  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.
