Linearly polarized classical light can be expressed in a vertical and a horizontal component. Geometrically rotating vertically polarized light by 90 degrees will convert it to the orthogonal horizontal polarization. We have experimentally generated a two-photon state of light which evolves into an orthogonal state upon geometrical rotation by 60 degrees. Rotating this state by an additional 60 degrees will yield a state which is mutually orthogonal to the first two states. Generalizing this procedure, one can generate N+1 mutually orthogonal N-photon states that cyclicly evolve from one to another upon a geometric rotation by 180/(N+1) degrees.