  In the series of models with interacting particles in stochastic geometry, a
new contribution presents the facet process which is defined in arbitrary
Euclidean dimension. In 2D, 3D specially it is a process of interacting
segments, flat surfaces, respectively. Its investigation is based on the theory
of functionals of finite spatial point processes given by a density with
respect to a Poisson process. The methodology based on L2 expansion of the
covariance of functionals of Poisson process is developed for U-statistics of
facet intersections which are building blocks of the model. The importance of
the concept of correlation functions of arbitrary order is emphasized. Some
basic properties of facet processes, such as local stability and repulsivness
are shown and a standard simulation algorithm mentioned. Further the situation
when the intensity of the process tends to infinity is studied. In the case of
Poisson processes a central limit theorem follows from recent results of
Wiener-Ito theory. In the case of non-Poisson processes we restrict to models
with finitely many orientations. Detailed analysis of correlation functions
exhibits various asymptotics for different combination of U-statistics and
submodels of the facet process.
