  Motivated by recent new Monte Carlo data we investigate a heuristic
asymptotic theory that applies to n-faced 3D Poisson-Voronoi cells in the limit
of large n. We show how this theory may be extended to n-edged cell faces. It
predicts the leading order large-n behavior of the average volume and surface
area of the n-faced cell, and of the average area and perimeter of the n-edged
face. Such a face is shown to be surrounded by a toroidal region of volume
n/lambda (with lambda the seed density) that is void of seeds. Two neighboring
cells sharing an n-edged face are found to have their seeds at a typical
distance that scales as n^{-1/6} and whose probability law we determine. We
present a new data set of 4*10^9 Monte Carlo generated 3D Poisson-Voronoi
cells, larger than any before. Full compatibility is found between the Monte
Carlo data and the theory. Deviations from the asymptotic predictions are
explained in terms of subleading corrections whose powers in n we estimate from
the data.
