Trigonal crystal system

In crystallography, the trigonal crystal system is one of the seven crystal systems. Sometimes the term rhombohedral lattice system is used as an exact synonym, whereas it is a subset. Crystals in the rhombohedral lattice system are always in the trigonal crystal system, but some crystals such as quartz are in the trigonal crystal system but not in the rhombohedral lattice system. The rhombohedral lattice system consists of the rhombohedral lattice, while the trigonal crystal system consists of the five point groups of the seven space groups with a rhombohedral lattice. There are 25 space groups whose point groups are one of the five in the trigonal crystal system, consisting of the seven space groups associated with the rhombohedral lattice system together with 18 of the 45 space groups associated with the hexagonal lattice system.

The trigonal point group describes the symmetry of an object produced by stretching a cube along the body diagonal. The resultant rhombohedral (or trigonal) Bravais lattice is generated by three primitive vectors of equal length that make equal angles with one another.