We present the key results from a comprehensive study of the refraction and focusing properties of a two-dimensional dodecagonal photonic “quasicrystal” (PQC), which was 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 an anomalous refraction and focusing in several frequency regions, which confirm some recently published results. However, our interpretation, which is based on numerical and experimental evidence, substantially differs 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.