Trigonal crystal system

A crystal system whose point groups include a principal threefold rotational axis. Its lattices are described using rhombohedral axes or, commonly, hexagonal axes.

Crystal system: A classification of crystals based on the symmetry of their point groups and lattices. Trigonal is one of the seven crystal systems.
Rhombohedral unit cell: A primitive unit cell with three equal edges and equal, non-right interaxial angles. This cell expresses trigonal lattice geometry directly.
Quartz: A crystalline form of silicon dioxide with trigonal symmetry in its common low-temperature structure. Quartz is a familiar mineral whose crystal structure belongs to the trigonal system.
Hexagonal crystal family: A crystallographic family grouping structures described with hexagonal lattice conventions, including trigonal and hexagonal systems. The family is broader than the trigonal crystal system itself.
Point group: A set of symmetry operations that leave at least one point fixed. The trigonal system is defined by the point groups it contains.
Hexagonal unit cell: A unit cell with two equal basal edges at 120 degrees and a distinct perpendicular axis. A larger hexagonal cell can represent the same rhombohedral lattice.
Calcite: A calcium carbonate mineral that crystallizes in the trigonal system. Its rhombohedral cleavage and crystal forms illustrate trigonal symmetry.
Rhombohedral crystal system: A historical and alternative classification name often used for the trigonal crystal system. The name overlaps with trigonal usage but can obscure the distinction between system and lattice type.
Threefold rotational symmetry: Symmetry in which rotation by 120 degrees leaves an object unchanged. A principal threefold axis is the defining symmetry shared by trigonal point groups.
Miller indices: Integer coordinates that label crystal planes and directions relative to chosen crystallographic axes. Axis conventions affect how trigonal crystal directions and planes are indexed.

Linked from 7 pages