  Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built
up from e.g. kites and darts, squares and equilateral triangles, rhombi or
shield shaped tiles and can have a variety of different symmetries. However,
almost all quasicrystals occurring in soft-matter are of the dodecagonal type.
Here, we investigate a class of aperiodic tilings with hexagonal symmetry that
are based on rectangles and two types of equilateral triangles. We show how to
design soft-matter systems of particles interacting via pair potentials
containing two length-scales that form aperiodic stable states with two
different examples of rectangle--triangle tilings. One of these is the
bronze-mean tiling, while the other is a generalization. Our work points to how
more general (beyond dodecagonal) quasicrystals can be designed in soft-matter.
