In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. Tetragonal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c, which is different from a).
There are two tetragonal Bravais lattices: the simple tetragonal (from stretching the simple-cubic lattice) and the centered tetragonal (from stretching either the face-centered or the body-centered cubic lattice).
| simple tetragonal
| body-centered
tetragonal
|
| 
|
The point groups that fall under this crystal system are listed below, followed by their representations in international notation and Schoenflies notation, and mineral examples.
| name
| international
| Schoenflies
| example
|
| ditetragonal bipyramidal
| 
| D4h
| rutile
|
| ditetragonal pyramidal
| 4mm
| C4v
|
|
| tetragonal bipyramidal
| 
| C4h
|
|
| tetragonal pyramidal
| 4
| C4
| wulfenite
|
| ditetragonal alternating
| 
| D2d
| chalcopyrite
|
| tetragonal trapezohedral
| 422
| D4
| phosgenite
|
| tetragonal alternating
| 
| S4
|
|