THE SECTIONAL POISSON VORONOI TESSELLATION IS NOT A VORONOI TESSELLATION

Is the intersection between an arbitrary but fixed plane and the spati al Poisson Voronoi tessellation a planar Voronoi tessellation? In this paper a negative answer is given to this long-standing question in st ochastic geometry. The answer remains negative for the intersection be tween a t-dimensional linear affine space and the d-dimensional Poisso n Voronoi tesssellation, where 2 less than or equal to t less than or equal to d-1. Moreover, it is shown that each cell on this intersectio n is almost surely a non-Voronoi cell.