Lattice versus structure, dimensionality versus periodicity: a crystallographic Babel?

In this article, several mistakes occurring in the description of crystal structures are pointed out. (1) The term 'lattice' is often used instead of 'structure'. (2) The two terms `superlattice' and 'sublattice' are incorrectly interchanged. (3) Substructures composed of a subset of the crystallographic orbits composing the structure are incorrectly called 'sublattices'. (4) Subperiodic structures are incorrectly referred to as 'low-dimensional' structures.