  For a three dimensional system we answer two questions, how simple a particle
system might be to show the quasicrystal order and, what system features are
the most important for quasicrystal formation? One-component system of
particles with isotropic pair interaction is one of the simplest ones. We show
that such system may be driven to three-dimensional decagonal (10-fold)
quasicrystalline state just by purely repulsive, isotropic and monotonic
interaction pair potential with two characteristic length scales; no attraction
is needed. The second question we answer defining universal (nearly independent
from the shape of the pair potential) effective integral parameters related to
the first peak of the radial distribution function. The universality is
illustrated by demonstrating the quasicrystalline order for a number of
particle systems with absolutely different interaction potentials, both purely
repulsive and attractive, but with the same effective integral parameters.
Simple models like we study qualitatively describe effective interaction in
molecular liquids, soft matter systems and metallic alloys for which
quasicrystals have been experimentally observed.
