  For soft matter to form quasicrystals an important ingredient is to have two
characteristic lengthscales in the interparticle interactions. To be more
precise, for stable quasicrystals, periodic modulations of the local density
distribution with two particular wavenumbers should be favored, and the ratio
of these wavenumbers should be close to certain special values. So, for simple
models, the answer to the title question is that only these two ingredients are
needed. However, for more realistic models, where in principle all wavenumbers
can be involved, other wavenumbers are also important, specifically those of
the second and higher reciprocal lattice vectors. We identify features in the
particle pair interaction potentials which can suppress or encourage density
modes with wavenumbers associated with one of the regular crystalline orderings
that compete with quasicrystals, enabling either the enhancement or suppression
of quasicrystals in a generic class of systems.
