sixfold rotational symmetry

crystallography

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July 13, 2026

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In crystallography, symmetry refers to the orderly arrangement of atoms within crystalline solids. This arrangement possesses elements of symmetry, such as rotation, translation, reflection, and inversion, which influence a crystal's shape and physical properties.1

A sixfold rotational symmetry means a crystal can be rotated around an axis, repeating its appearance six times in a full 360° turn. This occurs when the crystal repeats itself every 60°. Crystals are classified based on their symmetry elements, leading to systems like hexagonal and isometric, each with specific combinations of rotational, reflectional, and inversion symmetries.21

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quasicrystal
Translational periodicity and symmetry
…Figure 1 has axes of sixfold rotational symmetry passing through each atomic position. The arrows represent translational symmetries of this crystalline structure. That is, if the entire array of atoms is displaced along one of these arrows, say the one labeled a, all new atomic positions coincide with the locations…
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…Figure 1 has axes of sixfold rotational symmetry passing through each atomic position. The arrows represent translational symmetries of this crystalline structure. That is, if the entire array of atoms is displaced along one of these arrows, say the one labeled a, all new atomic positions coincide with the locations…
Read More