trigonalsystem

Trigonalsystem, in crystallography, is one of the seven crystal systems used to classify crystalline materials by symmetry. Crystals in this system exhibit threefold rotational symmetry around a principal axis, and may possess additional symmetry elements consistent with the space group.

Two lattice representations are used to describe trigonal crystals: a rhombohedral lattice and a hexagonal lattice. In the rhombohedral representation, the unit cell has three equal edges and a rhombohedral angle that is not 90 degrees. In the hexagonal representation, a conventional hexagonal cell with a 120-degree angle in the basal plane and a distinct axis is used. Both representations describe the same lattice, just with different choices of the unit cell.

Historically, the trigonal system has been discussed as including both rhombohedral and hexagonal forms; in modern crystallography, the rhombohedral lattice is associated with the trigonal system, while the hexagonal lattice is treated as a separate hexagonal crystal system in standard classifications.

Representative minerals include calcite and dolomite, which crystallize in a trigonal lattice (rhombohedral). The trigonal system is important in mineralogy and materials science, particularly for characterizing anisotropic properties and for interpreting X-ray diffraction patterns.

See also: crystal system, lattice, space group.