How do quasicrystals differ from ordinary crystals?

In materials science, the primary distinction between quasicrystals and ordinary crystals lies in their symmetry and translational order.

• Translational Periodicity: Ordinary crystals are defined by translational periodicity, meaning their atomic structure repeats at regular intervals in space. Quasicrystals lack this spatial periodicity; instead, they exhibit translational quasiperiodicity.1
• Rotational Symmetry: Ordinary crystals are restricted to twofold, threefold, fourfold, and sixfold rotational symmetry axes because these are compatible with a periodic lattice. Quasicrystals, however, frequently display "forbidden" symmetries, such as fivefold, eightfold, tenfold, or twelvefold axes.1
• Long-Range Order: While both materials possess long-range order—meaning there are strict rules governing the placement of atoms at remote locations—the nature of this order differs. In ordinary crystals, this order is periodic, whereas in quasicrystals, it is quasiperiodic.1

Unlike amorphous solids, which lack both periodic and long-range order, quasicrystals produce sharp electron diffraction patterns, confirming their highly ordered, non-periodic atomic arrangements.1