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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).
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 | C4v | ||
| tetragonal bipyramidal | C4h | ||
| tetragonal pyramidal | 4 | C4 | wulfenite |
| ditetragonal alternating | D2d | chalcopyrite | |
| tetragonal trapezohedral | 422 | D4 | phosgenite |
| tetragonal alternating | S4 |
Tetragonales Kristallsystem | Tetragonaalne süngoonia | Тетрагональная сингония | 四方晶系 | 정방정계
"Tetragonal crystal system"