15.9: Crystal Systems
 Page ID
 31579
The rotational symmetry of a crystal places constraints on the shape of the conventional unit cell we choose to describe the structure. On this basis we divide all structures into one of 7 crystal systems. For example, for crystals with 4 fold symmetry it will always be possible to choose a unit cell that has a square base with a = b and γ = 90°:
There are 14 unique combinations of the 7 crystal systems with the possible types of primitive and nonprimitive lattices. These are referred to as the 14 Bravais lattices.
Crystal systems, lattices and symmetry elements
Crystal System 
Defining Symmetry 
Unit Cell Geometry 


Triclinic 
Translational Only 
a≠b≠c; α≠β≠γ 

Monoclinic 
A diad axis 
a≠b≠c; α=γ=90°; β>90° 

Orthorhombic 
3 diads 
a≠b≠c; α=β=γ=90° 

Trigonal For more information click here 
1 triad 
a=b≠c; α=β=90°; 

Hexagonal 
1 hexad (parallel to [001]) 
a=b≠c; α=β=90°; 

Tetragonal 
One tetrad 
a=b≠c; α=β=γ=90° 

Cubic 
4 triads 
a=b=c; α=β=γ=90° 