We present the key results from a comprehensive study of the refraction and focusing properties of a two-dimensional dodecagonal photonic ``quasicrystal (PQC), carried out via both full-wave numerical simulations and microwave measurements on a slab
made of alumina rods inserted in a parallel-plate waveguide. We observe anomalous refraction and focusing in several frequency regions, confirming some recently published results. However, our interpretation, based on numerical and experimental evidence, differs substantially from the one in terms of ``effective negative refractive-index that was originally proposed. Instead, our study highlights the critical role played by short-range interactions associated with local order and symmetry.
