trigonalrombohedral

Trigonal rhombohedral is a term used in crystallography to describe crystals that exhibit threefold rotational symmetry and whose lattice can be described as rhombohedral. In modern practice, rhombohedral lattices are treated as part of the hexagonal crystal family, with the hexagonal setting often used for convenience. Consequently, materials are sometimes described as trigonal (rhombohedral) to acknowledge both the threefold symmetry and the rhombohedral lattice description. The terminology can vary, and some sources distinguish between the trigonal crystal class and the rhombohedral lattice, leading to overlapping usage.

Lattice and symmetry-wise, a rhombohedral lattice has a unit cell that is a rhombohedron, with a = b = c and α = β = γ ≠ 90°. In the hexagonal setting, the same lattice is described by a = b ≠ c with γ = 120°, α = β = 90°. The characteristic threefold axis is the primary symmetry element, and the overall symmetry depends on the specific space group. This framework emphasizes threefold symmetry rather than cubic or tetragonal metrics.

Common examples and usage: calcite and dolomite are classic minerals described as trigonal rhombohedral due to their rhombohedral lattice and threefold symmetry. Quartz is often described as trigonal in crystal class but is typically treated within the hexagonal system for lattice description. Because of historical and methodological differences between mineralogy and crystallography, the exact labeling can vary, and “trigonal rhombohedral” is sometimes used informally to refer to the rhombohedral lattice in the trigonal crystal family.

See also: crystal system, rhombohedral lattice, trigonal crystal system, space group.