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In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. Tetragonal 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
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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
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| ditetragonal bipyramidal
| <math>\frac4m \frac2m \frac2m<math>
| D4h
| rutile
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| ditetragonal pyramidal
| <math>4mm<math>
| C4v
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| tetragonal bipyramidal
| <math>\frac4m<math>
| C4h
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| tetragonal pyramidal
| 4
| C4
| wulfenite
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| ditetragonal alternating
| <math>\overline{4}2m<math>
| D2d
| chalcopyrite
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| tetragonal trapezohedral
| 422
| D4
| phosgenite
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| tetragonal alternating
| <math>\overline{4}<math>
| S4
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