Vibrating a thin layer of silicon oil in a flat container can produce standing waves of a kind never seen before. Jean Rajchenbach and colleagues of the University of Nice find that for strong enough vertical vibrations, patterns emerge that alternate between a star and a polygon, with n-fold symmetry determined by the frequency and intensity of the vibrations but not by the shape of the container. The team tracks these brand-new forms of standing waves down to a nonlinear resonance-coupling between waves.