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We consider the 3D Poisson-Voronoi tessellation. We investigate the jointprobability distribution pi_n(L) for an arbitrarily selected cell face to ben-edged and for the distance between the seeds of its adjacent cells to beequal to 2L. We derive an exact expression for this quantity, valid in thelimit n->infty with n^{1/6}L fixed. The leading order correction term isdetermined. Good agreement with earlier Monte Carlo data is obtained. The cellface is surrounded by a three-dimensional excluded domain that is the union ofn balls; it is pumpkin-shaped and analogous to the flower of the 2D Voronoicell. For n->infty this domain tends towards a torus of equal major and minorradii. The radii scale as n^{1/3}, in agreement with earlier heuristic work. Weachieve a detailed understanding of several other statistical properties of then-edged cell face.

Exact asymptotic statistics of the n-edged face in a 3D Poisson-Voronoi tessellation