be given. In the paper basic properties of facet processes are investigated, based on the fact that the densities come from exponential family as studied in [@RefM] for the disc process with an analogous density type. It is shown that the given class of processes is characterized by a repulsive behavior. Conditions for local stability are given and a standard simulation algorithm based on birth-death algorithm in Markov chain Monte Carlo is mentioned, which enables to observe realizations of the facet process.

As an application of the moment formulas we are interested in the limit behaviour when the intensity of the reference Poisson process tends to infinity. Central limit theorems for $U$-statistics of Poisson processes were derived based on Malliavin calculus and the Stein method in [@RefR]. The results were extended to the multivariate case in [@RefL] and they apply to the vector of model characteristics of the Poisson facet process in our setting. In the paper [@RefX] the authors give conditions for functionals of Gibbs point processes under which they are asymptotically Gaussian with increasing window. Another related work is [@RefP], where the central limit theorem for the number of intersections in expanding window is derived for the stationary 