fivefold rotational symmetry
Quick Summary
In crystallography, symmetry refers to the orderly arrangement of atoms within crystalline solids. Elements of symmetry, such as rotation, translation, reflection, and inversion, determine a crystal's shape and physical properties.1
Rotational symmetry involves turning a crystal around an axis. In traditional crystals, rotations are limited to angles that divide 360° by 1, 2, 3, 4, or 6. However, quasicrystals, a distinct form of matter, can exhibit fivefold rotational symmetry, which is forbidden in conventional crystals. This fivefold symmetry means a pattern repeats five times within a 360° rotation, occurring every 72°.12
Quasicrystals possess long-range order but lack the precise, repeating patterns of crystals. Instead, their structures are formed from two or more unit cells assembled in a non-repeating, quasiperiodic array. This unique structure allows for symmetries like fivefold rotation, which is not compatible with the translational periodicity found in regular crystals.231
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