The phononic band diagram of a periodic square structure fabricated by femtosecond laser pulse-induced two photon polymerization is recorded by Brillouin light scattering (BLS) at hypersonic (GHz) frequencies and computed by finite element method. The theoretical calculations along the two main symmetry directions quantitatively capture the band diagrams of the air- and liquid-filled structure and moreover represent the BLS intensities. The theory helps identify the observed modes, reveals the origin of the observed bandgaps at the Brillouin zone boundaries, and unravels direction dependent effective medium behavior.