Journal of Statistical Physics, Vol. 52, Nos. 1/2, 1988. p. 453-461.
Hamiltonians for nonperiodic tilings are considered. It is shown that the quasicrystalline tiling obtained by the cut-and-strip method from a D-dimensional cubic lattice may be a ground state only if the tiling possesses a high orientational symmetry: the (2, D)-quasicrystal should have D-fold symmetry if D is even and 2D-fold symmetry if D is odd. For interactions of a finite range the restrictions are stronger: only a (2, 5)-quasicrystal (Penrose tiling) may be a stable ground state.