Random geometry and the statistics of two-dimensional cells

We obtain accurate values of P_n, the probability of finding an n-sided Voronoï cell in a two-dimensional Poisson random lattice up to large values of n(∼50). Numerical as well as analytical evidence points to a n^{- an} behavior for large n with a of order 2. We also study the mean area and the mean distance to a neighbor as functions of n, and check accurately several sum rules.