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Tetragonal crystal system

Lattice point group

An example of tetragonal crystals, [[wulfenite

In crystallography, the tetragonal crystal system is one of the seven crystal systems. 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).

Bravais lattices

There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal.

Bravais lattice	Primitive
tetragonal	Body-centered
tetragonal	Pearson symbol	Unit cell
tP	tI
[[File:Tetragonal.svg	class=skin-invert-image	100px]]	[[File:Body-centered tetragonal.svg	class=skin-invert-image	100px]]

The face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell.

Crystal classes

The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.

#	Point group	Type	Example	Space groups	Name	Intl	Schoen.	Orb.
Tetragonal pyramidal	4	C4	44	[4]+	enantiomorphic polar	pinnoite,
piypite	P4, P41, P42, P43	I4, I41
Tetragonal disphenoidal		S4	2×	[2+,4+]		cahnite, tugtupite	P	I
Tetragonal dipyramidal	4/m	C4h	4*	[2,4+]	centrosymmetric	scheelite, wulfenite, leucite	P4/m, P42/m, P4/n, P42/n	I4/m, I41/a
Tetragonal trapezohedral	422	D4	224	[2,4]+	enantiomorphic	cristobalite, wardite	P422, P4212, P4122, P41212, P4222, P42212, P4322, P43212	I422, I4122
Ditetragonal pyramidal	4mm	C4v	*44	[4]	polar	diaboleite	P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bc	I4mm, I4cm, I41md, I41cd
Tetragonal scalenohedral	2m	D2d (Vd)	2*2	[2+,4]		chalcopyrite, stannite	P2m, P2c, P21m, P21c, Pm2, Pc2, Pb2, Pn2	Im2, Ic2, I2m, I2d
Ditetragonal dipyramidal	4/mmm	D4h	*224	[2,4]	centrosymmetric	rutile, pyrolusite, zircon	P4/mmm, P4/mcc, P4/nbm, P4/nnc, P4/mbm, P4/mnc, P4/nmm, P4/ncc, P42/mmc, P42/mcm, P42/nbc, P42/nnm, P42/mbc, P42/mnm, P42/nmc, P42/ncm	I4/mmm, I4/mcm, I41/amd, I41/acd

In two dimensions

Main article: Square lattice

There is only one tetragonal Bravais lattice in two dimensions: the square lattice.

Bravais lattice	Square	Pearson symbol	Unit cell
tp
[[File:2d tp.svg	class=skin-invert-image	100px]]

References

[http://www.aem.umn.edu/people/faculty/shield/hane/tet.html Cubic-to-Tetragonal Transition]
[http://webmineral.com/crystal/Tetragonal.shtml Webmineral data]
Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., pp. 73–78, {{isbn. 0-471-80580-7
"The 32 crystal classes".

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