  Quasicrystals are frequently encountered in condensed matter. They are
important candidates for equilibrium phases from the atomic scale to the
nanoscale. Here, we investigate the computational self-assembly of four
quasicrystals in a single model system of identical particles interacting with
a tunable isotropic pair potential. We reproduce a known icosahedral
quasicrystal and report a decagonal quasicrystal, a dodecagonal quasicrystal,
and an octagonal quasicrystal. The quasicrystals have low coordination number
or occur in systems with mesoscale density variations. We also report a network
gel phase.
