi Diagrams is reviewed.