Engineering of the orbital angular momentum (OAM) of light due to interaction with photonic lattices reveals rich physics and motivates potential applications. We report the experimental creation of regularly-distributed quantized vortex arrays in momentum space by probing the honeycomb and hexagonal photonic lattices with a single focused Gaussian beam. For the honeycomb lattice, the vortices are associated with Dirac points. However, we show that the resulting spatial patterns of vortices are strongly defined by the symmetry of the wave packet evolving in the optical lattice, and not by lattice topological properties. Our findings reveal the underlying physics by connecting the symmetry and OAM conversion, and provide a simple and efficient method to create regularly-distributed multiple vortices from unstructured light.