List Of Space Groups

There are 230 space groups in three dimensions, given by a number index, and a full name in Hermann–Mauguin notation, and a short name (international short symbol). The long names are given with spaces for readability. The groups each have a point group of the unit cell.

Symbols

In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group.

These are the Bravais lattices in three dimensions:
*P primitive
*I body centered (from the German ''Innenzentriert'')
*F face centered (from the German ''Flächenzentriert'')
*A centered on A faces only
*B centered on B faces only
*C centered on C faces only
*R rhombohedral

A reflection plane m within the point groups can be replaced by a glide plane, labeled as a, b, or c depending on which axis the glide is along. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, which is along a quarter of either a face or space diagonal of the unit cell. The d glide is often called the diamond glide plane as it features in the diamond structure.
* $a$, $b$, or $c$: glide translation along half the lattice vector of this face
* $n$: glide translation along half the diagonal of this face
* $d$: glide planes with translation along a quarter of a face diagonal
* $e$: two glides with the same glide plane and translation along two (different) half-lattice vectors.

A gyration point can be replaced by a screw axis denoted by a number, ''n'', where the angle of rotation is $\color\tfrac$. The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2₁ is a 180° (twofold) rotation followed by a translation of of the lattice vector. 3₁ is a 120° (threefold) rotation followed by a translation of of the lattice vector. The possible screw axes are: 2₁, 3₁, 3₂, 4₁, 4₂, 4₃, 6₁, 6₂, 6₃, 6₄, and 6₅.

Wherever there is both a rotation or screw axis ''n'' and a mirror or glide plane ''m'' along the same crystallographic direction, they are represented as a fraction $\frac$ or ''n/m''. For example, 4₁/a means that the crystallographic axis in question contains both a 4₁ screw axis as well as a glide plane along a.

In Schoenflies notation, the symbol of a space group is represented by the symbol of corresponding point group with additional superscript. The superscript doesn't give any additional information about symmetry elements of the space group, but is instead related to the order in which Schoenflies derived the space groups. This is sometimes supplemented with a symbol of the form $\Gamma_x^y$ which specifies the Bravais lattice. Here $x \in \$ is the lattice system, and $y \in \$ is the centering type.

In Fedorov symbol, the type of space group is denoted as ''s'' (''symmorphic'' ), ''h'' (''hemisymmorphic''), or ''a'' (''asymmorphic''). The number is related to the order in which Fedorov derived space groups. There are 73 symmorphic, 54 hemisymmorphic, and 103 asymmorphic space groups.

Symmorphic

The 73 symmorphic space groups can be obtained as combination of Bravais lattices with corresponding point group. These groups contain the same symmetry elements as the corresponding point groups. Example for point group 4/mmm ($\tfrac\tfrac\tfrac$): the symmorphic space groups are P4/mmm ($P\tfrac\tfrac\tfrac$, ''36s'') and I4/mmm ($I\tfrac\tfrac\tfrac$, ''37s'').

Hemisymmorphic

The 54 hemisymmorphic space groups contain only axial combination of symmetry elements from the corresponding point groups. Example for point group 4/mmm ($\tfrac\tfrac\tfrac$): hemisymmorphic space groups contain the axial combination 422, but at least one mirror plane ''m'' will be substituted with glide plane, for example P4/mcc ($P\tfrac\tfrac\tfrac$, ''35h''), P4/nbm ($P\tfrac\tfrac\tfrac$, ''36h''), P4/nnc ($P\tfrac\tfrac\tfrac$, ''37h''), and I4/mcm ($I\tfrac\tfrac\tfrac$, ''38h'').

Asymmorphic

The remaining 103 space groups are asymmorphic. Example for point group 4/mmm ($\tfrac\tfrac\tfrac$): P4/mbm ($P\tfrac\tfrac\tfrac$, ''54a''), P4₂/mmc ($P\tfrac\tfrac\tfrac$, ''60a''), I4₁/acd ($I\tfrac\tfrac\tfrac$, ''58a'') - none of these groups contains the axial combination 422.

List of triclinic

List of monoclinic

List of orthorhombic

{, class=wikitable
, + Orthorhombic crystal system
!Number
! Point group
! Orbifold
! Short name
! Full name
! Schoenflies
! Fedorov
! Shubnikov
! Fibrifold (primary)
! Fibrifold (secondary)
, - align=center
, 16, , rowspan=9, 222, , rowspan=9, $222$, , P222, , P 2 2 2, , $\Gamma_oD_2^1$ , , ''9s'' , , $(c:a:b):2:2$ , , $(*2_02_02_02_0)$ , ,
, - align=center
, 17, , P222₁, , P 2 2 2₁, , $\Gamma_oD_2^2$ , , ''4a'' , , $(c:a:b):2_1:2$ , , $(*2_12_12_12_1)$ , , $(2_02_0{*})$
, - align=center
, 18, , P2₁2₁2, , P 2₁ 2₁ 2, , $\Gamma_oD_2^3$ , , ''7a'' , , $(c:a:b):2$ $2_1$ , , $(2_02_0\bar{\times})$ , , $(2_12_1{*})$
, - align=center
, 19, , P2₁2₁2₁, , P 2₁ 2₁ 2₁, , $\Gamma_oD_2^4$ , , ''8a'' , , $(c:a:b):2_1$ $2_1$ , , $(2_12_1\bar{\times})$ , ,
, - align=center
, 20, , C222₁, , C 2 2 2₁, , $\Gamma_o^bD_2^5$ , , ''5a'' , , $\left ( \tfrac{a+b}{2}:c:a:b\right ) :2_1:2$ , , $(2_1{*}2_12_1)$ , , $(2_02_1{*})$
, - align=center
, 21, , C222, , C 2 2 2, , $\Gamma_o^bD_2^6$ , , ''10s'' , , $\left ( \tfrac{a+b}{2}:c:a:b\right ) :2:2$ , , $(2_0{*}2_02_0)$ , , $(*2_02_02_12_1)$
, - align=center
, 22, , F222, , F 2 2 2, , $\Gamma_o^fD_2^7$ , , ''12s'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:c:a:b\right ) :2:2$ , , $(*2_02_12_02_1)$ , ,
, - align=center
, 23, , I222, , I 2 2 2, , $\Gamma_o^vD_2^8$ , , ''11s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:b\right ) :2:2$ , , $(2_1{*}2_02_0)$ , ,
, - align=center
, 24, , I2₁2₁2₁, , I 2₁ 2₁ 2₁, , $\Gamma_o^vD_2^9$ , , ''6a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:b \right ) :2:2_1$ , , $(2_0{*}2_12_1)$ , ,
, - align=center
, 25, , rowspan=22, mm2, , rowspan=22, $*22$, , Pmm2, , P m m 2, , $\Gamma_oC_{2v}^1$ , , ''13s'' , , $(c:a:b):m \cdot 2$ , , $(*{\cdot}2{\cdot}2{\cdot}2{\cdot}2)$ , , *}_0{\cdot}{*}_0{\cdot}/math>
, - align=center
, 26, , Pmc2₁, , P m c 2₁, , $\Gamma_oC_{2v}^2$ , , ''9a'' , , $(c:a:b): \tilde c \cdot 2_1$ , , $(*{\cdot}2{:}2{\cdot}2{:}2)$ , , $(\bar{*}{\cdot}\bar{*}{\cdot})$, \times_0}{\times_0}/math>
, - align=center
, 27, , Pcc2, , P c c 2 , , $\Gamma_oC_{2v}^3$ , , ''5h'' , , $(c:a:b): \tilde c \cdot 2$ , , $(*{:}2{:}2{:}2{:}2)$ , , $(\bar{*}_0\bar{*}_0)$
, - align=center
, 28, , Pma2, , P m a 2 , , $\Gamma_oC_{2v}^4$ , , ''6h'' , , $(c:a:b): \tilde a \cdot 2$ , , $(2_02_0{*}{\cdot})$ , , *}_0{:}{*}_0{:}/math>, $(*{\cdot}{*}_0)$
, - align=center
, 29, , Pca2₁, , P c a 2₁ , , $\Gamma_oC_{2v}^5$ , , ''11a'' , , $(c:a:b): \tilde a \cdot 2_1$ , , $(2_12_1{*}{:})$ , , $(\bar{*}{:}\bar{*}{:})$
, - align=center
, 30, , Pnc2, , P n c 2 , , $\Gamma_oC_{2v}^6$ , , ''7h'' , , $(c:a:b): \tilde c \odot 2$ , , $(2_02_0{*}{:})$ , , $(\bar{*}_1\bar{*}_1)$, $({*}_0{\times}_0)$
, - align=center
, 31, , Pmn2₁, , P m n 2₁ , , $\Gamma_oC_{2v}^7$ , , ''10a'' , , $(c:a:b): \widetilde{ac} \cdot 2_1$ , , $(2_12_1{*}{\cdot})$ , , $(*{\cdot}\bar{\times})$, \times}_0{\times}_1/math>
, - align=center
, 32, , Pba2, , P b a 2 , , $\Gamma_oC_{2v}^8$ , , ''9h'' , , $(c:a:b): \tilde a \odot 2$ , , $(2_02_0{\times}_0)$ , , $(*{:}{*}_0)$
, - align=center
, 33, , Pna2₁, , P n a 2₁ , , $\Gamma_oC_{2v}^9$ , , ''12a'' , , $(c:a:b): \tilde a \odot 2_1$ , , $(2_12_1{\times})$ , , $(*{:}{\times})$, $({\times}{\times}_1)$
, - align=center
, 34, , Pnn2, , P n n 2 , , $\Gamma_oC_{2v}^{10}$ , , ''8h'' , , $(c:a:b): \widetilde{ac} \odot 2$ , , $(2_02_0{\times}_1)$ , , $(*_0{\times}_1)$
, - align=center
, 35, , Cmm2, , C m m 2, , $\Gamma_o^bC_{2v}^{11}$ , , ''14s'' , , $\left ( \tfrac{a+b}{2}:c:a:b\right ) :m \cdot 2$ , , $(2_0{*}{\cdot}2{\cdot}2)$ , , _0{\cdot}{*}_0{:}/math>
, - align=center
, 36, , Cmc2₁, , C m c 2₁ , , $\Gamma_o^bC_{2v}^{12}$ , , ''13a'' , , $\left ( \tfrac{a+b}{2}:c:a:b\right ) :\tilde c \cdot 2_1$ , , $(2_1{*}{\cdot}2{:}2)$ , , $(\bar{*}{\cdot}\bar{*}{:})$, \times}_1{\times}_1/math>
, - align=center
, 37, , Ccc2, , C c c 2 , , $\Gamma_o^bC_{2v}^{13}$ , , ''10h'' , , $\left ( \tfrac{a+b}{2}:c:a:b\right ) : \tilde c \cdot 2$ , , $(2_0{*}{:}2{:}2)$ , , $(\bar{*}_0\bar{*}_1)$
, - align=center
, 38, , Amm2, , A m m 2 , , $\Gamma_o^bC_{2v}^{14}$ , , ''15s'' , , $\left ( \tfrac{b+c}{2}/c:a:b\right ):m \cdot 2$ , , $(*{\cdot}2{\cdot}2{\cdot}2{:}2)$ , , *}_1{\cdot}{*}_1{\cdot}/math>, {\cdot}{\times}_0/math>
, - align=center
, 39, , Aem2, , A b m 2 , , $\Gamma_o^bC_{2v}^{15}$ , , ''11h'' , , $\left ( \tfrac{b+c}{2}/c:a:b\right ) :m \cdot 2_1$ , , $(*{\cdot}2{:}2{:}2{:}2)$ , , *}_1{:}{*}_1{:}/math>, $(\bar{*}{\cdot}\bar{*}_0)$
, - align=center
, 40, , Ama2, , A m a 2 , , $\Gamma_o^bC_{2v}^{16}$ , , ''12h'' , , $\left ( \tfrac{b+c}{2}/c:a:b\right ) : \tilde a \cdot 2$ , , $(2_02_1{*}{\cdot})$ , , $(*{\cdot}{*}_1)$, {:}{\times}_1/math>
, - align=center
, 41, , Aea2, , A b a 2 , , $\Gamma_o^bC_{2v}^{17}$ , , ''13h'' , , $\left ( \tfrac{b+c}{2}/c:a:b\right ) : \tilde a \cdot 2_1$ , , $(2_02_1{*}{:})$ , , $(*{:}{*}_1)$, $(\bar{*}{:}\bar{*}_1)$
, - align=center
, 42, , Fmm2, , F m m 2 , , $\Gamma_o^fC_{2v}^{18}$ , , ''17s'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:c:a:b\right ) :m \cdot 2$ , , $(*{\cdot}2{\cdot}2{:}2{:}2)$ , , *}_1{\cdot}{*}_1{:}/math>
, - align=center
, 43, , Fdd2, , F d d 2 , , $\Gamma_o^fC_{2v}^{19}$ , , ''16h'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:c:a:b \right ) : \tfrac{1}{2} \widetilde{ac} \odot 2$ , , $(2_02_1{\times})$ , , $({*}_1{\times})$
, - align=center
, 44, , Imm2, , I m m 2 , , $\Gamma_o^vC_{2v}^{20}$ , , ''16s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:b \right ) :m \cdot 2$ , , $(2_1{*}{\cdot}2{\cdot}2)$ , , {\cdot}{\times}_1/math>
, - align=center
, 45, , Iba2, , I b a 2 , , $\Gamma_o^vC_{2v}^{21}$ , , ''15h'' , , $\left ( \tfrac{a+b+c}{2}/c:a:b \right ) : \tilde c \cdot 2$ , , $(2_1{*}{:}2{:}2)$ , , $(\bar{*}{:}\bar{*}_0)$
, - align=center
, 46, , Ima2, , I m a 2 , , $\Gamma_o^vC_{2v}^{22}$ , , ''14h'' , , $\left ( \tfrac{a+b+c}{2}/c:a:b \right ) : \tilde a \cdot 2$ , , $(2_0{*}{\cdot}2{:}2)$ , , $(\bar{*}{\cdot}\bar{*}_1)$, {:}{\times}_0/math>
, - align=center
, 47, , rowspan=28, $\tfrac{2}{m}\tfrac{2}{m}\tfrac{2}{m}$, , rowspan=28, $*222$, , Pmmm, , P 2/m 2/m 2/m , , $\Gamma_oD_{2h}^1$ , , ''18s'' , , $\left ( c:a:b \right ) \cdot m:2 \cdot m$ , , {\cdot}2{\cdot}2{\cdot}2{\cdot}2/math> , ,
, - align=center
, 48, , Pnnn, , P 2/n 2/n 2/n , , $\Gamma_oD_{2h}^2$ , , ''19h'' , , $\left ( c:a:b \right ) \cdot \widetilde{ab}:2 \odot \widetilde{ac}$ , , $(2\bar{*}_12_02_0)$, ,
, - align=center
, 49, , Pccm, , P 2/c 2/c 2/m , , $\Gamma_oD_{2h}^3$ , , ''17h'' , , $\left ( c:a:b \right ) \cdot m:2 \cdot \tilde c$ , , {:}2{:}2{:}2{:}2/math> , , $(*2_02_02{\cdot}2)$
, - align=center
, 50, , Pban, , P 2/b 2/a 2/n , , $\Gamma_oD_{2h}^4$ , , ''18h'' , , $\left ( c:a:b \right ) \cdot \widetilde{ab}:2 \odot \tilde a$ , , $(2\bar{*}_02_02_0)$ , , $(*2_02_02{:}2)$
, - align=center
, 51, , Pmma, , P 2₁/m 2/m 2/a , , $\Gamma_oD_{2h}^5$ , , ''14a'' , , $\left ( c:a:b \right ) \cdot \tilde a :2 \cdot m$ , , _02_0{*}{\cdot}/math> , , {\cdot}2{:}2{\cdot}2{:}2/math>, 2{\cdot}2{\cdot}2{\cdot}2/math>
, - align=center
, 52, , Pnna, , P 2/n 2₁/n 2/a , , $\Gamma_oD_{2h}^6$ , , ''17a'' , , $\left ( c:a:b \right ) \cdot \tilde a:2 \odot \widetilde{ac}$ , , $(2_02\bar{*}_1)$ , , $(2_0{*}2{:}2)$, $(2\bar{*}2_12_1)$
, - align=center
, 53, , Pmna, , P 2/m 2/n 2₁/a , , $\Gamma_oD_{2h}^7$ , , ''15a'' , , $\left ( c:a:b \right ) \cdot \tilde a:2_1 \cdot \widetilde{ac}$ , , _02_0{*}{:}/math> , , $(*2_12_12{\cdot}2)$, $(2_0{*}2{\cdot}2)$
, - align=center
, 54, , Pcca, , P 2₁/c 2/c 2/a , , $\Gamma_oD_{2h}^8$ , , ''16a'' , , $\left ( c:a:b \right ) \cdot \tilde a:2 \cdot \tilde c$ , , $(2_02\bar{*}_0)$ , , $(*2{:}2{:}2{:}2)$, $(*2_12_12{:}2)$
, - align=center
, 55, , Pbam, , P 2₁/b 2₁/a 2/m , , $\Gamma_oD_{2h}^9$ , , ''22a'' , , $\left ( c:a:b \right ) \cdot m:2 \odot \tilde a$ , , _02_0{\times}_0/math> , , $(*2{\cdot}2{:}2{\cdot}2)$
, - align=center
, 56, , Pccn, , P 2₁/c 2₁/c 2/n , , $\Gamma_oD_{2h}^{10}$ , , ''27a'' , , $\left ( c:a:b \right ) \cdot \widetilde{ab}:2 \cdot \tilde c$ , , $(2\bar{*}{:}2{:}2)$ , , $(2_12\bar{*}_0)$
, - align=center
, 57, , Pbcm, , P 2/b 2₁/c 2₁/m , , $\Gamma_oD_{2h}^{11}$ , , ''23a'' , , $\left ( c:a:b \right ) \cdot m:2_1 \odot \tilde c$ , , $(2_02\bar{*}{\cdot})$ , , $(*2{:}2{\cdot}2{:}2)$, _12_1{*}{:}/math>
, - align=center
, 58, , Pnnm, , P 2₁/n 2₁/n 2/m , , $\Gamma_oD_{2h}^{12}$ , , ''25a'' , , $\left ( c:a:b \right ) \cdot m:2 \odot \widetilde{ac}$ , , _02_0{\times}_1/math> , , $(2_1{*}2{\cdot}2)$
, - align=center
, 59, , Pmmn, , P 2₁/m 2₁/m 2/n , , $\Gamma_oD_{2h}^{13}$ , , ''24a'' , , $\left ( c:a:b \right ) \cdot \widetilde{ab}:2 \cdot m$ , , $(2\bar{*}{\cdot}2{\cdot}2)$ , , _12_1{*}{\cdot}/math>
, - align=center
, 60, , Pbcn, , P 2₁/b 2/c 2₁/n , , $\Gamma_oD_{2h}^{14}$ , , ''26a'' , , $\left ( c:a:b \right ) \cdot \widetilde{ab}:2_1 \odot \tilde c$ , , $(2_02\bar{*}{:})$ , , $(2_1{*}2{:}2)$, $(2_12\bar{*}_1)$
, - align=center
, 61, , Pbca, , P 2₁/b 2₁/c 2₁/a , , $\Gamma_oD_{2h}^{15}$ , , ''29a'' , , $\left ( c:a:b \right ) \cdot \tilde a:2_1 \odot \tilde c$ , , $(2_12\bar{*}{:})$ , ,
, - align=center
, 62, , Pnma, , P 2₁/n 2₁/m 2₁/a , , $\Gamma_oD_{2h}^{16}$ , , ''28a'' , , $\left ( c:a:b \right ) \cdot \tilde a:2_1 \odot m$ , , $(2_12\bar{*}{\cdot})$ , , $(2\bar{*}{\cdot}2{:}2)$, _12_1{\times}/math>
, - align=center
, 63, , Cmcm, , C 2/m 2/c 2₁/m , , $\Gamma_o^bD_{2h}^{17}$ , , ''18a'' , , $\left ( \tfrac{a+b}{2}:c:a:b\right ) \cdot m:2_1 \cdot \tilde c$ , , _02_1{*}{\cdot}/math> , , $(*2{\cdot}2{\cdot}2{:}2)$, _1{*}{\cdot}2{:}2/math>
, - align=center
, 64, , Cmce, , C 2/m 2/c 2₁/a , , $\Gamma_o^bD_{2h}^{18}$ , , ''19a'', , $\left ( \tfrac{a+b}{2}:c:a:b\right ) \cdot \tilde a :2_1 \cdot \tilde c$ , , _02_1{*}{:}/math> , , $(*2{\cdot}2{:}2{:}2)$, $(*2_12{\cdot}2{:}2)$
, - align=center
, 65, , Cmmm, , C 2/m 2/m 2/m , , $\Gamma_o^bD_{2h}^{19}$ , , ''19s'', , $\left ( \tfrac{a+b}{2}:c:a:b\right ) \cdot m:2 \cdot m$ , , _0{*}{\cdot}2{\cdot}2/math> , , {\cdot}2{\cdot}2{\cdot}2{:}2/math>
, - align=center
, 66, , Cccm, , C 2/c 2/c 2/m , , $\Gamma_o^bD_{2h}^{20}$ , , ''20h'', , $\left ( \tfrac{a+b}{2}:c:a:b\right ) \cdot m:2 \cdot \tilde c$ , , _0{*}{:}2{:}2/math> , , $(*2_02_12{\cdot}2)$
, - align=center
, 67, , Cmme, , C 2/m 2/m 2/e , , $\Gamma_o^bD_{2h}^{21}$ , , ''21h'', , $\left ( \tfrac{a+b}{2}:c:a:b\right ) \cdot \tilde a :2 \cdot m$ , , $(*2_02{\cdot}2{\cdot}2)$ , , {\cdot}2{:}2{:}2{:}2/math>
, - align=center
, 68, , Ccce, , C 2/c 2/c 2/e , , $\Gamma_o^bD_{2h}^{22}$ , , ''22h'', , $\left ( \tfrac{a+b}{2}:c:a:b\right ) \cdot \tilde a :2 \cdot \tilde c$ , , $(*2_02{:}2{:}2)$ , , $(*2_02_12{:}2)$
, - align=center
, 69, , Fmmm, , F 2/m 2/m 2/m , , $\Gamma_o^fD_{2h}^{23}$ , , ''21s'', , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:c:a:b\right ) \cdot m:2 \cdot m$ , , {\cdot}2{\cdot}2{:}2{:}2/math> , ,
, - align=center
, 70, , Fddd, , F 2/d 2/d 2/d , , $\Gamma_o^fD_{2h}^{24}$ , , ''24h'', , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:c:a:b\right ) \cdot \tfrac{1}{2}\widetilde{ab}:2 \odot \tfrac{1}{2}\widetilde{ac}$ , , $(2\bar{*}2_02_1)$ , ,
, - align=center
, 71, , Immm, , I 2/m 2/m 2/m , , $\Gamma_o^vD_{2h}^{25}$ , , ''20s'', , $\left ( \tfrac{a+b+c}{2}/c:a:b\right ) \cdot m:2 \cdot m$ , , _1{*}{\cdot}2{\cdot}2/math> , ,
, - align=center
, 72, , Ibam, , I 2/b 2/a 2/m , , $\Gamma_o^vD_{2h}^{26}$ , , ''23h'', , $\left ( \tfrac{a+b+c}{2}/c:a:b\right ) \cdot m:2 \cdot \tilde c$ , , _1{*}{:}2{:}2/math> , , $(*2_02{\cdot}2{:}2)$
, - align=center
, 73, , Ibca, , I 2/b 2/c 2/a , , $\Gamma_o^vD_{2h}^{27}$ , , ''21a'', , $\left ( \tfrac{a+b+c}{2}/c:a:b\right ) \cdot \tilde a :2 \cdot \tilde c$ , , $(*2_12{:}2{:}2)$ , ,
, - align=center
, 74, , Imma, , I 2/m 2/m 2/a , , $\Gamma_o^vD_{2h}^{28}$ , , ''20a'', , $\left ( \tfrac{a+b+c}{2}/c:a:b\right ) \cdot \tilde a :2 \cdot m$ , , $(*2_12{\cdot}2{\cdot}2)$ , , _0{*}{\cdot}2{:}2/math>

List of tetragonal

{, class="wikitable floatright"
, + Tetragonal Bravais lattice
, -
! Simple (P)
! Body (I)
, -
,
,

{, class=wikitable
, + Tetragonal crystal system
!Number
! Point group
! Orbifold
! Short name
! Full name
! Schoenflies
! Fedorov
! Shubnikov
! Fibrifold
, - align=center
, 75, , rowspan=6, 4, , rowspan=6, $44$, , P4, , P 4 , , $\Gamma_qC_4^1$ , , ''22s'' , , $(c:a:a):4$ , , $(4_04_02_0)$
, - align=center
, 76, , P4₁, , P 4₁ , , $\Gamma_qC_4^2$ , , ''30a'' , , $(c:a:a) :4_1$ , , $(4_14_12_1)$
, - align=center
, 77, , P4₂, , P 4₂ , , $\Gamma_qC_4^3$ , , ''33a'' , , $(c:a:a) :4_2$ , , $(4_24_22_0)$
, - align=center
, 78, , P4₃, , P 4₃ , , $\Gamma_qC_4^4$ , , ''31a'' , , $(c:a:a) :4_3$ , , $(4_14_12_1)$
, - align=center
, 79, , I4, , I 4 , , $\Gamma_q^vC_4^5$ , , ''23s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4$ , , $(4_24_02_1)$
, - align=center
, 80, , I4₁, , I 4₁ , , $\Gamma_q^vC_4^6$ , , ''32a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4_1$ , , $(4_34_12_0)$
, - align=center
, 81, , rowspan=2, , , rowspan=2, $2\times$, , P, , P , , $\Gamma_qS_4^1$ , , ''26s'' , , $(c:a:a):\tilde 4$ , , $(442_0)$
, - align=center
, 82, , I, , I , , $\Gamma_q^vS_4^2$ , , ''27s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :\tilde 4$ , , $(442_1)$
, - align=center
, 83, , rowspan=6, 4/m, , rowspan=6, $4*$, , P4/m, , P 4/m, , $\Gamma_qC_{4h}^1$ , , ''28s'' , , $(c:a:a)\cdot m:4$ , , _04_02_0/math>
, - align=center
, 84, , P4₂/m, , P 4₂/m, , $\Gamma_qC_{4h}^2$ , , ''41a'' , , $(c:a:a)\cdot m:4_2$ , , _24_22_0/math>
, - align=center
, 85, , P4/n, , P 4/n, , $\Gamma_qC_{4h}^3$ , , ''29h'' , , $(c:a:a)\cdot \widetilde{ab}:4$ , , $(44_02)$
, - align=center
, 86, , P4₂/n, , P 4₂/n, , $\Gamma_qC_{4h}^4$ , , ''42a'' , , $(c:a:a)\cdot \widetilde{ab}:4_2$ , , $(44_22)$
, - align=center
, 87, , I4/m, , I 4/m, , $\Gamma_q^vC_{4h}^5$ , , ''29s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) \cdot m:4$ , , _24_02_1/math>
, - align=center
, 88, , I4₁/a, , I 4₁/a, , $\Gamma_q^vC_{4h}^6$ , , ''40a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) \cdot \tilde a :4_1$ , , $(44_12)$
, - align=center
, 89, , rowspan=10, 422, , rowspan=10, $224$, , P422, , P 4 2 2 , , $\Gamma_qD_4^1$ , , ''30s'' , , $(c:a:a):4:2$ , , $(*4_04_02_0)$
, - align=center
, 90, , P42₁2, , P42₁2 , , $\Gamma_qD_4^2$ , , ''43a'' , , $(c:a:a):4$ $2_1$ , , $(4_0{*}2_0)$
, - align=center
, 91, , P4₁22, , P 4₁ 2 2 , , $\Gamma_qD_4^3$ , , ''44a'' , , $(c:a:a):4_1:2$ , , $(*4_14_12_1)$
, - align=center
, 92, , P4₁2₁2, , P 4₁ 2₁ 2 , , $\Gamma_qD_4^4$ , , ''48a'' , , $(c:a:a):4_1$ $2_1$ , , $(4_1{*}2_1)$
, - align=center
, 93, , P4₂22, , P 4₂ 2 2 , , $\Gamma_qD_4^5$ , , ''47a'' , , $(c:a:a):4_2:2$ , , $(*4_24_22_0)$
, - align=center
, 94, , P4₂2₁2, , P 4₂ 2₁ 2 , , $\Gamma_qD_4^6$ , , ''50a'' , , $(c:a:a):4_2$ $2_1$ , , $(4_2{*}2_0)$
, - align=center
, 95, , P4₃22, , P 4₃ 2 2 , , $\Gamma_qD_4^7$ , , ''45a'' , , $(c:a:a):4_3:2$ , , $(*4_14_12_1)$
, - align=center
, 96, , P4₃2₁2, , P 4₃ 2₁ 2 , , $\Gamma_qD_4^8$ , , ''49a'' , , $(c:a:a):4_3$ $2_1$ , , $(4_1{*}2_1)$
, - align=center
, 97, , I422, , I 4 2 2 , , $\Gamma_q^vD_4^9$ , , ''31s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4:2$ , , $(*4_24_02_1)$
, - align=center
, 98, , I4₁22, , I 4₁ 2 2 , , $\Gamma_q^vD_4^{10}$ , , ''46a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4:2_1$ , , $(*4_34_12_0)$
, - align=center
, 99, , rowspan=12, 4mm, , rowspan=12, $*44$, , P4mm, , P 4 m m , , $\Gamma_qC_{4v}^1$ , , ''24s'' , , $(c:a:a):4\cdot m$ , , $(*{\cdot}4{\cdot}4{\cdot}2)$
, - align=center
, 100, , P4bm, , P 4 b m , , $\Gamma_qC_{4v}^2$ , , ''26h'' , , $(c:a:a):4\odot \tilde a$ , , $(4_0{*}{\cdot}2)$
, - align=center
, 101, , P4₂cm, , P 4₂ c m , , $\Gamma_qC_{4v}^3$ , , ''37a'' , , $(c:a:a):4_2\cdot \tilde c$ , , $(*{:}4{\cdot}4{:}2)$
, - align=center
, 102, , P4₂nm, , P 4₂ n m , , $\Gamma_qC_{4v}^4$ , , ''38a'' , , $(c:a:a):4_2\odot \widetilde{ac}$ , , $(4_2{*}{\cdot}2)$
, - align=center
, 103, , P4cc, , P 4 c c , , $\Gamma_qC_{4v}^5$ , , ''25h'' , , $(c:a:a):4\cdot \tilde c$ , , $(*{:}4{:}4{:}2)$
, - align=center
, 104, , P4nc, , P 4 n c , , $\Gamma_qC_{4v}^6$ , , ''27h'' , , $(c:a:a):4\odot \widetilde{ac}$ , , $(4_0{*}{:}2)$
, - align=center
, 105, , P4₂mc, , P 4₂ m c , , $\Gamma_qC_{4v}^7$ , , ''36a'' , , $(c:a:a):4_2\cdot m$ , , $(*{\cdot}4{:}4{\cdot}2)$
, - align=center
, 106, , P4₂bc, , P 4₂ b c , , $\Gamma_qC_{4v}^8$ , , ''39a'' , , $(c:a:a):4\odot \tilde a$ , , $(4_2{*}{:}2)$
, - align=center
, 107, , I4mm, , I 4 m m , , $\Gamma_q^vC_{4v}^9$ , , ''25s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4\cdot m$ , , $(*{\cdot}4{\cdot}4{:}2)$
, - align=center
, 108, , I4cm, , I 4 c m , , $\Gamma_q^vC_{4v}^{10}$ , , ''28h'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4\cdot \tilde c$ , , $(*{\cdot}4{:}4{:}2)$
, - align=center
, 109, , I4₁md, , I 4₁ m d , , $\Gamma_q^vC_{4v}^{11}$ , , ''34a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4_1\odot m$ , , $(4_1{*}{\cdot}2)$
, - align=center
, 110, , I4₁cd, , I 4₁ c d , , $\Gamma_q^vC_{4v}^{12}$ , , ''35a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :4_1\odot \tilde c$ , , $(4_1{*}{:}2)$
, - align=center
, 111, , rowspan=12, 2m, , rowspan=12, $2{*}2$, , P2m, , P 2 m , , $\Gamma_qD_{2d}^1$ , , ''32s'' , , $(c:a:a):\tilde 4 :2$ , , $(*4{\cdot}42_0)$
, - align=center
, 112, , P2c, , P 2 c , , $\Gamma_qD_{2d}^2$ , , ''30h'' , , $(c:a:a):\tilde 4$ $2$ , , $(*4{:}42_0)$
, - align=center
, 113, , P2₁m, , P 2₁ m , , $\Gamma_qD_{2d}^3$ , , ''52a'' , , $(c:a:a):\tilde 4 \cdot \widetilde{ab}$ , , $(4\bar{*}{\cdot}2)$
, - align=center
, 114, , P2₁c, , P 2₁ c , , $\Gamma_qD_{2d}^4$ , , ''53a'' , , $(c:a:a):\tilde 4 \cdot \widetilde{abc}$ , , $(4\bar{*}{:}2)$
, - align=center
, 115, , Pm2, , P m 2 , , $\Gamma_qD_{2d}^5$ , , ''33s'' , , $(c:a:a):\tilde 4 \cdot m$ , , $(*{\cdot}44{\cdot}2)$
, - align=center
, 116, , Pc2, , P c 2 , , $\Gamma_qD_{2d}^6$ , , ''31h'' , , $(c:a:a):\tilde 4 \cdot \tilde c$ , , $(*{:}44{:}2)$
, - align=center
, 117, , Pb2, , P b 2 , , $\Gamma_qD_{2d}^7$ , , ''32h'' , , $(c:a:a):\tilde 4 \odot \tilde a$ , , $(4\bar{*}_02_0)$
, - align=center
, 118, , Pn2, , P n 2 , , $\Gamma_qD_{2d}^8$ , , ''33h'' , , $(c:a:a):\tilde 4 \cdot \widetilde{ac}$ , , $(4\bar{*}_12_0)$
, - align=center
, 119, , Im2, , I m 2 , , $\Gamma_q^vD_{2d}^9$ , , ''35s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :\tilde 4 \cdot m$ , , $(*4{\cdot}42_1)$
, - align=center
, 120, , Ic2, , I c 2 , , $\Gamma_q^vD_{2d}^{10}$ , , ''34h'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :\tilde 4 \cdot \tilde c$ , , $(*4{:}42_1)$
, - align=center
, 121, , I2m, , I 2 m , , $\Gamma_q^vD_{2d}^{11}$ , , ''34s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :\tilde 4 :2$ , , $(*{\cdot}44{:}2)$
, - align=center
, 122, , I2d, , I 2 d , , $\Gamma_q^vD_{2d}^{12}$ , , ''51a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) :\tilde 4 \odot \tfrac{1}{2}\widetilde{abc}$ , , $(4\bar{*}2_1)$
, - align=center
, 123, , rowspan=20, 4/m 2/m 2/m, , rowspan=20, $*224$, , P4/mmm, , P 4/m 2/m 2/m , , $\Gamma_qD_{4h}^1$ , , ''36s'' , , $(c:a:a)\cdot m:4\cdot m$ , , {\cdot}4{\cdot}4{\cdot}2/math>
, - align=center
, 124, , P4/mcc, , P 4/m 2/c 2/c , , $\Gamma_qD_{4h}^2$ , , ''35h'' , , $(c:a:a)\cdot m:4\cdot \tilde c$ , , {:}4{:}4{:}2/math>
, - align=center
, 125, , P4/nbm, , P 4/n 2/b 2/m, , $\Gamma_qD_{4h}^3$ , , ''36h'' , , $(c:a:a)\cdot \widetilde{ab}:4\odot \tilde a$ , , $(*4_04{\cdot}2)$
, - align=center
, 126, , P4/nnc, , P 4/n 2/n 2/c , , $\Gamma_qD_{4h}^4$ , , ''37h'' , , $(c:a:a)\cdot \widetilde{ab}:4\odot \widetilde{ac}$ , , $(*4_04{:}2)$
, - align=center
, 127, , P4/mbm, , P 4/m 2₁/b 2/m , , $\Gamma_qD_{4h}^5$ , , ''54a'' , , $(c:a:a)\cdot m:4\odot \tilde a$ , , _0{*}{\cdot}2/math>
, - align=center
, 128, , P4/mnc, , P 4/m 2₁/n 2/c , , $\Gamma_qD_{4h}^6$ , , ''56a'' , , $(c:a:a)\cdot m:4\odot \widetilde{ac}$ , , _0{*}{:}2/math>
, - align=center
, 129, , P4/nmm, , P 4/n 2₁/m 2/m , , $\Gamma_qD_{4h}^7$ , , ''55a'' , , $(c:a:a)\cdot \widetilde{ab}:4\cdot m$ , , $(*4{\cdot}4{\cdot}2)$
, - align=center
, 130, , P4/ncc, , P 4/n 2₁/c 2/c , , $\Gamma_qD_{4h}^8$ , , ''57a'' , , $(c:a:a)\cdot \widetilde{ab}:4\cdot \tilde c$ , , $(*4{:}4{:}2)$
, - align=center
, 131, , P4₂/mmc, , P 4₂/m 2/m 2/c , , $\Gamma_qD_{4h}^9$ , , ''60a'' , , $(c:a:a)\cdot m:4_2\cdot m$ , , {\cdot}4{:}4{\cdot}2/math>
, - align=center
, 132, , P4₂/mcm, , P 4₂/m 2/c 2/m , , $\Gamma_qD_{4h}^{10}$ , , ''61a'' , , $(c:a:a)\cdot m:4_2\cdot \tilde c$ , , {:}4{\cdot}4{:}2/math>
, - align=center
, 133, , P4₂/nbc, , P 4₂/n 2/b 2/c , , $\Gamma_qD_{4h}^{11}$ , , ''63a'' , , $(c:a:a)\cdot \widetilde{ab}:4_2\odot \tilde a$ , , $(*4_24{:}2)$
, - align=center
, 134, , P4₂/nnm, , P 4₂/n 2/n 2/m , , $\Gamma_qD_{4h}^{12}$ , , ''62a'' , , $(c:a:a)\cdot \widetilde{ab}:4_2\odot \widetilde{ac}$ , , $(*4_24{\cdot}2)$
, - align=center
, 135, , P4₂/mbc, , P 4₂/m 2₁/b 2/c , , $\Gamma_qD_{4h}^{13}$ , , ''66a'' , , $(c:a:a)\cdot m:4_2\odot \tilde a$ , , _2{*}{:}2/math>
, - align=center
, 136, , P4₂/mnm, , P 4₂/m 2₁/n 2/m , , $\Gamma_qD_{4h}^{14}$ , , ''65a'' , , $(c:a:a)\cdot m:4_2\odot \widetilde{ac}$ , , _2{*}{\cdot}2/math>
, - align=center
, 137, , P4₂/nmc, , P 4₂/n 2₁/m 2/c , , $\Gamma_qD_{4h}^{15}$ , , ''67a'' , , $(c:a:a)\cdot \widetilde{ab}:4_2\cdot m$ , , $(*4{\cdot}4{:}2)$
, - align=center
, 138, , P4₂/ncm, , P 4₂/n 2₁/c 2/m , , $\Gamma_qD_{4h}^{16}$ , , ''65a'' , , $(c:a:a)\cdot \widetilde{ab}:4_2\cdot \tilde c$ , , $(*4{:}4{\cdot}2)$
, - align=center
, 139, , I4/mmm, , I 4/m 2/m 2/m , , $\Gamma_q^vD_{4h}^{17}$ , , ''37s'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) \cdot m:4\cdot m$ , , {\cdot}4{\cdot}4{:}2/math>
, - align=center
, 140, , I4/mcm, , I 4/m 2/c 2/m , , $\Gamma_q^vD_{4h}^{18}$ , , ''38h'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) \cdot m:4\cdot \tilde c$ , , {\cdot}4{:}4{:}2/math>
, - align=center
, 141, , I4₁/amd, , I 4₁/a 2/m 2/d , , $\Gamma_q^vD_{4h}^{19}$ , , ''59a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) \cdot \tilde a :4_1\odot m$ , , $(*4_14{\cdot}2)$
, - align=center
, 142, , I4₁/acd, , I 4₁/a 2/c 2/d , , $\Gamma_q^vD_{4h}^{20}$ , , ''58a'' , , $\left ( \tfrac{a+b+c}{2}/c:a:a\right ) \cdot \tilde a :4_1\odot \tilde c$ , , $(*4_14{:}2)$

List of trigonal

{, class="wikitable floatright"
, + Trigonal Bravais lattice
, -
! Rhombohedral (R)
! Hexagonal (P)
, - style="vertical-align:top;"
,
,

{, class=wikitable
, + Trigonal crystal system
!Number
! Point group
! Orbifold
! Short name
! Full name
! Schoenflies
! Fedorov
! Shubnikov
! Fibrifold
, - align=center
, 143, , rowspan=4, 3, , rowspan=4, $33$, , P3, , P 3 , , $\Gamma_hC_3^1$ , , ''38s'' , , $(c:(a/a)):3$ , , $(3_03_03_0)$
, - align=center
, 144, , P3₁, , P 3₁ , , $\Gamma_hC_3^2$ , , ''68a'' , , $(c:(a/a)):3_1$ , , $(3_13_13_1)$
, - align=center
, 145, , P3₂, , P 3₂ , , $\Gamma_hC_3^3$ , , ''69a'' , , $(c:(a/a)):3_2$ , , $(3_13_13_1)$
, - align=center
, 146, , R3, , R 3 , , $\Gamma_{rh}C_3^4$ , , ''39s'' , , $(a/a/a)/3$ , , $(3_03_13_2)$
, - align=center
, 147, , rowspan=2, , , rowspan=2, $3\times$, , P, , P , , $\Gamma_hC_{3i}^1$ , , ''51s'' , , $(c:(a/a)):\tilde 6$ , , $(63_02)$
, - align=center
, 148, , R, , R , , $\Gamma_{rh}C_{3i}^2$ , , ''52s'' , , $(a/a/a)/\tilde 6$ , , $(63_12)$
, - align=center
, 149, , rowspan=7, 32, , rowspan=7, $223$, , P312, , P 3 1 2 , , $\Gamma_hD_3^1$ , , ''45s'' , , $(c:(a/a)):2:3$ , , $(*3_03_03_0)$
, - align=center
, 150, , P321, , P 3 2 1 , , $\Gamma_hD_3^2$ , , ''44s'' , , $(c:(a/a))\cdot 2:3$ , , $(3_0{*}3_0)$
, - align=center
, 151, , P3₁12, , P 3₁ 1 2 , , $\Gamma_hD_3^3$ , , ''72a'' , , $(c:(a/a)):2:3_1$ , , $(*3_13_13_1)$
, - align=center
, 152, , P3₁21, , P 3₁ 2 1 , , $\Gamma_hD_3^4$ , , ''70a'' , , $(c:(a/a))\cdot 2:3_1$ , , $(3_1{*}3_1)$
, - align=center
, 153, , P3₂12, , P 3₂ 1 2 , , $\Gamma_hD_3^5$ , , ''73a'' , , $(c:(a/a)):2:3_2$ , , $(*3_13_13_1)$
, - align=center
, 154, , P3₂21, , P 3₂ 2 1 , , $\Gamma_hD_3^6$ , , ''71a'' , , $(c:(a/a))\cdot 2:3_2$ , , $(3_1{*}3_1)$
, - align=center
, 155, , R32, , R 3 2 , , $\Gamma_{rh}D_3^7$ , , ''46s'' , , $(a/a/a)/3:2$ , , $(*3_03_13_2)$
, - align=center
, 156, , rowspan=6, 3m, , rowspan=6, $*33$, , P3m1, , P 3 m 1 , , $\Gamma_hC_{3v}^1$ , , ''40s'' , , $(c:(a/a)):m\cdot 3$ , , $(*{\cdot}3{\cdot}3{\cdot}3)$
, - align=center
, 157, , P31m, , P 3 1 m , , $\Gamma_hC_{3v}^2$ , , ''41s'' , , $(c:(a/a))\cdot m\cdot 3$ , , $(3_0{*}{\cdot}3)$
, - align=center
, 158, , P3c1, , P 3 c 1 , , $\Gamma_hC_{3v}^3$ , , ''39h'' , , $(c:(a/a)):\tilde c:3$ , , $(*{:}3{:}3{:}3)$
, - align=center
, 159, , P31c, , P 3 1 c , , $\Gamma_hC_{3v}^4$ , , ''40h'' , , $(c:(a/a))\cdot\tilde c :3$ , , $(3_0{*}{:}3)$
, - align=center
, 160, , R3m, , R 3 m , , $\Gamma_{rh}C_{3v}^5$ , , ''42s'' , , $(a/a/a)/3\cdot m$ , , $(3_1{*}{\cdot}3)$
, - align=center
, 161, , R3c, , R 3 c , , $\Gamma_{rh}C_{3v}^6$ , , ''41h'' , , $(a/a/a)/3\cdot\tilde c$ , , $(3_1{*}{:}3)$
, - align=center
, 162, , rowspan=6, 2/m, , rowspan=6, $2{*}3$, , P1m, , P 1 2/m , , $\Gamma_hD_{3d}^1$ , , ''56s'' , , $(c:(a/a))\cdot m\cdot\tilde 6$ , , $(*{\cdot}63_02)$
, - align=center
, 163, , P1c, , P 1 2/c , , $\Gamma_hD_{3d}^2$ , , ''46h'' , , $(c:(a/a))\cdot\tilde c \cdot\tilde 6$ , , $(*{:}63_02)$
, - align=center
, 164, , Pm1, , P 2/m 1 , , $\Gamma_hD_{3d}^3$ , , ''55s'' , , $(c:(a/a)):m\cdot\tilde 6$ , , $(*6{\cdot}3{\cdot}2)$
, - align=center
, 165, , Pc1, , P 2/c 1 , , $\Gamma_hD_{3d}^4$ , , ''45h'' , , $(c:(a/a)):\tilde c \cdot\tilde 6$ , , $(*6{:}3{:}2)$
, - align=center
, 166, , Rm, , R 2/m , , $\Gamma_{rh}D_{3d}^5$ , , ''57s'' , , $(a/a/a)/\tilde 6 \cdot m$ , , $(*{\cdot}63_12)$
, - align=center
, 167, , Rc, , R 2/c , , $\Gamma_{rh}D_{3d}^6$ , , ''47h'' , , $(a/a/a)/\tilde 6 \cdot\tilde c$ , , $(*{:}63_12)$

List of hexagonal

{, class="wikitable floatright"
, + Hexagonal Bravais lattice
, -
,

{, class=wikitable
, + Hexagonal crystal system
!Number
! Point group
! Orbifold
! Short name
! Full name
! Schoenflies
! Fedorov
! Shubnikov
! Fibrifold
, - align=center
, 168, , rowspan=6, 6, , rowspan=6, $66$, , P6, , P 6 , , $\Gamma_hC_6^1$ , , ''49s'' , , $(c:(a/a)):6$ , , $(6_03_02_0)$
, - align=center
, 169, , P6₁, , P 6₁ , , $\Gamma_hC_6^2$ , , ''74a'' , , $(c:(a/a)):6_1$ , , $(6_13_12_1)$
, - align=center
, 170, , P6₅, , P 6₅ , , $\Gamma_hC_6^3$ , , ''75a'' , , $(c:(a/a)):6_5$ , , $(6_13_12_1)$
, - align=center
, 171, , P6₂, , P 6₂ , , $\Gamma_hC_6^4$ , , ''76a'' , , $(c:(a/a)):6_2$ , , $(6_23_22_0)$
, - align=center
, 172, , P6₄, , P 6₄ , , $\Gamma_hC_6^5$ , , ''77a'' , , $(c:(a/a)):6_4$ , , $(6_23_22_0)$
, - align=center
, 173, , P6₃, , P 6₃ , , $\Gamma_hC_6^6$ , , ''78a'' , , $(c:(a/a)):6_3$ , , $(6_33_02_1)$
, - align=center
, 174, , , , $3*$, , P, , P , , $\Gamma_hC_{3h}^1$ , , ''43s'' , , $(c:(a/a)):3:m$ , , _03_03_0/math>
, - align=center
, 175, , rowspan=2, 6/m, , rowspan=2, $6*$, , P6/m, , P 6/m , , $\Gamma_hC_{6h}^1$ , , ''53s'' , , $(c:(a/a))\cdot m :6$ , , _03_02_0/math>
, - align=center
, 176, , P6₃/m, , P 6₃/m , , $\Gamma_hC_{6h}^2$ , , ''81a'' , , $(c:(a/a))\cdot m :6_3$ , , _33_02_1/math>
, - align=center
, 177, , rowspan=6, 622, , rowspan=6, $226$, , P622, , P 6 2 2 , , $\Gamma_hD_6^1$ , , ''54s'' , , $(c:(a/a))\cdot 2 :6$ , , $(*6_03_02_0)$
, - align=center
, 178, , P6₁22, , P 6₁ 2 2 , , $\Gamma_hD_6^2$ , , ''82a'' , , $(c:(a/a))\cdot 2 :6_1$ , , $(*6_13_12_1)$
, - align=center
, 179, , P6₅22, , P 6₅ 2 2 , , $\Gamma_hD_6^3$ , , ''83a'' , , $(c:(a/a))\cdot 2 :6_5$ , , $(*6_13_12_1)$
, - align=center
, 180, , P6₂22, , P 6₂ 2 2 , , $\Gamma_hD_6^4$ , , ''84a'' , , $(c:(a/a))\cdot 2 :6_2$ , , $(*6_23_22_0)$
, - align=center
, 181, , P6₄22, , P 6₄ 2 2 , , $\Gamma_hD_6^5$ , , ''85a'' , , $(c:(a/a))\cdot 2 :6_4$ , , $(*6_23_22_0)$
, - align=center
, 182, , P6₃22, , P 6₃ 2 2 , , $\Gamma_hD_6^6$ , , ''86a'' , , $(c:(a/a))\cdot 2 :6_3$ , , $(*6_33_02_1)$
, - align=center
, 183, , rowspan=4, 6mm, , rowspan=4, $*66$, , P6mm, , P 6 m m , , $\Gamma_hC_{6v}^1$ , , ''50s'' , , $(c:(a/a)):m\cdot 6$ , , $(*{\cdot}6{\cdot}3{\cdot}2)$
, - align=center
, 184, , P6cc, , P 6 c c , , $\Gamma_hC_{6v}^2$ , , ''44h'' , , $(c:(a/a)):\tilde c \cdot 6$ , , $(*{:}6{:}3{:}2)$
, - align=center
, 185, , P6₃cm, , P 6₃ c m , , $\Gamma_hC_{6v}^3$ , , ''80a'' , , $(c:(a/a)):\tilde c \cdot 6_3$ , , $(*{\cdot}6{:}3{:}2)$
, - align=center
, 186, , P6₃mc, , P 6₃ m c , , $\Gamma_hC_{6v}^4$ , , ''79a'' , , $(c:(a/a)):m\cdot 6_3$ , , $(*{:}6{\cdot}3{\cdot}2)$
, - align=center
, 187, , rowspan=4, m2, , rowspan=4, $*223$, , Pm2, , P m 2 , , $\Gamma_hD_{3h}^1$ , , ''48s'' , , $(c:(a/a)):m\cdot 3:m$ , , {\cdot}3{\cdot}3{\cdot}3/math>
, - align=center
, 188, , Pc2, , P c 2 , , $\Gamma_hD_{3h}^2$ , , ''43h'' , , $(c:(a/a)):\tilde c \cdot 3:m$ , , {:}3{:}3{:}3/math>
, - align=center
, 189, , P2m, , P 2 m , , $\Gamma_hD_{3h}^3$ , , ''47s'' , , $(c:(a/a))\cdot m:3\cdot m$ , , _0{*}{\cdot}3/math>
, - align=center
, 190, , P2c, , P 2 c , , $\Gamma_hD_{3h}^4$ , , ''42h'' , , $(c:(a/a))\cdot m:3\cdot \tilde c$ , , _0{*}{:}3/math>
, - align=center
, 191, , rowspan=4, 6/m 2/m 2/m, , rowspan=4, $*226$, , P6/mmm, , P 6/m 2/m 2/m , , $\Gamma_hD_{6h}^1$ , , ''58s'' , , $(c:(a/a))\cdot m:6\cdot m$ , , {\cdot}6{\cdot}3{\cdot}2/math>
, - align=center
, 192, , P6/mcc, , P 6/m 2/c 2/c , , $\Gamma_hD_{6h}^2$ , , ''48h'' , , $(c:(a/a))\cdot m:6\cdot\tilde c$ , , {:}6{:}3{:}2/math>
, - align=center
, 193, , P6₃/mcm, , P 6₃/m 2/c 2/m , , $\Gamma_hD_{6h}^3$ , , ''87a'' , , $(c:(a/a))\cdot m:6_3\cdot\tilde c$ , , {\cdot}6{:}3{:}2/math>
, - align=center
, 194, , P6₃/mmc, , P 6₃/m 2/m 2/c , , $\Gamma_hD_{6h}^4$ , , ''88a'' , , $(c:(a/a))\cdot m:6_3\cdot m$ , , {:}6{\cdot}3{\cdot}2/math>

List of cubic

{, class="wikitable" style="text-align:center;"
, + Cubic Bravais lattice
, -
! Simple (P)
! Body centered (I)
! Face centered (F)
, -
,
,
,

{, class=wikitable
, + Cubic crystal system
!Number
! Point group
! Orbifold
! Short name
! Full name
! Schoenflies
! Fedorov
! Shubnikov
! Conway
! Fibrifold (preserving $z$)
! Fibrifold (preserving $x$, $y$, $z$)
, - align=center
, 195, , rowspan=5, 23, , rowspan=5, $332$, , P23, , P 2 3 , , $\Gamma_cT^1$ , , ''59s'' , , $\left ( a:a:a\right ) :2/3$ , , $2^\circ$ , , $(*2_02_02_02_0){:}3$ , , $(*2_02_02_02_0){:}3$
, - align=center
, 196, , F23, , F 2 3 , , $\Gamma_c^fT^2$ , , ''61s'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :2/3$ , , $1^\circ$ , , $(*2_02_12_02_1){:}3$ , , $(*2_02_12_02_1){:}3$
, - align=center
, 197, , I23, , I 2 3 , , $\Gamma_c^vT^3$ , , ''60s'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) :2/3$, , $4^{\circ\circ}$ , , $(2_1{*}2_02_0){:}3$ , , $(2_1{*}2_02_0){:}3$
, - align=center
, 198, , P2₁3, , P 2₁ 3 , , $\Gamma_cT^4$ , , ''89a'' , , $\left ( a:a:a\right ) :2_1/3$, , $1^\circ/4$ , , $(2_12_1\bar{\times}){:}3$ , , $(2_12_1\bar{\times}){:}3$
, - align=center
, 199, , I2₁3, , I 2₁ 3 , , $\Gamma_c^vT^5$ , , ''90a'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) :2_1/3$, , $2^\circ/4$ , , $(2_0{*}2_12_1){:}3$ , , $(2_0{*}2_12_1){:}3$
, - align=center
, 200, , rowspan=7, 2/m , , rowspan=7, $3{*}2$, , Pm, , P 2/m , , $\Gamma_cT_h^1$ , , ''62s'' , , $\left ( a:a:a\right ) \cdot m/ \tilde 6$ , , $4^-$ , , {\cdot}2{\cdot}2{\cdot}2{\cdot}2:}3 , , {\cdot}2{\cdot}2{\cdot}2{\cdot}2:}3
, - align=center
, 201, , Pn, , P 2/n , , $\Gamma_cT_h^2$ , , ''49h'' , , $\left ( a:a:a\right ) \cdot \widetilde{ab} / \tilde 6$ , , $4^{\circ+}$ , , $(2\bar{*}_12_02_0){:}3$ , , $(2\bar{*}_12_02_0){:}3$
, - align=center
, 202, , Fm, , F 2/m , , $\Gamma_c^fT_h^3$ , , ''64s'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) \cdot m/ \tilde 6$ , , $2^-$ , , {\cdot}2{\cdot}2{:}2{:}2:}3 , , {\cdot}2{\cdot}2{:}2{:}2:}3
, - align=center
, 203, , Fd, , F 2/d , , $\Gamma_c^fT_h^4$ , , ''50h'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) \cdot \tfrac{1}{2}\widetilde{ab} / \tilde 6$ , , $2^{\circ+}$ , , $(2\bar{*}2_02_1){:}3$ , , $(2\bar{*}2_02_1){:}3$
, - align=center
, 204, , Im, , I 2/m , , $\Gamma_c^vT_h^5$ , , ''63s'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) \cdot m/\tilde 6$ , , $8^{-\circ}$ , , _1{*}{\cdot}2{\cdot}2:}3 , , _1{*}{\cdot}2{\cdot}2:}3
, - align=center
, 205, , Pa, , P 2₁/a , , $\Gamma_cT_h^6$ , , ''91a'' , , $\left ( a:a:a\right ) \cdot \tilde a /\tilde 6$ , , $2^-/4$ , , $(2_12\bar{*}{:}){:}3$, , $(2_12\bar{*}{:}){:}3$
, - align=center
, 206, , Ia, , I 2₁/a , , $\Gamma_c^vT_h^7$ , , ''92a'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) \cdot \tilde a /\tilde 6$ , , $4^-/4$ , , $(*2_12{:}2{:}2){:}3$ , , $(*2_12{:}2{:}2){:}3$
, - align=center
, 207, , rowspan=8, 432, , rowspan=8, $432$, , P432, , P 4 3 2 , , $\Gamma_cO^1$ , , ''68s'' , , $\left ( a:a:a\right ) :4/3$ , , $4^{\circ-}$ , , $(*4_04_02_0){:}3$ , , $(*2_02_02_02_0){:}6$
, - align=center
, 208, , P4₂32, , P 4₂ 3 2 , , $\Gamma_cO^2$ , , ''98a'' , , $\left ( a:a:a\right ) :4_2//3$ , , $4^+$ , , $(*4_24_22_0){:}3$ , , $(*2_02_02_02_0){:}6$
, - align=center
, 209, , F432, , F 4 3 2 , , $\Gamma_c^fO^3$ , , ''70s'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :4/3$ , , $2^{\circ-}$ , , $(*4_24_02_1){:}3$ , , $(*2_02_12_02_1){:}6$
, - align=center
, 210, , F4₁32, , F 4₁ 3 2 , , $\Gamma_c^fO^4$ , , ''97a'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :4_1//3$ , , $2^+$ , , $(*4_34_12_0){:}3$ , , $(*2_02_12_02_1){:}6$
, - align=center
, 211, , I432, , I 4 3 2 , , $\Gamma_c^vO^5$ , , ''69s'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) :4/3$ , , $8^{+\circ}$ , , $(4_24_02_1){:}3$, , $(2_1{*}2_02_0){:}6$
, - align=center
, 212, , P4₃32, , P 4₃ 3 2 , , $\Gamma_cO^6$ , , ''94a'' , , $\left ( a:a:a\right ) :4_3//3$ , , $2^+/4$ , , $(4_1{*}2_1){:}3$ , , $(2_12_1\bar{\times}){:}6$
, - align=center
, 213, , P4₁32, , P 4₁ 3 2 , , $\Gamma_cO^7$ , , ''95a'' , , $\left ( a:a:a\right ) :4_1//3$ , , $2^+/4$ , , $(4_1{*}2_1){:}3$ , , $(2_12_1\bar{\times}){:}6$
, - align=center
, 214, , I4₁32, , I 4₁ 3 2 , , $\Gamma_c^vO^8$ , , ''96a'' , , $\left ( \tfrac{a+b+c}{2}/:a:a:a\right ) :4_1//3$ , , $4^+/4$ , , $(*4_34_12_0){:}3$ , , $(2_0{*}2_12_1){:}6$
, - align=center
, 215, , rowspan=6, 3m, , rowspan=6, $*332$, , P3m, , P 3 m , , $\Gamma_cT_d^1$ , , ''65s'' , , $\left ( a:a:a\right ) :\tilde 4 /3$ , , $2^\circ{:}2$ , , $(*4{\cdot}42_0){:}3$ , , $(*2_02_02_02_0){:}6$
, - align=center
, 216, , F3m, , F 3 m , , $\Gamma_c^fT_d^2$ , , ''67s'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :\tilde 4 /3$ , , $1^\circ{:}2$ , , $(*4{\cdot}42_1){:}3$ , , $(*2_02_12_02_1){:}6$
, - align=center
, 217, , I3m, , I 3 m , , $\Gamma_c^vT_d^3$ , , ''66s'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) :\tilde 4 /3$ , , $4^\circ{:}2$ , , $(*{\cdot}44{:}2){:}3$ , , $(2_1{*}2_02_0){:}6$
, - align=center
, 218, , P3n, , P 3 n , , $\Gamma_cT_d^4$ , , ''51h'' , , $\left ( a:a:a\right ) :\tilde 4 //3$ , , $4^\circ$ , , $(*4{:}42_0){:}3$ , , $(*2_02_02_02_0){:}6$
, - align=center
, 219, , F3c, , F 3 c , , $\Gamma_c^fT_d^5$ , , ''52h'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :\tilde 4 //3$ , , $2^{\circ\circ}$ , , $(*4{:}42_1){:}3$ , , $(*2_02_12_02_1){:}6$
, - align=center
, 220, , I3d, , I 3 d , , $\Gamma_c^vT_d^6$ , , ''93a'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) :\tilde 4 //3$ , , $4^\circ/4$ , , $(4\bar{*}2_1){:}3$ , , $(2_0{*}2_12_1){:}6$
, - align=center
, 221, , rowspan=10, 4/m 2/m, , rowspan=10, $*432$, , Pmm, , P 4/m 2/m , , $\Gamma_cO_h^1$ , , ''71s'' , , $\left ( a:a:a\right ) :4/\tilde 6 \cdot m$ , , $4^-{:}2$ , , {\cdot}4{\cdot}4{\cdot}2:}3 , , {\cdot}2{\cdot}2{\cdot}2{\cdot}2:}6
, - align=center
, 222, , Pnn, , P 4/n 2/n , , $\Gamma_cO_h^2$ , , ''53h'' , , $\left ( a:a:a\right ) :4/\tilde 6 \cdot \widetilde{abc}$ , , $8^{\circ\circ}$ , , $(*4_04{:}2){:}3$ , , $(2\bar{*}_12_02_0){:}6$
, - align=center
, 223, , Pmn, , P 4₂/m 2/n , , $\Gamma_cO_h^3$ , , ''102a'' , , $\left ( a:a:a\right ) :4_2//\tilde 6 \cdot \widetilde{abc}$ , , $8^\circ$ , , {\cdot}4{:}4{\cdot}2:}3 , , {\cdot}2{\cdot}2{\cdot}2{\cdot}2:}6
, - align=center
, 224, , Pnm, , P 4₂/n 2/m , , $\Gamma_cO_h^4$ , , ''103a'' , , $\left ( a:a:a\right ) :4_2//\tilde 6 \cdot m$ , , $4^+{:}2$ , , $(*4_24{\cdot}2){:}3$ , , $(2\bar{*}_12_02_0){:}6$
, - align=center
, 225, , Fmm, , F 4/m 2/m , , $\Gamma_c^fO_h^5$ , , ''73s'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :4/\tilde 6 \cdot m$ , , $2^-{:}2$ , , {\cdot}4{\cdot}4{:}2:}3 , , {\cdot}2{\cdot}2{:}2{:}2:}6
, - align=center
, 226, , Fmc, , F 4/m 2/c , , $\Gamma_c^fO_h^6$ , , ''54h'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :4/\tilde 6 \cdot \tilde c$ , , $4^{--}$ , , {\cdot}4{:}4{:}2:}3 , , {\cdot}2{\cdot}2{:}2{:}2:}6
, - align=center
, 227, , Fdm, , F 4₁/d 2/m , , $\Gamma_c^fO_h^7$ , , ''100a'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :4_1//\tilde 6 \cdot m$ , , $2^+{:}2$ , , $(*4_14{\cdot}2){:}3$ , , $(2\bar{*}2_02_1){:}6$
, - align=center
, 228, , Fdc, , F 4₁/d 2/c , , $\Gamma_c^fO_h^8$ , , ''101a'' , , $\left ( \tfrac{a+c}{2}/\tfrac{b+c}{2}/\tfrac{a+b}{2}:a:a:a\right ) :4_1//\tilde 6 \cdot \tilde c$ , , $4^{++}$ , , $(*4_14{:}2){:}3$ , , $(2\bar{*}2_02_1){:}6$
, - align=center
, 229, , Imm, , I 4/m 2/m , , $\Gamma_c^vO_h^9$ , , ''72s'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) :4/\tilde 6 \cdot m$ , , $8^\circ{:}2$ , , {\cdot}4{\cdot}4{:}2:}3 , , _1{*}{\cdot}2{\cdot}2:}6
, - align=center
, 230, , Iad, , I 4₁/a 2/d , , $\Gamma_c^vO_h^{10}$ , , ''99a'' , , $\left ( \tfrac{a+b+c}{2}/a:a:a\right ) :4_1//\tilde 6 \cdot \tfrac{1}{2}\widetilde{abc}$ , , $8^\circ/4$ , , $(*4_14{:}2){:}3$ , , $(*2_12{:}2{:}2){:}6$

Notes

References

External links

{{Commons category, Space groups

International Union of Crystallography

Point Groups and Bravais Lattices



Conway et al. on fibrifold notation

Symmetry
Crystallography