  We propose the theory which unifies the description of quasicrystal assembly
thermodynamics and quasicrystal structure formation by combining the Landau
theory of crystallization and the cluster approach to quasicrystals. The theory
is illustrated on the example of pentagonal Penrose quasilattice. The
coordinates of the quasilattice nodes are calculated by minimizing the Landau
free energy with the constraint imposed by internal organization of atomic
clusters, without explicit use of high-dimensional crystallography. The
procedure proposed establishes direct relations between the cluster
organization, quasicrystalline structure and thermodynamic properties of the
quasicrystalline state. The correspondence is shown between the basic features
of the proposed algorithm for quasilattice construction, on the one hand, and
the conventional projection method, on the other hand. It provides a new
physical justification for high-dimensional crystallography methods
application.
