О строении множества орбит отражений

Let $G$ be an infinite reflection group acting on a non-cylindrical algebraic surface. It is shown, that the set of all reflections belonging to group $G$ has the partition consisting of element-wise commuting «standard» subsets, each of which is the union no more than two $G$-orbits of reflections. The linear classification of all «standard» sets of reflections is given and the basis invariants of groups generated by these sets are calculated.