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In the series of models with interacting particles in stochastic geometry, anew contribution presents the facet process which is defined in arbitraryEuclidean dimension. In 2D, 3D specially it is a process of interactingsegments, flat surfaces, respectively. Its investigation is based on the theoryof functionals of finite spatial point processes given by a density withrespect to a Poisson process. The methodology based on L2 expansion of thecovariance of functionals of Poisson process is developed for U-statistics offacet intersections which are building blocks of the model. The importance ofthe concept of correlation functions of arbitrary order is emphasized. Somebasic properties of facet processes, such as local stability and repulsivnessare shown and a standard simulation algorithm mentioned. Further the situationwhen the intensity of the process tends to infinity is studied. In the case ofPoisson processes a central limit theorem follows from recent results ofWiener-Ito theory. In the case of non-Poisson processes we restrict to modelswith finitely many orientations. Detailed analysis of correlation functionsexhibits various asymptotics for different combination of U-statistics andsubmodels of the facet process.

Interaction processes for unions of facets, a limit behavior