The sectional Poisson Voronoi tessellation is not a Voronoi tessellation

Abstract

Is the intersection between an arbitrary but fixed plane and the spatial Poisson Voronoi tessellation a planar Voronoi tessellation? In this paper a negative answer is given to this long-standing question in stochastic geometry. The answer remains negative for the intersection between at-dimensional linear affine space and thed-dimensional Poisson Voronoi tesssellation, where 2 ≦t≦d− 1. Moreover, it is shown that each cell on this intersection is almost surely a non-Voronoi cell.