We consider (m-1)-dimensional noncylindrical algebraic surfaces in a real space R m with infinite symmetry groups G generated by skew reflections with respect to planes, along with the relative locations of linear hulls of four G-orbits of the directions of symmetry.Let F. be an (m-1)-dimensional noncylindrical surface of order n in a real space Era: assume that F is invariant with respect to an infinite group G that is generated by skew reflections relative to planes and does not admit extension. In proving the theorem (Sections l~ ~ we obtain equations for the surfaces F,, that are invariant under the corresponding groups G. t ~ We set dj = 1 and cr = v (there is no loss of generality). In the space E m we specify a Cartesian coordinate system Oyl ...y4zl ...z,zl ...zr (m = r + r + 4). We define a surface Fn (n > 2) with complete symmetry group G by means of the equation
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