Crystal system

A crystal system is one of seven categories that classify crystals by their symmetry and unit-cell geometry. The categories are cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and trigonal.

Unit cell: The repeating structural unit from which a crystal lattice can be generated by translation. Its edge lengths and angles supply the geometric criteria used to assign a crystal system.
Cubic crystal system: A crystal system with three equal cell edges meeting at right angles. Its maximal cubic symmetry makes it the most geometrically constrained system.
Trigonal crystal system: A crystal system characterized by a threefold rotation axis, represented in hexagonal or rhombohedral axes. Its symmetry is distinct, though its lattices are often described using hexagonal axes.
X-ray crystallography: A method that uses X-ray diffraction to determine the atomic structure of crystalline materials. Diffraction symmetry and cell dimensions help identify a crystal system.
Crystal lattice: An infinite periodic arrangement of points representing equivalent positions in a crystalline solid. Crystal systems classify the symmetries and geometries possible for periodic crystal structures.
Tetragonal crystal system: A crystal system with two equal cell edges, a third unequal edge, and three right angles. It retains a fourfold axis while relaxing cubic edge equality.
Crystal class: A classification of crystals by their crystallographic point-group symmetry. Crystal classes are grouped into systems, but are not themselves systems.
Crystallographic database: A structured collection of information about crystal structures and their properties. Crystal-system labels provide a standard way to organize and retrieve structures.
Crystallographic point group: A group of symmetry operations that leaves at least one point fixed and is compatible with lattice periodicity. Its symmetry classes are grouped among the seven crystal systems.
Orthorhombic crystal system: A crystal system with three unequal cell edges and three right angles. It preserves right-angle geometry but has no equal cell edges.

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