We propose a technique for the generation of polygonal optical patterns in real space using a combined effect of the spin-orbit interaction and confinement of light in the plane of a dielectric optical microcavity. The spin-orbit interaction emerging from the splitting in transverse electric (TE) and transverse magnetic (TM) optical modes of the microcavity gives rise to oscillations in space of propagating macroscopic wave packets of polarized photons. Confined in a harmonic potential, the latter follow closed trajectories of a polygonal form. We demonstrate the possibility of excitation by a continuous wave resonant optical pumping of polygonal optical patterns with a controllable (both even and odd) number of vertices.