Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations

Stationary and isotropic iteration stable random tessellations are considered, which are constructed by a random process of iterative cell division. The collection of maximal polytopes at a fixed time tt within a convex window W⊂RdW⊂Rd is regarded and formulas for mean values, variances and a characterization of certain covariance measures are proved. The focus is on the case d≥3d≥3, which is different from the planar one, treated separately in Schreiber and Thäle (2010) [12]. Moreover, a limit theorem for suitably rescaled intrinsic volumes is established, leading — in sharp contrast to the situation in the plane — to a non-Gaussian limit.