  We investigate quasicrystal-forming soft matter using a two-scale phase field
crystal model. At state points near thermodynamic coexistence between bulk
quasicrystals and the liquid phase, we find multiple metastable spatially
localized quasicrystals embedded in a background of liquid. In three dimensions
we obtain spatially localized icosahedral quasicrystals. In two dimensions, we
compute several families of spatially localized quasicrystals with dodecagonal
structure and investigate their properties as a function of the system
parameters. In both cases the localized quasicrystals are metastable, and so
correspond to energetically locally favored structures. The presence of such
structures is expected to crucially affect the dynamics of the crystallization
process.
