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).

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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.

Name	International	Schoenflies	Example
ditetragonal bipyramidal	$\frac4mmm$	D_4h	rutile
ditetragonal pyramidal	$4 m m$	C_4v	diaboleite
tetragonal bipyramidal	$\frac4m$	C_4h	scheelite
tetragonal pyramidal	4	C₄	wulfenite
ditetragonal alternating	$\overline{4}2m$	D_2d	chalcopyrite
tetragonal trapezohedral	422	D₄	phosgenite
tetragonal alternating	$\overline{4}$	S₄	cahnite