This paper focuses on the analysis of the dispersion diagram of a two-dimensional hexagonal periodic structure. The periodic inclusions are placed in a parallel plate waveguide environment and are circular holes located at the vertices of the hexagonal unit cells. The connection between the geometry of the periodic structure and the dispersion diagram is discussed. The wavevector information in the Brillouin zone is illustrated using the reciprocal lattice, from which the shape of the irreducible zone can be derived. The results give insight into the characteristics of the wave propagation characteristic of hexagonal units.