Regular crystals have translational symmetry, where the same unit part is repeated over and over again with no rotation. Quasicrystals have rotational symmetry, where the same unit part is repeated over and over, but with a rotation about an angle.

Quasicrystals are structural forms that are both ordered and nonperiodic. They form patterns that fill all the space but lack translational symmetry. The term and the concept were introduced originally to denote a specific arrangement observed in solids which can be said to be in a state intermediary between crystal and glass. Producing Bragg diffraction, they share a defining property with crystals, but differ from them by lacking a simple repeating structure.

Mathematical artefacts known as 'aperiodic tilings' were invented in the early 1960s, but some twenty years later physical experiments gave conclusive evidence of their material existence. Within the field of crystallography and solid state physics the discovery has produced a paradigm shift which is indeed a minor scientific revolution.

[1] It was realized that quasicrystals had been investigated and observed earlier

[2] but until then the prevailing views about atomic structure of matter lead to their being explained away.

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