Ordered structures in decagonal quasicrystals with simple and body-centered hypercubic lattices

Ordered structures in decagonal quasicrystals are discussed by the projection of five-dimensional periodic lattices on two-dimensional space. Superlattices in rhombic and pentagonal Penrose lattices can be derived from simple and body-centered hypercubic lattices, respectively. The superlattices are compared with ordered structures observed in Al–Ni–Co and Al–Ni–Ru decagonal quasicrystals in which two types of atom clusters with different orientations of pentagonal symmetry are placed at lattice points in pentagonal or rhombic quasiperiodic lattices with definite ordered manners.