trigonalhexagonal

Trigonal hexagonal is not a standard separate crystal system. In crystallography, trigonal and hexagonal refer to two related but distinct ways of describing crystal symmetry and lattice geometry. The phrase can arise when a rhombohedral lattice, which belongs to the trigonal system, is described using hexagonal coordinates, producing a descriptive label that blends the two terms.

The hexagonal system is defined by lattice parameters a = b ≠ c with angles α = β = 90°, γ = 120°. The trigonal system (often described using a rhombohedral lattice) has equal edge lengths but oblique angles, and it features a threefold rotational axis. Although both describe threefold symmetry, they organize the lattice differently and use different conventional cells.

In practice, scientists sometimes describe trigonal crystals in a hexagonal setting for convenience or consistency with related minerals, especially when indexing or comparing structures. In such cases, the same material can be represented by hexagonal lattice parameters even though its true lattice is rhombohedral. Examples include minerals whose crystal structure is trigonal but may be indexed or catalogued using hexagonal coordinates; quartz, while hexagonal in classification, illustrates how hexagonal descriptions are standard for certain systems.

Modern crystallography clarifies terminology by treating trigonal (rhombohedral) and hexagonal as separate systems, with the rhombohedral lattice sometimes described in a hexagonal setting as a historical or practical convention. Therefore, “trigonal hexagonal” generally reflects a representation choice rather than a distinct, uniform category.