Hexagonal crystal family

The hexagonal crystal family groups the hexagonal and trigonal crystal systems. Its lattices possess a sixfold rotational symmetry axis.

Crystal system: A classification of crystals based on the symmetry of their unit cells. The hexagonal family groups two crystal systems under a shared lattice-symmetry criterion.
Hexagonal lattice system: The crystal lattice system with hexagonal axes and a sixfold rotational symmetry axis. It supplies the family’s sixfold lattice symmetry and underlies the hexagonal crystal system.
Crystal family: A grouping of crystal systems based on lattice symmetry and compatible point groups. The hexagonal family is one of the seven standard crystal families.
X-ray crystallography: A method that determines crystal structures from the diffraction of X-rays. Diffraction patterns can reveal the lattice symmetry used to assign a crystal family.
Bravais lattice: A periodic arrangement of points describing the translational symmetry of a crystal. The family is defined through lattice symmetry, not merely the shapes of individual crystals.
Rhombohedral lattice system: The lattice system whose primitive cell is a rhombohedron and whose principal axis is threefold. It is the lattice system associated with the family’s trigonal crystal system.
Cubic crystal family: A crystal family containing the cubic crystal system, characterized by cubic lattice symmetry. Its cubic lattice symmetry distinguishes it from the hexagonal family.
Crystal structure: The ordered arrangement of atoms, ions, or molecules in a crystalline solid. Family classification connects lattice symmetry to the structures measured in materials.
Point group: A set of symmetry operations that leave at least one point fixed. Point groups distinguish the symmetry classes found within its two crystal systems.
Sixfold rotational symmetry: Rotational symmetry in which a 60-degree turn leaves a structure unchanged. This lattice symmetry is the stated hallmark of the hexagonal crystal family.

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