threefold rotational symmetry

crystallography

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July 14, 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 dictate the crystal's shape and physical properties.1

A threefold rotational symmetry means a crystal can be rotated around an axis by 120 degrees (360°/3) and appear unchanged. This type of symmetry is found in certain crystal systems, such as the hexagonal and trigonal systems. The presence and combination of these symmetry elements classify crystals into 32 point groups and 230 space groups.1234

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quasicrystal
Microscopic images of quasicrystalline structures
…the edges and axes of threefold rotational symmetry passing through the vertices. This is also known as icosahedral symmetry because the icosahedron is the geometric dual of the pentagonal dodecahedron. At the centre of each face on an icosahedron, the dodecahedron places a vertex, and vice versa. The symmetry of…
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…the edges and axes of threefold rotational symmetry passing through the vertices. This is also known as icosahedral symmetry because the icosahedron is the geometric dual of the pentagonal dodecahedron. At the centre of each face on an icosahedron, the dodecahedron places a vertex, and vice versa. The symmetry of…
Read More