  We consider the d-dimensional Poisson-Voronoi tessellation and investigate
the applicability of heuristic methods developed recently for two dimensions.
Let p_n(d) be the probability that a cell have n neighbors (be `n-faced') and
m_n(d) the average facedness of a cell adjacent to an n-faced cell. We obtain
the leading order terms of the asymptotic large-n expansions for p_n(d) and
m_n(3). It appears that, just as in dimension two, the Poisson-Voronoi
tessellation violates Aboav's `linear law' also in dimension three. A
confrontation of this statement with existing Monte Carlo work remains
inconclusive. However, simulations upgraded to the level of present-day
computer capacity will in principle be able to confirm (or invalidate) our
theory.
