The equation of a special algebraic surface with an infinite set of planes of oblique symmetry

Let G be an infinite group generated by oblique reflections with respect to hyperplanes in the real space E ^m ; let II , II , II be the linear spans of dimensions , , of three G-orbits of directions of symmetry, where II II II =0 and dim(II + II + II ) < + +. Some singularities of the equation of an algebraic hypersurface invariant with respect to G are established. Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 34–38, 1992.