  Model patchy particles have been shown to be able to form a wide variety of
structures, including symmetric clusters, complex crystals and even
two-dimensional quasicrystals. Here, we investigate whether we can design
patchy particles that form three-dimensional quasicrystals, in particular
targeting a quasicrystal with dodecagonal symmetry that is made up of stacks of
two-dimensional quasicrystalline layers. We obtain two designs that are able to
form such a dodecagonal quasicrystal in annealing simulations. The first is a
one-component system of 7-patch particles but with wide patches that allow them
to adopt both 7- and 8-coordinated environments. The second is a ternary system
that contains a mixture of 7- and 8-patch particles, and is likely to be more
realizable in experiments, for example, using DNA origami. One interesting
feature of the first system is that the resulting quasicrystals very often
contain a screw dislocation.
