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# Tetragonal crystal system

In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. Tetragonal crystal 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).

### Additional recommended knowledge

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).

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.

NameInternationalSchoenfliesExample
ditetragonal bipyramidal $\frac4mmm$ D4h rutile
ditetragonal pyramidal 4mm C4v diaboleite
tetragonal bipyramidal $\frac4m$ C4h scheelite
tetragonal pyramidal 4 C4 wulfenite
ditetragonal alternating $\overline{4}2m$ D2d chalcopyrite
tetragonal trapezohedral 422 D4 phosgenite
tetragonal alternating $\overline{4}$ S4 cahnite