  The relative stability of three-dimensional icosahedral quasicrystals in
multi-component systems has been investigated based on a coupled-mode
Swift-Hohenberg model with two-length-scales. A recently developed projection
method, which provides a unified numerical framework to study periodic crystals
and quasicrystals, is used to compute free energies to high accuracy. Compared
with traditional approaches, the advantage of the projection method has been
also discussed detailedly. A rigorous and systematical computation demonstrates
that three-dimensional icosahedral quasicrystal, two-dimensional decagonal
quasicrystal are stable phases in such a simple multi-component coupled-mode
Swift-Hohenberg model. The result extends the multiple length-scales
interaction mechanism which can stabilize quasicrystals from single-component
to multi-component systems.
