The 7 crystal systems and 14 Bravais lattices that classify crystals based on symmetry.
Overview
Crystal Structure Types
Crystal structures are classified into 7 crystal systems (cubic, hexagonal, tetragonal, trigonal, orthorhombic, monoclinic, and triclinic) based on their symmetry. Considering the arrangement of lattice points, 14 types of Bravais lattices are defined. The cubic system has the highest symmetry, while the triclinic system has the lowest. This classification system forms the foundation for systematically understanding crystal structures in materials science and crystallography.
crystallography
materials science
Bravais lattice
crystal system
symmetry
solid state physics
| code | slug | name | description | axialAngles | bravaisLattices | examples | latticeParameters | symmetry |
|---|---|---|---|---|---|---|---|---|
| 1 | cubic | Cubic System | The crystal system with the highest symmetry, featuring three equal axes at right angles to each other. | α = β = γ = 90° | ["cP","cI","cF"] | ["Sodium chloride (NaCl)","Diamond","Gold","Copper","Iron","Fluorite","Pyrite"] | a = b = c | highest |
| 2 | hexagonal | Hexagonal System | A crystal system with a 6-fold symmetry axis, featuring a base in the shape of a 60-degree rhombus. | α = β = 90°, γ = 120° | ["hP"] | ["Graphite","Zinc","Beryl","Apatite","Magnetite"] | a = b ≠ c | high |
| 3 | tetragonal | Tetragonal System | A crystal system with a 4-fold symmetry axis, featuring a square base with different height. | α = β = γ = 90° | ["tP","tI"] | ["Zircon","Rutile (TiO₂)","Tin (β-tin)"] | a = b ≠ c | high |
| 4 | trigonal | Trigonal System | A crystal system with a 3-fold symmetry axis, featuring a rhombohedral unit cell. | α = β = γ ≠ 90° | ["hR"] | ["Quartz","Calcite","Corundum (Ruby, Sapphire)","Tourmaline"] | a = b = c | high |
| 5 | orthorhombic | Orthorhombic System | A crystal system where three axes are at right angles to each other but have different lengths. | α = β = γ = 90° | ["oP","oC","oI","oF"] | ["Topaz","Sulfur","Olivine","Aragonite","Barite"] | a ≠ b ≠ c | medium |
| 6 | monoclinic | Monoclinic System | A crystal system where one axis intersects obliquely with the other two axes. | α = γ = 90°, β ≠ 90° | ["mP","mC"] | ["Gypsum","Augite","Orthoclase","Mica","Azurite"] | a ≠ b ≠ c | low |
| 7 | triclinic | Triclinic System | The crystal system with the lowest symmetry, featuring three axes intersecting at different angles. | α ≠ β ≠ γ ≠ 90° | ["aP"] | ["Kyanite","Microcline","Albite","Turquoise"] | a ≠ b ≠ c | lowest |