total length of intersection segments of pairs of particles, $G_3$ is the total number of intersections of triplets of particles. The size of negative parameter $\nu_2$ or $\nu_3$ gives the measure of neglection of intersections (repulsion) of the corresponding type. If $\nu $ is a zero vector, then the facet process is Poisson (with no repulsion).

We will consider special types of facet processes $\mu^{(k)},\; k=1,\dots ,d,$ such that in (\[den\]) we have $\nu_k\leq 0$ while $\nu_j=0,\; j\neq k.$ We say that $\mu^{(k)}$ is a submodel of order $k$, especially $\mu^{(1)}$ is a Poisson process and $\mu^{(k)}$ is a Poisson process if and only if $\nu_k=0,\;k=2,\dots ,d.$

Local stability of a facet process is defined by the existence of $\alpha >0$ such that $$\begin{gathered}
\label{locst}\lambda^*(u;{\mathbf x})\leq\alpha ,\; {\mathbf x}\in{\bf N},\;u\in Y\setminus\{{\mathbf x}\} \end{gathered}$$ and under given conditions the processes $\mu^{(k)},\; k=1,\dots ,d$ are locally stable. Simulation of a facet process $\mu $ is available using the birth-death Metropolis-Hastings algorithm [@RefGM].

In [@RefM] the process with conditional intensity $\lambda^*$ is called attractive if $$\lambda^*(y;{\mathbf x}_1)\geq \lambda^*(y;{\mathbf x}_2),$$ for any ${\mathbf x}_1,{\mathbf x}_2\in {\bf N},\;{\mathbf x}_2\subset {\mathbf x}_1.$ It is repulsive if $$\lambda^*(y;{\mathbf x}_1)\leq \lambda^*(y;{\mathbf x}_2),$$ for any ${\mathbf x}_1,{\mathbf x}_2\in {\bf 