  We use Monte Carlo simulations and free-energy techniques to show that binary
solutions of penta- and hexavalent two-dimensional patchy particles can form
thermodynamically stable quasicrystals even at very narrow patch widths,
provided their patch interactions are chosen in an appropriate way. Such patchy
particles can be thought of as a coarse-grained representation of DNA multi-arm
`star' motifs, which can be chosen to bond with one another very specifically
by tuning the DNA sequences of the protruding arms. We explore several possible
design strategies and conclude that DNA star tiles that are designed to
interact with one another in a specific but not overly constrained way could
potentially be used to construct soft quasicrystals in experiment. We verify
that such star tiles can form stable dodecagonal motifs using oxDNA, a
realistic coarse-grained model of DNA.
