What does translational periodicity mean in an ordinary crystal?

In an ordinary crystal, translational periodicity refers to the property where the arrangement of atoms repeats itself at regular, fixed intervals throughout the structure.1

This order is defined by the unit cell, a fundamental building block that is precisely repeated in space. When the entire atomic array is displaced by a specific vector—a symmetry operation known as translation—every atom coincides with the position previously occupied by an identical neighbor, leaving the overall structure appearing unchanged.231

This periodic repetition ensures that there is a consistent, minimum spacing between atomic sites, which is a requirement for the existence of standard crystal lattices. In contrast, quasicrystals lack this translational periodicity, as their atomic patterns are quasiperiodic—meaning they possess long-range order but never repeat the same unit at equal intervals.12