The concept of sublattices in quasi-lattices is applied to the two-lay
er structure of decagonal quasi-crystals such as Al65Cu20Co15 and Al70
Ni15Co15. The Penrose pentagon pattern is chosen as the parent lattice
for this procedure. This application shows that non-locally derivable
sublattices and non-locally derivable patterns play an important role
in the crystallography of ordered quasi-crystals. The relationships b
etween the sublattices in question are discussed.