We consider the steady Swift-Hohenberg partial differential equation. It is a one-parameter family of PDE on the plane, modeling for example Rayleigh-Bénard con-vection. For values of the parameter near its critical value, we look for small solutions, quasiperiodic in all directions of the plane and which are invariant under rotations of angle π/q, q ≥ 4. We solve an unusual small divisor problem, and prove the existence of solutions for small parameter values. Notice a gap in the proof between Lemma 14 and Lemma 15. A forthcomming paper solves the problem.