Editing Tetragonal crystal system (section)

==Crystal classes==
{{further|Crystallographic point group}}
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.<ref>[http://webmineral.com/crystal/Tetragonal.shtml Webmineral data]</ref><ref>Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., pp. 73–78, {{isbn|0-471-80580-7}} </ref>

{| class="wikitable"
! rowspan=2 width=60|#
! colspan=5| Point group
! rowspan=2| Type
! rowspan=2| Example
! colspan=2| [[Space group]]s
|-
!Name<ref>{{cite web |title=The 32 crystal classes |url=https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm |access-date=2018-06-19}}</ref>
! [[Hermann–Mauguin_notation|Intl]]
! [[Schoenflies notation|Schoen.]]
! [[Orbifold|Orb.]]
! [[Coxeter notation|Cox.]]
! Primitive
! Body-centered
|- align=center
! 75–80
| Tetragonal pyramidal
| 4
| ''C''<sub>4</sub>
| 44
| [4]<sup>+</sup>
| [[enantiomorphic]] [[Polar point group|polar]]
| [[pinnoite]], <br>[[piypite]]
| align=left| P4,  P4<sub>1</sub>, P4<sub>2</sub>, P4<sub>3</sub>
| I4, I4<sub>1</sub>
|- align=center
! 81–82
| Tetragonal disphenoidal
| {{overline|4}}
| ''S''<sub>4</sub>
| 2×
| [2<sup>+</sup>,4<sup>+</sup>]
|
| [[cahnite]], [[tugtupite]]
| align=left| P{{overline|4}}
| I{{overline|4}}
|- align=center
! 83–88
| Tetragonal dipyramidal
| 4/m
| ''C''<sub>4''h''</sub>
| 4*
| [2,4<sup>+</sup>]
| [[centrosymmetric]]
| [[scheelite]], [[wulfenite]], [[leucite]]
| align=left| P4/m, P4<sub>2</sub>/m, P4/n, P4<sub>2</sub>/n
| I4/m, I4<sub>1</sub>/a
|- align=center
! 89–98
| Tetragonal trapezohedral
| 422
| ''D''<sub>4</sub>
| 224
| [2,4]<sup>+</sup>
| [[enantiomorphic]]
| [[cristobalite]], [[wardite]]
| align=left| P422, P42<sub>1</sub>2, P4<sub>1</sub>22, P4<sub>1</sub>2<sub>1</sub>2, P4<sub>2</sub>22, P4<sub>2</sub>2<sub>1</sub>2, P4<sub>3</sub>22, P4<sub>3</sub>2<sub>1</sub>2
| I422, I4<sub>1</sub>22
|- align=center
! 99–110
| Ditetragonal pyramidal
| 4mm
| ''C''<sub>4''v''</sub>
| *44
| [4]
| [[Polar point group|polar]]
| [[diaboleite]]
| align=left| P4mm, P4bm, P4<sub>2</sub>cm, P4<sub>2</sub>nm, P4cc, P4nc, P4<sub>2</sub>mc, P4<sub>2</sub>bc
| I4mm, I4cm, I4<sub>1</sub>md, I4<sub>1</sub>cd
|- align=center
! 111–122
| Tetragonal scalenohedral
| {{overline|4}}2m
| ''D''<sub>2''d''</sub> (V<sub>d</sub>)
| 2*2
| [2<sup>+</sup>,4]
|
| [[chalcopyrite]], [[stannite]]
| align=left| P{{overline|4}}2m, P{{overline|4}}2c, P{{overline|4}}2<sub>1</sub>m, P{{overline|4}}2<sub>1</sub>c, P{{overline|4}}m2, P{{overline|4}}c2, P{{overline|4}}b2, P{{overline|4}}n2
| I{{overline|4}}m2, I{{overline|4}}c2, I{{overline|4}}2m, I{{overline|4}}2d
|- align=center
! 123–142
| Ditetragonal dipyramidal
| 4/mmm
| ''D''<sub>4''h''</sub>
| *224
| [2,4]
| [[centrosymmetric]]
| [[rutile]], [[pyrolusite]], [[zircon]] 
| align=left| P4/mmm, P4/mcc, P4/nbm, P4/nnc, P4/mbm, P4/mnc, P4/nmm, P4/ncc, P4<sub>2</sub>/mmc, P4<sub>2</sub>/mcm, P4<sub>2</sub>/nbc, P4<sub>2</sub>/nnm, P4<sub>2</sub>/mbc, P4<sub>2</sub>/mnm, P4<sub>2</sub>/nmc, P4<sub>2</sub>/ncm
| I4/mmm, I4/mcm, I4<sub>1</sub>/amd, I4<sub>1</sub>/acd
|}