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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

• Crystal classes

• In two dimensions

• See also

• References

• External links

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

| Bravais lattice | Primitive tetragonal | Body-centered tetragonal |

|---|---|---|

| Pearson symbol | tP | tI |

| Unit cell | | |

The body-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell.cite-ref-1[1]

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.cite-ref-2[2]cite-ref-3[3]

| # | Point group | Point group | Point group | Point group | Point group | Type | Example | Space groups | Space groups |

|---|---|---|---|---|---|---|---|---|---|

| # | Name [ 4 ] | Intl | Schoen. | Orb. | Cox. | Type | Example | Primitive | Body-centered |

| 75–80 | Tetragonal pyramidal | 4 | C 4 | 44 | [4] + | enantiomorphic polar | pinnoite , piypite | P4, P4 1 , P4 2 , P4 3 | I4, I4 1 |

| 81–82 | Tetragonal disphenoidal | 4 | S 4 | 2× | [2 + ,4 + ] | | cahnite , tugtupite | P 4 | I 4 |

| 83–88 | Tetragonal dipyramidal | 4/m | C 4 h | 4* | [2,4 + ] | centrosymmetric | scheelite , wulfenite , leucite | P4/m, P4 2 /m, P4/n, P4 2 /n | I4/m, I4 1 /a |

| 89–98 | Tetragonal trapezohedral | 422 | D 4 | 224 | [2,4] + | enantiomorphic | cristobalite , wardite | P422, P42 1 2, P4 1 22, P4 1 2 1 2, P4 2 22, P4 2 2 1 2, P4 3 22, P4 3 2 1 2 | I422, I4 1 22 |

| 99–110 | Ditetragonal pyramidal | 4mm | C 4 v | *44 | [4] | polar | diaboleite | P4mm, P4bm, P4 2 cm, P4 2 nm, P4cc, P4nc, P4 2 mc, P4 2 bc | I4mm, I4cm, I4 1 md, I4 1 cd |

| 111–122 | Tetragonal scalenohedral | 4 2m | D 2 d (V d ) | 2*2 | [2 + ,4] | | chalcopyrite , stannite | P 4 2m, P 4 2c, P 4 2 1 m, P 4 2 1 c, P 4 m2, P 4 c2, P 4 b2, P 4 n2 | I 4 m2, I 4 c2, I 4 2m, I 4 2d |

| 123–142 | Ditetragonal dipyramidal | 4/mmm | D 4 h | *224 | [2,4] | centrosymmetric | rutile , pyrolusite , zircon | P4/mmm, P4/mcc, P4/nbm, P4/nnc, P4/mbm, P4/mnc, P4/nmm, P4/ncc, P4 2 /mmc, P4 2 /mcm, P4 2 /nbc, P4 2 /nnm, P4 2 /mbc, P4 2 /mnm, P4 2 /nmc, P4 2 /ncm | I4/mmm, I4/mcm, I4 1 /amd, I4 1 /acd |

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

| Bravais lattice | Square |

|---|---|

| Pearson symbol | tp |

| Unit cell | |

• Bravais lattices

• Crystal system

• Crystal structure

• Point groups

cite-note-11. ↑ Cubic-to-Tetragonal Transition

cite-note-22. ↑ Webmineral data

cite-note-33. ↑ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, ISBN 0-471-80580-7

cite-note-41. "The 32 crystal classes". Retrieved 2018-06-19.

• Media related to Tetragonal lattices at Wikimedia Commons