  We investigate the formation and stability of icosahedral quasicrytalline
structures using a dynamic phase field crystal model. Nonlinear interactions
between density waves at two length scales stabilize three-dimensional
quasicrystals. We determine the phase diagram and parameter values required for
the quasicrystal to be the global minimum free energy state. We demonstrate
that traits that promote the formation of two-dimensional quasicrystals are
extant in three dimensions, and highlight the characteristics required for 3D
soft matter quasicrystal formation.
