# 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 $\color {Black}{\tfrac {360^{\circ }}{n}}$. 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, 2$_1$ is a 180° (twofold) rotation followed by a translation of ⁠1/2⁠ of the lattice vector. 3$_1$ is a 120° (threefold) rotation followed by a translation of ⁠1/3⁠ of the lattice vector. The possible screw axes are: 2$_1$, 3$_1$, 3$_2$, 4$_1$, 4$_2$, 4$_3$, 6$_1$, 6$_2$, 6$_3$, 6$_4$, and 6$_5$.
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 n/m {\textstyle {\frac {n}{m}}} or n/m. For example, 4$_1$/a means that the crystallographic axis in question contains both a 4$_1$ 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 $x\in \{t,m,o,q,rh,h,c\}$ is the lattice system, and $y\in \{\emptyset ,b,v,f\}$ 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 (${\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$): the symmorphic space groups are P4/mmm ($P{\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$, 36s) and I4/mmm ($I{\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$, 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 (${\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$): 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 ($P{\tfrac {4}{m}}{\tfrac {2}{c}}{\tfrac {2}{c}}$, 35h), P4/nbm ($P{\tfrac {4}{n}}{\tfrac {2}{b}}{\tfrac {2}{m}}$, 36h), P4/nnc ($P{\tfrac {4}{n}}{\tfrac {2}{n}}{\tfrac {2}{c}}$, 37h), and I4/mcm ($I{\tfrac {4}{m}}{\tfrac {2}{c}}{\tfrac {2}{m}}$, 38h).

### Asymmorphic

The remaining 103 space groups are asymmorphic. Example for point group 4/mmm (${\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$): P4/mbm ($P{\tfrac {4}{m}}{\tfrac {2_{1}}{b}}{\tfrac {2}{m}}$, 54a), P4$_2$/mmc ($P{\tfrac {4_{2}}{m}}{\tfrac {2}{m}}{\tfrac {2}{c}}$, 60a), I4$_1$/acd ($I{\tfrac {4_{1}}{a}}{\tfrac {2}{c}}{\tfrac {2}{d}}$, 58a) - none of these groups contains the axial combination 422.

## List of triclinic

Triclinic crystal system :
| Number | Point group | Orbifold | Short name | Full name | Schoenflies | Fedorov | Shubnikov | Fibrifold |
| 1 | 1 | $1$ | P1 | P 1 | $\Gamma _{t}C_{1}^{1}$ | 1s | $(a/b/c)\cdot 1$ | $(\circ )$ |
| 2 | 1 | $\times$ | P1 | P 1 | $\Gamma _{t}C_{i}^{1}$ | 2s | $(a/b/c)\cdot {\tilde {2}}$ | $(2222)$ |

## List of monoclinic

Monoclinic Bravais lattice :
| Simple (P) | Base (C) |
Monoclinic crystal system :
| Number | Point group | Orbifold | Short name | Full name(s) | Full name(s) | Schoenflies | Fedorov | Shubnikov | Fibrifold (primary) | Fibrifold (secondary) |
| 3 | 2 | $22$ | P2 | P 1 2 1 | P 1 1 2 | $\Gamma _{m}C_{2}^{1}$ | 3s | $(b:(c/a)):2$ | $(2_{0}2_{0}2_{0}2_{0})$ | $({*}_{0}{*}_{0})$ |
| 4 | 2 | $22$ | P2$_1$ | P 1 2$_1$ 1 | P 1 1 2$_1$ | $\Gamma _{m}C_{2}^{2}$ | 1a | $(b:(c/a)):2_{1}$ | $(2_{1}2_{1}2_{1}2_{1})$ | $({\bar {\times }}{\bar {\times }})$ |
| 5 | 2 | $22$ | C2 | C 1 2 1 | B 1 1 2 | $\Gamma _{m}^{b}C_{2}^{3}$ | 4s | $\left({\tfrac {a+b}{2}}/b:(c/a)\right):2$ | $(2_{0}2_{0}2_{1}2_{1})$ | $({*}_{1}{*}_{1})$, $({*}{\bar {\times }})$ |
| 6 | m | $*$ | Pm | P 1 m 1 | P 1 1 m | $\Gamma _{m}C_{s}^{1}$ | 5s | $(b:(c/a))\cdot m$ | $[\circ _{0}]$ | $({*}{\cdot }{*}{\cdot })$ |
| 7 | m | $*$ | Pc | P 1 c 1 | P 1 1 b | $\Gamma _{m}C_{s}^{2}$ | 1h | $(b:(c/a))\cdot {\tilde {c}}$ | $({\bar {\circ }}_{0})$ | $({*}{:}{*}{:})$, $({\times }{\times }_{0})$ |
| 8 | m | $*$ | Cm | C 1 m 1 | B 1 1 m | $\Gamma _{m}^{b}C_{s}^{3}$ | 6s | $\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m$ | $[\circ _{1}]$ | $({*}{\cdot }{*}{:})$, $({*}{\cdot }{\times })$ |
| 9 | m | $*$ | Cc | C 1 c 1 | B 1 1 b | $\Gamma _{m}^{b}C_{s}^{4}$ | 2h | $\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}$ | $({\bar {\circ }}_{1})$ | $({*}{:}{\times })$, $({\times }{\times }_{1})$ |
| 10 | 2/m | $2*$ | P2/m | P 1 2/m 1 | P 1 1 2/m | $\Gamma _{m}C_{2h}^{1}$ | 7s | $(b:(c/a))\cdot m:2$ | $[2_{0}2_{0}2_{0}2_{0}]$ | $[*2{\cdot }22{\cdot }2)$ |
| 11 | 2/m | $2*$ | P2$_1$/m | P 1 2$_1$/m 1 | P 1 1 2$_1$/m | $\Gamma _{m}C_{2h}^{2}$ | 2a | $(b:(c/a))\cdot m:2_{1}$ | $[2_{1}2_{1}2_{1}2_{1}]$ | $(22{*}{\cdot })$ |
| 12 | 2/m | $2*$ | C2/m | C 1 2/m 1 | B 1 1 2/m | $\Gamma _{m}^{b}C_{2h}^{3}$ | 8s | $\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m:2$ | $[2_{0}2_{0}2_{1}2_{1}]$ | $(*2{\cdot }22{:}2)$, $(2{\bar {*}}2{\cdot }2)$ |
| 13 | 2/m | $2*$ | P2/c | P 1 2/c 1 | P 1 1 2/b | $\Gamma _{m}C_{2h}^{4}$ | 3h | $(b:(c/a))\cdot {\tilde {c}}:2$ | $(2_{0}2_{0}22)$ | $(*2{:}22{:}2)$, $(22{*}_{0})$ |
| 14 | 2/m | $2*$ | P2$_1$/c | P 1 2$_1$/c 1 | P 1 1 2$_1$/b | $\Gamma _{m}C_{2h}^{5}$ | 3a | $(b:(c/a))\cdot {\tilde {c}}:2_{1}$ | $(2_{1}2_{1}22)$ | $(22{*}{:})$, $(22{\times })$ |
| 15 | 2/m | $2*$ | C2/c | C 1 2/c 1 | B 1 1 2/b | $\Gamma _{m}^{b}C_{2h}^{6}$ | 4h | $\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}:2$ | $(2_{0}2_{1}22)$ | $(2{\bar {*}}2{:}2)$, $(22{*}_{1})$ |

## List of orthorhombic

Orthorhombic Bravais lattice :
| Simple (P) | Body (I) | Face (F) | Base (A or C) |
Orthorhombic crystal system :
| Number | Point group | Orbifold | Short name | Full name | Schoenflies | Fedorov | Shubnikov | Fibrifold (primary) | Fibrifold (secondary) |
| 16 | 222 | $222$ | P222 | P 2 2 2 | $\Gamma _{o}D_{2}^{1}$ | 9s | $(c:a:b):2:2$ | $(*2_{0}2_{0}2_{0}2_{0})$ | |
| 17 | 222 | $222$ | P222$_1$ | P 2 2 2$_1$ | $\Gamma _{o}D_{2}^{2}$ | 4a | $(c:a:b):2_{1}:2$ | $(*2_{1}2_{1}2_{1}2_{1})$ | $(2_{0}2_{0}{*})$ |
| 18 | 222 | $222$ | P2$_1$2$_1$2 | P 2$_1$ 2$_1$ 2 | $\Gamma _{o}D_{2}^{3}$ | 7a | $(c:a:b):2$ $2_{1}$ | $(2_{0}2_{0}{\bar {\times }})$ | $(2_{1}2_{1}{*})$ |
| 19 | 222 | $222$ | P2$_1$2$_1$2$_1$ | P 2$_1$ 2$_1$ 2$_1$ | $\Gamma _{o}D_{2}^{4}$ | 8a | $(c:a:b):2_{1}$ $2_{1}$ | $(2_{1}2_{1}{\bar {\times }})$ | |
| 20 | 222 | $222$ | C222$_1$ | C 2 2 2$_1$ | $\Gamma _{o}^{b}D_{2}^{5}$ | 5a | $\left({\tfrac {a+b}{2}}:c:a:b\right):2_{1}:2$ | $(2_{1}{*}2_{1}2_{1})$ | $(2_{0}2_{1}{*})$ |
| 21 | 222 | $222$ | C222 | C 2 2 2 | $\Gamma _{o}^{b}D_{2}^{6}$ | 10s | $\left({\tfrac {a+b}{2}}:c:a:b\right):2:2$ | $(2_{0}{*}2_{0}2_{0})$ | $(*2_{0}2_{0}2_{1}2_{1})$ |
| 22 | 222 | $222$ | F222 | F 2 2 2 | $\Gamma _{o}^{f}D_{2}^{7}$ | 12s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):2:2$ | $(*2_{0}2_{1}2_{0}2_{1})$ | |
| 23 | 222 | $222$ | I222 | I 2 2 2 | $\Gamma _{o}^{v}D_{2}^{8}$ | 11s | $\left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2$ | $(2_{1}{*}2_{0}2_{0})$ | |
| 24 | 222 | $222$ | I2$_1$2$_1$2$_1$ | I 2$_1$ 2$_1$ 2$_1$ | $\Gamma _{o}^{v}D_{2}^{9}$ | 6a | $\left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2_{1}$ | $(2_{0}{*}2_{1}2_{1})$ | |
| 25 | mm2 | $*22$ | Pmm2 | P m m 2 | $\Gamma _{o}C_{2v}^{1}$ | 13s | $(c:a:b):m\cdot 2$ | $(*{\cdot }2{\cdot }2{\cdot }2{\cdot }2)$ | $[{*}_{0}{\cdot }{*}_{0}{\cdot }]$ |
| 26 | mm2 | $*22$ | Pmc2$_1$ | P m c 2$_1$ | $\Gamma _{o}C_{2v}^{2}$ | 9a | $(c:a:b):{\tilde {c}}\cdot 2_{1}$ | $(*{\cdot }2{:}2{\cdot }2{:}2)$ | $({\bar {*}}{\cdot }{\bar {*}}{\cdot })$, $[{\times _{0}}{\times _{0}}]$ |
| 27 | mm2 | $*22$ | Pcc2 | P c c 2 | $\Gamma _{o}C_{2v}^{3}$ | 5h | $(c:a:b):{\tilde {c}}\cdot 2$ | $(*{:}2{:}2{:}2{:}2)$ | $({\bar {*}}_{0}{\bar {*}}_{0})$ |
| 28 | mm2 | $*22$ | Pma2 | P m a 2 | $\Gamma _{o}C_{2v}^{4}$ | 6h | $(c:a:b):{\tilde {a}}\cdot 2$ | $(2_{0}2_{0}{*}{\cdot })$ | $[{*}_{0}{:}{*}_{0}{:}]$, $(*{\cdot }{*}_{0})$ |
| 29 | mm2 | $*22$ | Pca2$_1$ | P c a 2$_1$ | $\Gamma _{o}C_{2v}^{5}$ | 11a | $(c:a:b):{\tilde {a}}\cdot 2_{1}$ | $(2_{1}2_{1}{*}{:})$ | $({\bar {*}}{:}{\bar {*}}{:})$ |
| 30 | mm2 | $*22$ | Pnc2 | P n c 2 | $\Gamma _{o}C_{2v}^{6}$ | 7h | $(c:a:b):{\tilde {c}}\odot 2$ | $(2_{0}2_{0}{*}{:})$ | $({\bar {*}}_{1}{\bar {*}}_{1})$, $({*}_{0}{\times }_{0})$ |
| 31 | mm2 | $*22$ | Pmn2$_1$ | P m n 2$_1$ | $\Gamma _{o}C_{2v}^{7}$ | 10a | $(c:a:b):{\widetilde {ac}}\cdot 2_{1}$ | $(2_{1}2_{1}{*}{\cdot })$ | $(*{\cdot }{\bar {\times }})$, $[{\times }_{0}{\times }_{1}]$ |
| 32 | mm2 | $*22$ | Pba2 | P b a 2 | $\Gamma _{o}C_{2v}^{8}$ | 9h | $(c:a:b):{\tilde {a}}\odot 2$ | $(2_{0}2_{0}{\times }_{0})$ | $(*{:}{*}_{0})$ |
| 33 | mm2 | $*22$ | Pna2$_1$ | P n a 2$_1$ | $\Gamma _{o}C_{2v}^{9}$ | 12a | $(c:a:b):{\tilde {a}}\odot 2_{1}$ | $(2_{1}2_{1}{\times })$ | $(*{:}{\times })$, $({\times }{\times }_{1})$ |
| 34 | mm2 | $*22$ | Pnn2 | P n n 2 | $\Gamma _{o}C_{2v}^{10}$ | 8h | $(c:a:b):{\widetilde {ac}}\odot 2$ | $(2_{0}2_{0}{\times }_{1})$ | $(*_{0}{\times }_{1})$ |
| 35 | mm2 | $*22$ | Cmm2 | C m m 2 | $\Gamma _{o}^{b}C_{2v}^{11}$ | 14s | $\left({\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2$ | $(2_{0}{*}{\cdot }2{\cdot }2)$ | $[*_{0}{\cdot }{*}_{0}{:}]$ |
| 36 | mm2 | $*22$ | Cmc2$_1$ | C m c 2$_1$ | $\Gamma _{o}^{b}C_{2v}^{12}$ | 13a | $\left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2_{1}$ | $(2_{1}{*}{\cdot }2{:}2)$ | $({\bar {*}}{\cdot }{\bar {*}}{:})$, $[{\times }_{1}{\times }_{1}]$ |
| 37 | mm2 | $*22$ | Ccc2 | C c c 2 | $\Gamma _{o}^{b}C_{2v}^{13}$ | 10h | $\left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2$ | $(2_{0}{*}{:}2{:}2)$ | $({\bar {*}}_{0}{\bar {*}}_{1})$ |
| 38 | mm2 | $*22$ | Amm2 | A m m 2 | $\Gamma _{o}^{b}C_{2v}^{14}$ | 15s | $\left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2$ | $(*{\cdot }2{\cdot }2{\cdot }2{:}2)$ | $[{*}_{1}{\cdot }{*}_{1}{\cdot }]$, $[*{\cdot }{\times }_{0}]$ |
| 39 | mm2 | $*22$ | Aem2 | A b m 2 | $\Gamma _{o}^{b}C_{2v}^{15}$ | 11h | $\left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2_{1}$ | $(*{\cdot }2{:}2{:}2{:}2)$ | $[{*}_{1}{:}{*}_{1}{:}]$, $({\bar {*}}{\cdot }{\bar {*}}_{0})$ |
| 40 | mm2 | $*22$ | Ama2 | A m a 2 | $\Gamma _{o}^{b}C_{2v}^{16}$ | 12h | $\left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2$ | $(2_{0}2_{1}{*}{\cdot })$ | $(*{\cdot }{*}_{1})$, $[*{:}{\times }_{1}]$ |
| 41 | mm2 | $*22$ | Aea2 | A b a 2 | $\Gamma _{o}^{b}C_{2v}^{17}$ | 13h | $\left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2_{1}$ | $(2_{0}2_{1}{*}{:})$ | $(*{:}{*}_{1})$, $({\bar {*}}{:}{\bar {*}}_{1})$ |
| 42 | mm2 | $*22$ | Fmm2 | F m m 2 | $\Gamma _{o}^{f}C_{2v}^{18}$ | 17s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2$ | $(*{\cdot }2{\cdot }2{:}2{:}2)$ | $[{*}_{1}{\cdot }{*}_{1}{:}]$ |
| 43 | mm2 | $*22$ | Fdd2 | F d d 2 | $\Gamma _{o}^{f}C_{2v}^{19}$ | 16h | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):{\tfrac {1}{2}}{\widetilde {ac}}\odot 2$ | $(2_{0}2_{1}{\times })$ | $({*}_{1}{\times })$ |
| 44 | mm2 | $*22$ | Imm2 | I m m 2 | $\Gamma _{o}^{v}C_{2v}^{20}$ | 16s | $\left({\tfrac {a+b+c}{2}}/c:a:b\right):m\cdot 2$ | $(2_{1}{*}{\cdot }2{\cdot }2)$ | $[*{\cdot }{\times }_{1}]$ |
| 45 | mm2 | $*22$ | Iba2 | I b a 2 | $\Gamma _{o}^{v}C_{2v}^{21}$ | 15h | $\left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {c}}\cdot 2$ | $(2_{1}{*}{:}2{:}2)$ | $({\bar {*}}{:}{\bar {*}}_{0})$ |
| 46 | mm2 | $*22$ | Ima2 | I m a 2 | $\Gamma _{o}^{v}C_{2v}^{22}$ | 14h | $\left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2$ | $(2_{0}{*}{\cdot }2{:}2)$ | $({\bar {*}}{\cdot }{\bar {*}}_{1})$, $[*{:}{\times }_{0}]$ |
| 47 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pmmm | P 2/m 2/m 2/m | $\Gamma _{o}D_{2h}^{1}$ | 18s | $\left(c:a:b\right)\cdot m:2\cdot m$ | $[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]$ | |
| 48 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pnnn | P 2/n 2/n 2/n | $\Gamma _{o}D_{2h}^{2}$ | 19h | $\left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\widetilde {ac}}$ | $(2{\bar {*}}_{1}2_{0}2_{0})$ | |
| 49 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pccm | P 2/c 2/c 2/m | $\Gamma _{o}D_{2h}^{3}$ | 17h | $\left(c:a:b\right)\cdot m:2\cdot {\tilde {c}}$ | $[*{:}2{:}2{:}2{:}2]$ | $(*2_{0}2_{0}2{\cdot }2)$ |
| 50 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pban | P 2/b 2/a 2/n | $\Gamma _{o}D_{2h}^{4}$ | 18h | $\left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\tilde {a}}$ | $(2{\bar {*}}_{0}2_{0}2_{0})$ | $(*2_{0}2_{0}2{:}2)$ |
| 51 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pmma | P 2$_1$/m 2/m 2/a | $\Gamma _{o}D_{2h}^{5}$ | 14a | $\left(c:a:b\right)\cdot {\tilde {a}}:2\cdot m$ | $[2_{0}2_{0}{*}{\cdot }]$ | $[*{\cdot }2{:}2{\cdot }2{:}2]$, $[*2{\cdot }2{\cdot }2{\cdot }2]$ |
| 52 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pnna | P 2/n 2$_1$/n 2/a | $\Gamma _{o}D_{2h}^{6}$ | 17a | $\left(c:a:b\right)\cdot {\tilde {a}}:2\odot {\widetilde {ac}}$ | $(2_{0}2{\bar {*}}_{1})$ | $(2_{0}{*}2{:}2)$, $(2{\bar {*}}2_{1}2_{1})$ |
| 53 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pmna | P 2/m 2/n 2$_1$/a | $\Gamma _{o}D_{2h}^{7}$ | 15a | $\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\widetilde {ac}}$ | $[2_{0}2_{0}{*}{:}]$ | $(*2_{1}2_{1}2{\cdot }2)$, $(2_{0}{*}2{\cdot }2)$ |
| 54 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pcca | P 2$_1$/c 2/c 2/a | $\Gamma _{o}D_{2h}^{8}$ | 16a | $\left(c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}$ | $(2_{0}2{\bar {*}}_{0})$ | $(*2{:}2{:}2{:}2)$, $(*2_{1}2_{1}2{:}2)$ |
| 55 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pbam | P 2$_1$/b 2$_1$/a 2/m | $\Gamma _{o}D_{2h}^{9}$ | 22a | $\left(c:a:b\right)\cdot m:2\odot {\tilde {a}}$ | $[2_{0}2_{0}{\times }_{0}]$ | $(*2{\cdot }2{:}2{\cdot }2)$ |
| 56 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pccn | P 2$_1$/c 2$_1$/c 2/n | $\Gamma _{o}D_{2h}^{10}$ | 27a | $\left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot {\tilde {c}}$ | $(2{\bar {*}}{:}2{:}2)$ | $(2_{1}2{\bar {*}}_{0})$ |
| 57 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pbcm | P 2/b 2$_1$/c 2$_1$/m | $\Gamma _{o}D_{2h}^{11}$ | 23a | $\left(c:a:b\right)\cdot m:2_{1}\odot {\tilde {c}}$ | $(2_{0}2{\bar {*}}{\cdot })$ | $(*2{:}2{\cdot }2{:}2)$, $[2_{1}2_{1}{*}{:}]$ |
| 58 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pnnm | P 2$_1$/n 2$_1$/n 2/m | $\Gamma _{o}D_{2h}^{12}$ | 25a | $\left(c:a:b\right)\cdot m:2\odot {\widetilde {ac}}$ | $[2_{0}2_{0}{\times }_{1}]$ | $(2_{1}{*}2{\cdot }2)$ |
| 59 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pmmn | P 2$_1$/m 2$_1$/m 2/n | $\Gamma _{o}D_{2h}^{13}$ | 24a | $\left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot m$ | $(2{\bar {*}}{\cdot }2{\cdot }2)$ | $[2_{1}2_{1}{*}{\cdot }]$ |
| 60 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pbcn | P 2$_1$/b 2/c 2$_1$/n | $\Gamma _{o}D_{2h}^{14}$ | 26a | $\left(c:a:b\right)\cdot {\widetilde {ab}}:2_{1}\odot {\tilde {c}}$ | $(2_{0}2{\bar {*}}{:})$ | $(2_{1}{*}2{:}2)$, $(2_{1}2{\bar {*}}_{1})$ |
| 61 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pbca | P 2$_1$/b 2$_1$/c 2$_1$/a | $\Gamma _{o}D_{2h}^{15}$ | 29a | $\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot {\tilde {c}}$ | $(2_{1}2{\bar {*}}{:})$ | |
| 62 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Pnma | P 2$_1$/n 2$_1$/m 2$_1$/a | $\Gamma _{o}D_{2h}^{16}$ | 28a | $\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot m$ | $(2_{1}2{\bar {*}}{\cdot })$ | $(2{\bar {*}}{\cdot }2{:}2)$, $[2_{1}2_{1}{\times }]$ |
| 63 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Cmcm | C 2/m 2/c 2$_1$/m | $\Gamma _{o}^{b}D_{2h}^{17}$ | 18a | $\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2_{1}\cdot {\tilde {c}}$ | $[2_{0}2_{1}{*}{\cdot }]$ | $(*2{\cdot }2{\cdot }2{:}2)$, $[2_{1}{*}{\cdot }2{:}2]$ |
| 64 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Cmce | C 2/m 2/c 2$_1$/a | $\Gamma _{o}^{b}D_{2h}^{18}$ | 19a | $\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\tilde {c}}$ | $[2_{0}2_{1}{*}{:}]$ | $(*2{\cdot }2{:}2{:}2)$, $(*2_{1}2{\cdot }2{:}2)$ |
| 65 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Cmmm | C 2/m 2/m 2/m | $\Gamma _{o}^{b}D_{2h}^{19}$ | 19s | $\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m$ | $[2_{0}{*}{\cdot }2{\cdot }2]$ | $[*{\cdot }2{\cdot }2{\cdot }2{:}2]$ |
| 66 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Cccm | C 2/c 2/c 2/m | $\Gamma _{o}^{b}D_{2h}^{20}$ | 20h | $\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot {\tilde {c}}$ | $[2_{0}{*}{:}2{:}2]$ | $(*2_{0}2_{1}2{\cdot }2)$ |
| 67 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Cmme | C 2/m 2/m 2/e | $\Gamma _{o}^{b}D_{2h}^{21}$ | 21h | $\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot m$ | $(*2_{0}2{\cdot }2{\cdot }2)$ | $[*{\cdot }2{:}2{:}2{:}2]$ |
| 68 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Ccce | C 2/c 2/c 2/e | $\Gamma _{o}^{b}D_{2h}^{22}$ | 22h | $\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}$ | $(*2_{0}2{:}2{:}2)$ | $(*2_{0}2_{1}2{:}2)$ |
| 69 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Fmmm | F 2/m 2/m 2/m | $\Gamma _{o}^{f}D_{2h}^{23}$ | 21s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m$ | $[*{\cdot }2{\cdot }2{:}2{:}2]$ | |
| 70 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Fddd | F 2/d 2/d 2/d | $\Gamma _{o}^{f}D_{2h}^{24}$ | 24h | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tfrac {1}{2}}{\widetilde {ab}}:2\odot {\tfrac {1}{2}}{\widetilde {ac}}$ | $(2{\bar {*}}2_{0}2_{1})$ | |
| 71 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Immm | I 2/m 2/m 2/m | $\Gamma _{o}^{v}D_{2h}^{25}$ | 20s | $\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot m$ | $[2_{1}{*}{\cdot }2{\cdot }2]$ | |
| 72 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Ibam | I 2/b 2/a 2/m | $\Gamma _{o}^{v}D_{2h}^{26}$ | 23h | $\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot {\tilde {c}}$ | $[2_{1}{*}{:}2{:}2]$ | $(*2_{0}2{\cdot }2{:}2)$ |
| 73 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Ibca | I 2/b 2/c 2/a | $\Gamma _{o}^{v}D_{2h}^{27}$ | 21a | $\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}$ | $(*2_{1}2{:}2{:}2)$ | |
| 74 | ${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$ | $*222$ | Imma | I 2/m 2/m 2/a | $\Gamma _{o}^{v}D_{2h}^{28}$ | 20a | $\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot m$ | $(*2_{1}2{\cdot }2{\cdot }2)$ | $[2_{0}{*}{\cdot }2{:}2]$ |

## List of tetragonal

Tetragonal Bravais lattice :
| Simple (P) | Body (I) |
Tetragonal crystal system :
| Number | Point group | Orbifold | Short name | Full name | Schoenflies | Fedorov | Shubnikov | Fibrifold |
| 75 | 4 | $44$ | P4 | P 4 | $\Gamma _{q}C_{4}^{1}$ | 22s | $(c:a:a):4$ | $(4_{0}4_{0}2_{0})$ |
| 76 | 4 | $44$ | P4$_1$ | P 4$_1$ | $\Gamma _{q}C_{4}^{2}$ | 30a | $(c:a:a):4_{1}$ | $(4_{1}4_{1}2_{1})$ |
| 77 | 4 | $44$ | P4$_2$ | P 4$_2$ | $\Gamma _{q}C_{4}^{3}$ | 33a | $(c:a:a):4_{2}$ | $(4_{2}4_{2}2_{0})$ |
| 78 | 4 | $44$ | P4$_3$ | P 4$_3$ | $\Gamma _{q}C_{4}^{4}$ | 31a | $(c:a:a):4_{3}$ | $(4_{1}4_{1}2_{1})$ |
| 79 | 4 | $44$ | I4 | I 4 | $\Gamma _{q}^{v}C_{4}^{5}$ | 23s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4$ | $(4_{2}4_{0}2_{1})$ |
| 80 | 4 | $44$ | I4$_1$ | I 4$_1$ | $\Gamma _{q}^{v}C_{4}^{6}$ | 32a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}$ | $(4_{3}4_{1}2_{0})$ |
| 81 | 4 | $2\times$ | P4 | P 4 | $\Gamma _{q}S_{4}^{1}$ | 26s | $(c:a:a):{\tilde {4}}$ | $(442_{0})$ |
| 82 | 4 | $2\times$ | I4 | I 4 | $\Gamma _{q}^{v}S_{4}^{2}$ | 27s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}$ | $(442_{1})$ |
| 83 | 4/m | $4*$ | P4/m | P 4/m | $\Gamma _{q}C_{4h}^{1}$ | 28s | $(c:a:a)\cdot m:4$ | $[4_{0}4_{0}2_{0}]$ |
| 84 | 4/m | $4*$ | P4$_2$/m | P 4$_2$/m | $\Gamma _{q}C_{4h}^{2}$ | 41a | $(c:a:a)\cdot m:4_{2}$ | $[4_{2}4_{2}2_{0}]$ |
| 85 | 4/m | $4*$ | P4/n | P 4/n | $\Gamma _{q}C_{4h}^{3}$ | 29h | $(c:a:a)\cdot {\widetilde {ab}}:4$ | $(44_{0}2)$ |
| 86 | 4/m | $4*$ | P4$_2$/n | P 4$_2$/n | $\Gamma _{q}C_{4h}^{4}$ | 42a | $(c:a:a)\cdot {\widetilde {ab}}:4_{2}$ | $(44_{2}2)$ |
| 87 | 4/m | $4*$ | I4/m | I 4/m | $\Gamma _{q}^{v}C_{4h}^{5}$ | 29s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4$ | $[4_{2}4_{0}2_{1}]$ |
| 88 | 4/m | $4*$ | I4$_1$/a | I 4$_1$/a | $\Gamma _{q}^{v}C_{4h}^{6}$ | 40a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}$ | $(44_{1}2)$ |
| 89 | 422 | $224$ | P422 | P 4 2 2 | $\Gamma _{q}D_{4}^{1}$ | 30s | $(c:a:a):4:2$ | $(*4_{0}4_{0}2_{0})$ |
| 90 | 422 | $224$ | P42$_1$2 | P42$_1$2 | $\Gamma _{q}D_{4}^{2}$ | 43a | $(c:a:a):4$ $2_{1}$ | $(4_{0}{*}2_{0})$ |
| 91 | 422 | $224$ | P4$_1$22 | P 4$_1$ 2 2 | $\Gamma _{q}D_{4}^{3}$ | 44a | $(c:a:a):4_{1}:2$ | $(*4_{1}4_{1}2_{1})$ |
| 92 | 422 | $224$ | P4$_1$2$_1$2 | P 4$_1$ 2$_1$ 2 | $\Gamma _{q}D_{4}^{4}$ | 48a | $(c:a:a):4_{1}$ $2_{1}$ | $(4_{1}{*}2_{1})$ |
| 93 | 422 | $224$ | P4$_2$22 | P 4$_2$ 2 2 | $\Gamma _{q}D_{4}^{5}$ | 47a | $(c:a:a):4_{2}:2$ | $(*4_{2}4_{2}2_{0})$ |
| 94 | 422 | $224$ | P4$_2$2$_1$2 | P 4$_2$ 2$_1$ 2 | $\Gamma _{q}D_{4}^{6}$ | 50a | $(c:a:a):4_{2}$ $2_{1}$ | $(4_{2}{*}2_{0})$ |
| 95 | 422 | $224$ | P4$_3$22 | P 4$_3$ 2 2 | $\Gamma _{q}D_{4}^{7}$ | 45a | $(c:a:a):4_{3}:2$ | $(*4_{1}4_{1}2_{1})$ |
| 96 | 422 | $224$ | P4$_3$2$_1$2 | P 4$_3$ 2$_1$ 2 | $\Gamma _{q}D_{4}^{8}$ | 49a | $(c:a:a):4_{3}$ $2_{1}$ | $(4_{1}{*}2_{1})$ |
| 97 | 422 | $224$ | I422 | I 4 2 2 | $\Gamma _{q}^{v}D_{4}^{9}$ | 31s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2$ | $(*4_{2}4_{0}2_{1})$ |
| 98 | 422 | $224$ | I4$_1$22 | I 4$_1$ 2 2 | $\Gamma _{q}^{v}D_{4}^{10}$ | 46a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2_{1}$ | $(*4_{3}4_{1}2_{0})$ |
| 99 | 4mm | $*44$ | P4mm | P 4 m m | $\Gamma _{q}C_{4v}^{1}$ | 24s | $(c:a:a):4\cdot m$ | $(*{\cdot }4{\cdot }4{\cdot }2)$ |
| 100 | 4mm | $*44$ | P4bm | P 4 b m | $\Gamma _{q}C_{4v}^{2}$ | 26h | $(c:a:a):4\odot {\tilde {a}}$ | $(4_{0}{*}{\cdot }2)$ |
| 101 | 4mm | $*44$ | P4$_2$cm | P 4$_2$ c m | $\Gamma _{q}C_{4v}^{3}$ | 37a | $(c:a:a):4_{2}\cdot {\tilde {c}}$ | $(*{:}4{\cdot }4{:}2)$ |
| 102 | 4mm | $*44$ | P4$_2$nm | P 4$_2$ n m | $\Gamma _{q}C_{4v}^{4}$ | 38a | $(c:a:a):4_{2}\odot {\widetilde {ac}}$ | $(4_{2}{*}{\cdot }2)$ |
| 103 | 4mm | $*44$ | P4cc | P 4 c c | $\Gamma _{q}C_{4v}^{5}$ | 25h | $(c:a:a):4\cdot {\tilde {c}}$ | $(*{:}4{:}4{:}2)$ |
| 104 | 4mm | $*44$ | P4nc | P 4 n c | $\Gamma _{q}C_{4v}^{6}$ | 27h | $(c:a:a):4\odot {\widetilde {ac}}$ | $(4_{0}{*}{:}2)$ |
| 105 | 4mm | $*44$ | P4$_2$mc | P 4$_2$ m c | $\Gamma _{q}C_{4v}^{7}$ | 36a | $(c:a:a):4_{2}\cdot m$ | $(*{\cdot }4{:}4{\cdot }2)$ |
| 106 | 4mm | $*44$ | P4$_2$bc | P 4$_2$ b c | $\Gamma _{q}C_{4v}^{8}$ | 39a | $(c:a:a):4\odot {\tilde {a}}$ | $(4_{2}{*}{:}2)$ |
| 107 | 4mm | $*44$ | I4mm | I 4 m m | $\Gamma _{q}^{v}C_{4v}^{9}$ | 25s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot m$ | $(*{\cdot }4{\cdot }4{:}2)$ |
| 108 | 4mm | $*44$ | I4cm | I 4 c m | $\Gamma _{q}^{v}C_{4v}^{10}$ | 28h | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot {\tilde {c}}$ | $(*{\cdot }4{:}4{:}2)$ |
| 109 | 4mm | $*44$ | I4$_1$md | I 4$_1$ m d | $\Gamma _{q}^{v}C_{4v}^{11}$ | 34a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot m$ | $(4_{1}{*}{\cdot }2)$ |
| 110 | 4mm | $*44$ | I4$_1$cd | I 4$_1$ c d | $\Gamma _{q}^{v}C_{4v}^{12}$ | 35a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot {\tilde {c}}$ | $(4_{1}{*}{:}2)$ |
| 111 | 42m | $2{*}2$ | P42m | P 4 2 m | $\Gamma _{q}D_{2d}^{1}$ | 32s | $(c:a:a):{\tilde {4}}:2$ | $(*4{\cdot }42_{0})$ |
| 112 | 42m | $2{*}2$ | P42c | P 4 2 c | $\Gamma _{q}D_{2d}^{2}$ | 30h | $(c:a:a):{\tilde {4}}$ $2$ | $(*4{:}42_{0})$ |
| 113 | 42m | $2{*}2$ | P42$_1$m | P 4 2$_1$ m | $\Gamma _{q}D_{2d}^{3}$ | 52a | $(c:a:a):{\tilde {4}}\cdot {\widetilde {ab}}$ | $(4{\bar {*}}{\cdot }2)$ |
| 114 | 42m | $2{*}2$ | P42$_1$c | P 4 2$_1$ c | $\Gamma _{q}D_{2d}^{4}$ | 53a | $(c:a:a):{\tilde {4}}\cdot {\widetilde {abc}}$ | $(4{\bar {*}}{:}2)$ |
| 115 | 42m | $2{*}2$ | P4m2 | P 4 m 2 | $\Gamma _{q}D_{2d}^{5}$ | 33s | $(c:a:a):{\tilde {4}}\cdot m$ | $(*{\cdot }44{\cdot }2)$ |
| 116 | 42m | $2{*}2$ | P4c2 | P 4 c 2 | $\Gamma _{q}D_{2d}^{6}$ | 31h | $(c:a:a):{\tilde {4}}\cdot {\tilde {c}}$ | $(*{:}44{:}2)$ |
| 117 | 42m | $2{*}2$ | P4b2 | P 4 b 2 | $\Gamma _{q}D_{2d}^{7}$ | 32h | $(c:a:a):{\tilde {4}}\odot {\tilde {a}}$ | $(4{\bar {*}}_{0}2_{0})$ |
| 118 | 42m | $2{*}2$ | P4n2 | P 4 n 2 | $\Gamma _{q}D_{2d}^{8}$ | 33h | $(c:a:a):{\tilde {4}}\cdot {\widetilde {ac}}$ | $(4{\bar {*}}_{1}2_{0})$ |
| 119 | 42m | $2{*}2$ | I4m2 | I 4 m 2 | $\Gamma _{q}^{v}D_{2d}^{9}$ | 35s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot m$ | $(*4{\cdot }42_{1})$ |
| 120 | 42m | $2{*}2$ | I4c2 | I 4 c 2 | $\Gamma _{q}^{v}D_{2d}^{10}$ | 34h | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot {\tilde {c}}$ | $(*4{:}42_{1})$ |
| 121 | 42m | $2{*}2$ | I42m | I 4 2 m | $\Gamma _{q}^{v}D_{2d}^{11}$ | 34s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}:2$ | $(*{\cdot }44{:}2)$ |
| 122 | 42m | $2{*}2$ | I42d | I 4 2 d | $\Gamma _{q}^{v}D_{2d}^{12}$ | 51a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\odot {\tfrac {1}{2}}{\widetilde {abc}}$ | $(4{\bar {*}}2_{1})$ |
| 123 | 4/m 2/m 2/m | $*224$ | P4/mmm | P 4/m 2/m 2/m | $\Gamma _{q}D_{4h}^{1}$ | 36s | $(c:a:a)\cdot m:4\cdot m$ | $[*{\cdot }4{\cdot }4{\cdot }2]$ |
| 124 | 4/m 2/m 2/m | $*224$ | P4/mcc | P 4/m 2/c 2/c | $\Gamma _{q}D_{4h}^{2}$ | 35h | $(c:a:a)\cdot m:4\cdot {\tilde {c}}$ | $[*{:}4{:}4{:}2]$ |
| 125 | 4/m 2/m 2/m | $*224$ | P4/nbm | P 4/n 2/b 2/m | $\Gamma _{q}D_{4h}^{3}$ | 36h | $(c:a:a)\cdot {\widetilde {ab}}:4\odot {\tilde {a}}$ | $(*4_{0}4{\cdot }2)$ |
| 126 | 4/m 2/m 2/m | $*224$ | P4/nnc | P 4/n 2/n 2/c | $\Gamma _{q}D_{4h}^{4}$ | 37h | $(c:a:a)\cdot {\widetilde {ab}}:4\odot {\widetilde {ac}}$ | $(*4_{0}4{:}2)$ |
| 127 | 4/m 2/m 2/m | $*224$ | P4/mbm | P 4/m 2$_1$/b 2/m | $\Gamma _{q}D_{4h}^{5}$ | 54a | $(c:a:a)\cdot m:4\odot {\tilde {a}}$ | $[4_{0}{*}{\cdot }2]$ |
| 128 | 4/m 2/m 2/m | $*224$ | P4/mnc | P 4/m 2$_1$/n 2/c | $\Gamma _{q}D_{4h}^{6}$ | 56a | $(c:a:a)\cdot m:4\odot {\widetilde {ac}}$ | $[4_{0}{*}{:}2]$ |
| 129 | 4/m 2/m 2/m | $*224$ | P4/nmm | P 4/n 2$_1$/m 2/m | $\Gamma _{q}D_{4h}^{7}$ | 55a | $(c:a:a)\cdot {\widetilde {ab}}:4\cdot m$ | $(*4{\cdot }4{\cdot }2)$ |
| 130 | 4/m 2/m 2/m | $*224$ | P4/ncc | P 4/n 2$_1$/c 2/c | $\Gamma _{q}D_{4h}^{8}$ | 57a | $(c:a:a)\cdot {\widetilde {ab}}:4\cdot {\tilde {c}}$ | $(*4{:}4{:}2)$ |
| 131 | 4/m 2/m 2/m | $*224$ | P4$_2$/mmc | P 4$_2$/m 2/m 2/c | $\Gamma _{q}D_{4h}^{9}$ | 60a | $(c:a:a)\cdot m:4_{2}\cdot m$ | $[*{\cdot }4{:}4{\cdot }2]$ |
| 132 | 4/m 2/m 2/m | $*224$ | P4$_2$/mcm | P 4$_2$/m 2/c 2/m | $\Gamma _{q}D_{4h}^{10}$ | 61a | $(c:a:a)\cdot m:4_{2}\cdot {\tilde {c}}$ | $[*{:}4{\cdot }4{:}2]$ |
| 133 | 4/m 2/m 2/m | $*224$ | P4$_2$/nbc | P 4$_2$/n 2/b 2/c | $\Gamma _{q}D_{4h}^{11}$ | 63a | $(c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\tilde {a}}$ | $(*4_{2}4{:}2)$ |
| 134 | 4/m 2/m 2/m | $*224$ | P4$_2$/nnm | P 4$_2$/n 2/n 2/m | $\Gamma _{q}D_{4h}^{12}$ | 62a | $(c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\widetilde {ac}}$ | $(*4_{2}4{\cdot }2)$ |
| 135 | 4/m 2/m 2/m | $*224$ | P4$_2$/mbc | P 4$_2$/m 2$_1$/b 2/c | $\Gamma _{q}D_{4h}^{13}$ | 66a | $(c:a:a)\cdot m:4_{2}\odot {\tilde {a}}$ | $[4_{2}{*}{:}2]$ |
| 136 | 4/m 2/m 2/m | $*224$ | P4$_2$/mnm | P 4$_2$/m 2$_1$/n 2/m | $\Gamma _{q}D_{4h}^{14}$ | 65a | $(c:a:a)\cdot m:4_{2}\odot {\widetilde {ac}}$ | $[4_{2}{*}{\cdot }2]$ |
| 137 | 4/m 2/m 2/m | $*224$ | P4$_2$/nmc | P 4$_2$/n 2$_1$/m 2/c | $\Gamma _{q}D_{4h}^{15}$ | 67a | $(c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot m$ | $(*4{\cdot }4{:}2)$ |
| 138 | 4/m 2/m 2/m | $*224$ | P4$_2$/ncm | P 4$_2$/n 2$_1$/c 2/m | $\Gamma _{q}D_{4h}^{16}$ | 65a | $(c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot {\tilde {c}}$ | $(*4{:}4{\cdot }2)$ |
| 139 | 4/m 2/m 2/m | $*224$ | I4/mmm | I 4/m 2/m 2/m | $\Gamma _{q}^{v}D_{4h}^{17}$ | 37s | $\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot m$ | $[*{\cdot }4{\cdot }4{:}2]$ |
| 140 | 4/m 2/m 2/m | $*224$ | I4/mcm | I 4/m 2/c 2/m | $\Gamma _{q}^{v}D_{4h}^{18}$ | 38h | $\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot {\tilde {c}}$ | $[*{\cdot }4{:}4{:}2]$ |
| 141 | 4/m 2/m 2/m | $*224$ | I4$_1$/amd | I 4$_1$/a 2/m 2/d | $\Gamma _{q}^{v}D_{4h}^{19}$ | 59a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot m$ | $(*4_{1}4{\cdot }2)$ |
| 142 | 4/m 2/m 2/m | $*224$ | I4$_1$/acd | I 4$_1$/a 2/c 2/d | $\Gamma _{q}^{v}D_{4h}^{20}$ | 58a | $\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot {\tilde {c}}$ | $(*4_{1}4{:}2)$ |

## List of trigonal

Trigonal Bravais lattice :
| Rhombohedral (R) | Hexagonal (P) |
Trigonal crystal system :
| Number | Point group | Orbifold | Short name | Full name | Schoenflies | Fedorov | Shubnikov | Fibrifold |
| 143 | 3 | $33$ | P3 | P 3 | $\Gamma _{h}C_{3}^{1}$ | 38s | $(c:(a/a)):3$ | $(3_{0}3_{0}3_{0})$ |
| 144 | 3 | $33$ | P3$_1$ | P 3$_1$ | $\Gamma _{h}C_{3}^{2}$ | 68a | $(c:(a/a)):3_{1}$ | $(3_{1}3_{1}3_{1})$ |
| 145 | 3 | $33$ | P3$_2$ | P 3$_2$ | $\Gamma _{h}C_{3}^{3}$ | 69a | $(c:(a/a)):3_{2}$ | $(3_{1}3_{1}3_{1})$ |
| 146 | 3 | $33$ | R3 | R 3 | $\Gamma _{rh}C_{3}^{4}$ | 39s | $(a/a/a)/3$ | $(3_{0}3_{1}3_{2})$ |
| 147 | 3 | $3\times$ | P3 | P 3 | $\Gamma _{h}C_{3i}^{1}$ | 51s | $(c:(a/a)):{\tilde {6}}$ | $(63_{0}2)$ |
| 148 | 3 | $3\times$ | R3 | R 3 | $\Gamma _{rh}C_{3i}^{2}$ | 52s | $(a/a/a)/{\tilde {6}}$ | $(63_{1}2)$ |
| 149 | 32 | $223$ | P312 | P 3 1 2 | $\Gamma _{h}D_{3}^{1}$ | 45s | $(c:(a/a)):2:3$ | $(*3_{0}3_{0}3_{0})$ |
| 150 | 32 | $223$ | P321 | P 3 2 1 | $\Gamma _{h}D_{3}^{2}$ | 44s | $(c:(a/a))\cdot 2:3$ | $(3_{0}{*}3_{0})$ |
| 151 | 32 | $223$ | P3$_1$12 | P 3$_1$ 1 2 | $\Gamma _{h}D_{3}^{3}$ | 72a | $(c:(a/a)):2:3_{1}$ | $(*3_{1}3_{1}3_{1})$ |
| 152 | 32 | $223$ | P3$_1$21 | P 3$_1$ 2 1 | $\Gamma _{h}D_{3}^{4}$ | 70a | $(c:(a/a))\cdot 2:3_{1}$ | $(3_{1}{*}3_{1})$ |
| 153 | 32 | $223$ | P3$_2$12 | P 3$_2$ 1 2 | $\Gamma _{h}D_{3}^{5}$ | 73a | $(c:(a/a)):2:3_{2}$ | $(*3_{1}3_{1}3_{1})$ |
| 154 | 32 | $223$ | P3$_2$21 | P 3$_2$ 2 1 | $\Gamma _{h}D_{3}^{6}$ | 71a | $(c:(a/a))\cdot 2:3_{2}$ | $(3_{1}{*}3_{1})$ |
| 155 | 32 | $223$ | R32 | R 3 2 | $\Gamma _{rh}D_{3}^{7}$ | 46s | $(a/a/a)/3:2$ | $(*3_{0}3_{1}3_{2})$ |
| 156 | 3m | $*33$ | P3m1 | P 3 m 1 | $\Gamma _{h}C_{3v}^{1}$ | 40s | $(c:(a/a)):m\cdot 3$ | $(*{\cdot }3{\cdot }3{\cdot }3)$ |
| 157 | 3m | $*33$ | P31m | P 3 1 m | $\Gamma _{h}C_{3v}^{2}$ | 41s | $(c:(a/a))\cdot m\cdot 3$ | $(3_{0}{*}{\cdot }3)$ |
| 158 | 3m | $*33$ | P3c1 | P 3 c 1 | $\Gamma _{h}C_{3v}^{3}$ | 39h | $(c:(a/a)):{\tilde {c}}:3$ | $(*{:}3{:}3{:}3)$ |
| 159 | 3m | $*33$ | P31c | P 3 1 c | $\Gamma _{h}C_{3v}^{4}$ | 40h | $(c:(a/a))\cdot {\tilde {c}}:3$ | $(3_{0}{*}{:}3)$ |
| 160 | 3m | $*33$ | R3m | R 3 m | $\Gamma _{rh}C_{3v}^{5}$ | 42s | $(a/a/a)/3\cdot m$ | $(3_{1}{*}{\cdot }3)$ |
| 161 | 3m | $*33$ | R3c | R 3 c | $\Gamma _{rh}C_{3v}^{6}$ | 41h | $(a/a/a)/3\cdot {\tilde {c}}$ | $(3_{1}{*}{:}3)$ |
| 162 | 3 2/m | $2{*}3$ | P31m | P 3 1 2/m | $\Gamma _{h}D_{3d}^{1}$ | 56s | $(c:(a/a))\cdot m\cdot {\tilde {6}}$ | $(*{\cdot }63_{0}2)$ |
| 163 | 3 2/m | $2{*}3$ | P31c | P 3 1 2/c | $\Gamma _{h}D_{3d}^{2}$ | 46h | $(c:(a/a))\cdot {\tilde {c}}\cdot {\tilde {6}}$ | $(*{:}63_{0}2)$ |
| 164 | 3 2/m | $2{*}3$ | P3m1 | P 3 2/m 1 | $\Gamma _{h}D_{3d}^{3}$ | 55s | $(c:(a/a)):m\cdot {\tilde {6}}$ | $(*6{\cdot }3{\cdot }2)$ |
| 165 | 3 2/m | $2{*}3$ | P3c1 | P 3 2/c 1 | $\Gamma _{h}D_{3d}^{4}$ | 45h | $(c:(a/a)):{\tilde {c}}\cdot {\tilde {6}}$ | $(*6{:}3{:}2)$ |
| 166 | 3 2/m | $2{*}3$ | R3m | R 3 2/m | $\Gamma _{rh}D_{3d}^{5}$ | 57s | $(a/a/a)/{\tilde {6}}\cdot m$ | $(*{\cdot }63_{1}2)$ |
| 167 | 3 2/m | $2{*}3$ | R3c | R 3 2/c | $\Gamma _{rh}D_{3d}^{6}$ | 47h | $(a/a/a)/{\tilde {6}}\cdot {\tilde {c}}$ | $(*{:}63_{1}2)$ |

## List of hexagonal

Hexagonal crystal system :
| Number | Point group | Orbifold | Short name | Full name | Schoenflies | Fedorov | Shubnikov | Fibrifold |
| 168 | 6 | $66$ | P6 | P 6 | $\Gamma _{h}C_{6}^{1}$ | 49s | $(c:(a/a)):6$ | $(6_{0}3_{0}2_{0})$ |
| 169 | 6 | $66$ | P6$_1$ | P 6$_1$ | $\Gamma _{h}C_{6}^{2}$ | 74a | $(c:(a/a)):6_{1}$ | $(6_{1}3_{1}2_{1})$ |
| 170 | 6 | $66$ | P6$_5$ | P 6$_5$ | $\Gamma _{h}C_{6}^{3}$ | 75a | $(c:(a/a)):6_{5}$ | $(6_{1}3_{1}2_{1})$ |
| 171 | 6 | $66$ | P6$_2$ | P 6$_2$ | $\Gamma _{h}C_{6}^{4}$ | 76a | $(c:(a/a)):6_{2}$ | $(6_{2}3_{2}2_{0})$ |
| 172 | 6 | $66$ | P6$_4$ | P 6$_4$ | $\Gamma _{h}C_{6}^{5}$ | 77a | $(c:(a/a)):6_{4}$ | $(6_{2}3_{2}2_{0})$ |
| 173 | 6 | $66$ | P6$_3$ | P 6$_3$ | $\Gamma _{h}C_{6}^{6}$ | 78a | $(c:(a/a)):6_{3}$ | $(6_{3}3_{0}2_{1})$ |
| 174 | 6 | $3*$ | P6 | P 6 | $\Gamma _{h}C_{3h}^{1}$ | 43s | $(c:(a/a)):3:m$ | $[3_{0}3_{0}3_{0}]$ |
| 175 | 6/m | $6*$ | P6/m | P 6/m | $\Gamma _{h}C_{6h}^{1}$ | 53s | $(c:(a/a))\cdot m:6$ | $[6_{0}3_{0}2_{0}]$ |
| 176 | 6/m | $6*$ | P6$_3$/m | P 6$_3$/m | $\Gamma _{h}C_{6h}^{2}$ | 81a | $(c:(a/a))\cdot m:6_{3}$ | $[6_{3}3_{0}2_{1}]$ |
| 177 | 622 | $226$ | P622 | P 6 2 2 | $\Gamma _{h}D_{6}^{1}$ | 54s | $(c:(a/a))\cdot 2:6$ | $(*6_{0}3_{0}2_{0})$ |
| 178 | 622 | $226$ | P6$_1$22 | P 6$_1$ 2 2 | $\Gamma _{h}D_{6}^{2}$ | 82a | $(c:(a/a))\cdot 2:6_{1}$ | $(*6_{1}3_{1}2_{1})$ |
| 179 | 622 | $226$ | P6$_5$22 | P 6$_5$ 2 2 | $\Gamma _{h}D_{6}^{3}$ | 83a | $(c:(a/a))\cdot 2:6_{5}$ | $(*6_{1}3_{1}2_{1})$ |
| 180 | 622 | $226$ | P6$_2$22 | P 6$_2$ 2 2 | $\Gamma _{h}D_{6}^{4}$ | 84a | $(c:(a/a))\cdot 2:6_{2}$ | $(*6_{2}3_{2}2_{0})$ |
| 181 | 622 | $226$ | P6$_4$22 | P 6$_4$ 2 2 | $\Gamma _{h}D_{6}^{5}$ | 85a | $(c:(a/a))\cdot 2:6_{4}$ | $(*6_{2}3_{2}2_{0})$ |
| 182 | 622 | $226$ | P6$_3$22 | P 6$_3$ 2 2 | $\Gamma _{h}D_{6}^{6}$ | 86a | $(c:(a/a))\cdot 2:6_{3}$ | $(*6_{3}3_{0}2_{1})$ |
| 183 | 6mm | $*66$ | P6mm | P 6 m m | $\Gamma _{h}C_{6v}^{1}$ | 50s | $(c:(a/a)):m\cdot 6$ | $(*{\cdot }6{\cdot }3{\cdot }2)$ |
| 184 | 6mm | $*66$ | P6cc | P 6 c c | $\Gamma _{h}C_{6v}^{2}$ | 44h | $(c:(a/a)):{\tilde {c}}\cdot 6$ | $(*{:}6{:}3{:}2)$ |
| 185 | 6mm | $*66$ | P6$_3$cm | P 6$_3$ c m | $\Gamma _{h}C_{6v}^{3}$ | 80a | $(c:(a/a)):{\tilde {c}}\cdot 6_{3}$ | $(*{\cdot }6{:}3{:}2)$ |
| 186 | 6mm | $*66$ | P6$_3$mc | P 6$_3$ m c | $\Gamma _{h}C_{6v}^{4}$ | 79a | $(c:(a/a)):m\cdot 6_{3}$ | $(*{:}6{\cdot }3{\cdot }2)$ |
| 187 | 6m2 | $*223$ | P6m2 | P 6 m 2 | $\Gamma _{h}D_{3h}^{1}$ | 48s | $(c:(a/a)):m\cdot 3:m$ | $[*{\cdot }3{\cdot }3{\cdot }3]$ |
| 188 | 6m2 | $*223$ | P6c2 | P 6 c 2 | $\Gamma _{h}D_{3h}^{2}$ | 43h | $(c:(a/a)):{\tilde {c}}\cdot 3:m$ | $[*{:}3{:}3{:}3]$ |
| 189 | 6m2 | $*223$ | P62m | P 6 2 m | $\Gamma _{h}D_{3h}^{3}$ | 47s | $(c:(a/a))\cdot m:3\cdot m$ | $[3_{0}{*}{\cdot }3]$ |
| 190 | 6m2 | $*223$ | P62c | P 6 2 c | $\Gamma _{h}D_{3h}^{4}$ | 42h | $(c:(a/a))\cdot m:3\cdot {\tilde {c}}$ | $[3_{0}{*}{:}3]$ |
| 191 | 6/m 2/m 2/m | $*226$ | P6/mmm | P 6/m 2/m 2/m | $\Gamma _{h}D_{6h}^{1}$ | 58s | $(c:(a/a))\cdot m:6\cdot m$ | $[*{\cdot }6{\cdot }3{\cdot }2]$ |
| 192 | 6/m 2/m 2/m | $*226$ | P6/mcc | P 6/m 2/c 2/c | $\Gamma _{h}D_{6h}^{2}$ | 48h | $(c:(a/a))\cdot m:6\cdot {\tilde {c}}$ | $[*{:}6{:}3{:}2]$ |
| 193 | 6/m 2/m 2/m | $*226$ | P6$_3$/mcm | P 6$_3$/m 2/c 2/m | $\Gamma _{h}D_{6h}^{3}$ | 87a | $(c:(a/a))\cdot m:6_{3}\cdot {\tilde {c}}$ | $[*{\cdot }6{:}3{:}2]$ |
| 194 | 6/m 2/m 2/m | $*226$ | P6$_3$/mmc | P 6$_3$/m 2/m 2/c | $\Gamma _{h}D_{6h}^{4}$ | 88a | $(c:(a/a))\cdot m:6_{3}\cdot m$ | $[*{:}6{\cdot }3{\cdot }2]$ |

## List of cubic

Cubic Bravais lattice :
| Simple (P) | Body centered (I) | Face centered (F) |
* (221) Caesium chloride. Different colors for the two atom types.
* (216) Sphalerite
* (223) Weaire–Phelan structure
Cubic crystal system :
| Number | Point group | Orbifold | Short name | Full name | Schoenflies | Fedorov | Shubnikov | Conway | Fibrifold (preserving $z$) | Fibrifold (preserving $x$, $y$, $z$) |
| 195 | 23 | $332$ | P23 | P 2 3 | $\Gamma _{c}T^{1}$ | 59s | $\left(a:a:a\right):2/3$ | $2^{\circ }$ | $(*2_{0}2_{0}2_{0}2_{0}){:}3$ | $(*2_{0}2_{0}2_{0}2_{0}){:}3$ |
| 196 | 23 | $332$ | F23 | F 2 3 | $\Gamma _{c}^{f}T^{2}$ | 61s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):2/3$ | $1^{\circ }$ | $(*2_{0}2_{1}2_{0}2_{1}){:}3$ | $(*2_{0}2_{1}2_{0}2_{1}){:}3$ |
| 197 | 23 | $332$ | I23 | I 2 3 | $\Gamma _{c}^{v}T^{3}$ | 60s | $\left({\tfrac {a+b+c}{2}}/a:a:a\right):2/3$ | $4^{\circ \circ }$ | $(2_{1}{*}2_{0}2_{0}){:}3$ | $(2_{1}{*}2_{0}2_{0}){:}3$ |
| 198 | 23 | $332$ | P2$_1$3 | P 2$_1$ 3 | $\Gamma _{c}T^{4}$ | 89a | $\left(a:a:a\right):2_{1}/3$ | $1^{\circ }/4$ | $(2_{1}2_{1}{\bar {\times }}){:}3$ | $(2_{1}2_{1}{\bar {\times }}){:}3$ |
| 199 | 23 | $332$ | I2$_1$3 | I 2$_1$ 3 | $\Gamma _{c}^{v}T^{5}$ | 90a | $\left({\tfrac {a+b+c}{2}}/a:a:a\right):2_{1}/3$ | $2^{\circ }/4$ | $(2_{0}{*}2_{1}2_{1}){:}3$ | $(2_{0}{*}2_{1}2_{1}){:}3$ |
| 200 | 2/m 3 | $3{*}2$ | Pm3 | P 2/m 3 | $\Gamma _{c}T_{h}^{1}$ | 62s | $\left(a:a:a\right)\cdot m/{\tilde {6}}$ | $4^{-}$ | $[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3$ | $[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3$ |
| 201 | 2/m 3 | $3{*}2$ | Pn3 | P 2/n 3 | $\Gamma _{c}T_{h}^{2}$ | 49h | $\left(a:a:a\right)\cdot {\widetilde {ab}}/{\tilde {6}}$ | $4^{\circ +}$ | $(2{\bar {*}}_{1}2_{0}2_{0}){:}3$ | $(2{\bar {*}}_{1}2_{0}2_{0}){:}3$ |
| 202 | 2/m 3 | $3{*}2$ | Fm3 | F 2/m 3 | $\Gamma _{c}^{f}T_{h}^{3}$ | 64s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right)\cdot m/{\tilde {6}}$ | $2^{-}$ | $[*{\cdot }2{\cdot }2{:}2{:}2]{:}3$ | $[*{\cdot }2{\cdot }2{:}2{:}2]{:}3$ |
| 203 | 2/m 3 | $3{*}2$ | Fd3 | F 2/d 3 | $\Gamma _{c}^{f}T_{h}^{4}$ | 50h | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right)\cdot {\tfrac {1}{2}}{\widetilde {ab}}/{\tilde {6}}$ | $2^{\circ +}$ | $(2{\bar {*}}2_{0}2_{1}){:}3$ | $(2{\bar {*}}2_{0}2_{1}){:}3$ |
| 204 | 2/m 3 | $3{*}2$ | Im3 | I 2/m 3 | $\Gamma _{c}^{v}T_{h}^{5}$ | 63s | $\left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot m/{\tilde {6}}$ | $8^{-\circ }$ | $[2_{1}{*}{\cdot }2{\cdot }2]{:}3$ | $[2_{1}{*}{\cdot }2{\cdot }2]{:}3$ |
| 205 | 2/m 3 | $3{*}2$ | Pa3 | P 2$_1$/a 3 | $\Gamma _{c}T_{h}^{6}$ | 91a | $\left(a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}$ | $2^{-}/4$ | $(2_{1}2{\bar {*}}{:}){:}3$ | $(2_{1}2{\bar {*}}{:}){:}3$ |
| 206 | 2/m 3 | $3{*}2$ | Ia3 | I 2$_1$/a 3 | $\Gamma _{c}^{v}T_{h}^{7}$ | 92a | $\left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}$ | $4^{-}/4$ | $(*2_{1}2{:}2{:}2){:}3$ | $(*2_{1}2{:}2{:}2){:}3$ |
| 207 | 432 | $432$ | P432 | P 4 3 2 | $\Gamma _{c}O^{1}$ | 68s | $\left(a:a:a\right):4/3$ | $4^{\circ -}$ | $(*4_{0}4_{0}2_{0}){:}3$ | $(*2_{0}2_{0}2_{0}2_{0}){:}6$ |
| 208 | 432 | $432$ | P4$_2$32 | P 4$_2$ 3 2 | $\Gamma _{c}O^{2}$ | 98a | $\left(a:a:a\right):4_{2}//3$ | $4^{+}$ | $(*4_{2}4_{2}2_{0}){:}3$ | $(*2_{0}2_{0}2_{0}2_{0}){:}6$ |
| 209 | 432 | $432$ | F432 | F 4 3 2 | $\Gamma _{c}^{f}O^{3}$ | 70s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/3$ | $2^{\circ -}$ | $(*4_{2}4_{0}2_{1}){:}3$ | $(*2_{0}2_{1}2_{0}2_{1}){:}6$ |
| 210 | 432 | $432$ | F4$_1$32 | F 4$_1$ 3 2 | $\Gamma _{c}^{f}O^{4}$ | 97a | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//3$ | $2^{+}$ | $(*4_{3}4_{1}2_{0}){:}3$ | $(*2_{0}2_{1}2_{0}2_{1}){:}6$ |
| 211 | 432 | $432$ | I432 | I 4 3 2 | $\Gamma _{c}^{v}O^{5}$ | 69s | $\left({\tfrac {a+b+c}{2}}/a:a:a\right):4/3$ | $8^{+\circ }$ | $(4_{2}4_{0}2_{1}){:}3$ | $(2_{1}{*}2_{0}2_{0}){:}6$ |
| 212 | 432 | $432$ | P4$_3$32 | P 4$_3$ 3 2 | $\Gamma _{c}O^{6}$ | 94a | $\left(a:a:a\right):4_{3}//3$ | $2^{+}/4$ | $(4_{1}{*}2_{1}){:}3$ | $(2_{1}2_{1}{\bar {\times }}){:}6$ |
| 213 | 432 | $432$ | P4$_1$32 | P 4$_1$ 3 2 | $\Gamma _{c}O^{7}$ | 95a | $\left(a:a:a\right):4_{1}//3$ | $2^{+}/4$ | $(4_{1}{*}2_{1}){:}3$ | $(2_{1}2_{1}{\bar {\times }}){:}6$ |
| 214 | 432 | $432$ | I4$_1$32 | I 4$_1$ 3 2 | $\Gamma _{c}^{v}O^{8}$ | 96a | $\left({\tfrac {a+b+c}{2}}/:a:a:a\right):4_{1}//3$ | $4^{+}/4$ | $(*4_{3}4_{1}2_{0}){:}3$ | $(2_{0}{*}2_{1}2_{1}){:}6$ |
| 215 | 43m | $*332$ | P43m | P 4 3 m | $\Gamma _{c}T_{d}^{1}$ | 65s | $\left(a:a:a\right):{\tilde {4}}/3$ | $2^{\circ }{:}2$ | $(*4{\cdot }42_{0}){:}3$ | $(*2_{0}2_{0}2_{0}2_{0}){:}6$ |
| 216 | 43m | $*332$ | F43m | F 4 3 m | $\Gamma _{c}^{f}T_{d}^{2}$ | 67s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}/3$ | $1^{\circ }{:}2$ | $(*4{\cdot }42_{1}){:}3$ | $(*2_{0}2_{1}2_{0}2_{1}){:}6$ |
| 217 | 43m | $*332$ | I43m | I 4 3 m | $\Gamma _{c}^{v}T_{d}^{3}$ | 66s | $\left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}/3$ | $4^{\circ }{:}2$ | $(*{\cdot }44{:}2){:}3$ | $(2_{1}{*}2_{0}2_{0}){:}6$ |
| 218 | 43m | $*332$ | P43n | P 4 3 n | $\Gamma _{c}T_{d}^{4}$ | 51h | $\left(a:a:a\right):{\tilde {4}}//3$ | $4^{\circ }$ | $(*4{:}42_{0}){:}3$ | $(*2_{0}2_{0}2_{0}2_{0}){:}6$ |
| 219 | 43m | $*332$ | F43c | F 4 3 c | $\Gamma _{c}^{f}T_{d}^{5}$ | 52h | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}//3$ | $2^{\circ \circ }$ | $(*4{:}42_{1}){:}3$ | $(*2_{0}2_{1}2_{0}2_{1}){:}6$ |
| 220 | 43m | $*332$ | I43d | I 4 3 d | $\Gamma _{c}^{v}T_{d}^{6}$ | 93a | $\left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}//3$ | $4^{\circ }/4$ | $(4{\bar {*}}2_{1}){:}3$ | $(2_{0}{*}2_{1}2_{1}){:}6$ |
| 221 | 4/m 3 2/m | $*432$ | Pm3m | P 4/m 3 2/m | $\Gamma _{c}O_{h}^{1}$ | 71s | $\left(a:a:a\right):4/{\tilde {6}}\cdot m$ | $4^{-}{:}2$ | $[*{\cdot }4{\cdot }4{\cdot }2]{:}3$ | $[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6$ |
| 222 | 4/m 3 2/m | $*432$ | Pn3n | P 4/n 3 2/n | $\Gamma _{c}O_{h}^{2}$ | 53h | $\left(a:a:a\right):4/{\tilde {6}}\cdot {\widetilde {abc}}$ | $8^{\circ \circ }$ | $(*4_{0}4{:}2){:}3$ | $(2{\bar {*}}_{1}2_{0}2_{0}){:}6$ |
| 223 | 4/m 3 2/m | $*432$ | Pm3n | P 4$_2$/m 3 2/n | $\Gamma _{c}O_{h}^{3}$ | 102a | $\left(a:a:a\right):4_{2}//{\tilde {6}}\cdot {\widetilde {abc}}$ | $8^{\circ }$ | $[*{\cdot }4{:}4{\cdot }2]{:}3$ | $[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6$ |
| 224 | 4/m 3 2/m | $*432$ | Pn3m | P 4$_2$/n 3 2/m | $\Gamma _{c}O_{h}^{4}$ | 103a | $\left(a:a:a\right):4_{2}//{\tilde {6}}\cdot m$ | $4^{+}{:}2$ | $(*4_{2}4{\cdot }2){:}3$ | $(2{\bar {*}}_{1}2_{0}2_{0}){:}6$ |
| 225 | 4/m 3 2/m | $*432$ | Fm3m | F 4/m 3 2/m | $\Gamma _{c}^{f}O_{h}^{5}$ | 73s | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot m$ | $2^{-}{:}2$ | $[*{\cdot }4{\cdot }4{:}2]{:}3$ | $[*{\cdot }2{\cdot }2{:}2{:}2]{:}6$ |
| 226 | 4/m 3 2/m | $*432$ | Fm3c | F 4/m 3 2/c | $\Gamma _{c}^{f}O_{h}^{6}$ | 54h | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot {\tilde {c}}$ | $4^{--}$ | $[*{\cdot }4{:}4{:}2]{:}3$ | $[*{\cdot }2{\cdot }2{:}2{:}2]{:}6$ |
| 227 | 4/m 3 2/m | $*432$ | Fd3m | F 4$_1$/d 3 2/m | $\Gamma _{c}^{f}O_{h}^{7}$ | 100a | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//{\tilde {6}}\cdot m$ | $2^{+}{:}2$ | $(*4_{1}4{\cdot }2){:}3$ | $(2{\bar {*}}2_{0}2_{1}){:}6$ |
| 228 | 4/m 3 2/m | $*432$ | Fd3c | F 4$_1$/d 3 2/c | $\Gamma _{c}^{f}O_{h}^{8}$ | 101a | $\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//{\tilde {6}}\cdot {\tilde {c}}$ | $4^{++}$ | $(*4_{1}4{:}2){:}3$ | $(2{\bar {*}}2_{0}2_{1}){:}6$ |
| 229 | 4/m 3 2/m | $*432$ | Im3m | I 4/m 3 2/m | $\Gamma _{c}^{v}O_{h}^{9}$ | 72s | $\left({\tfrac {a+b+c}{2}}/a:a:a\right):4/{\tilde {6}}\cdot m$ | $8^{\circ }{:}2$ | $[*{\cdot }4{\cdot }4{:}2]{:}3$ | $[2_{1}{*}{\cdot }2{\cdot }2]{:}6$ |
| 230 | 4/m 3 2/m | $*432$ | Ia3d | I 4$_1$/a 3 2/d | $\Gamma _{c}^{v}O_{h}^{10}$ | 99a | $\left({\tfrac {a+b+c}{2}}/a:a:a\right):4_{1}//{\tilde {6}}\cdot {\tfrac {1}{2}}{\widetilde {abc}}$ | $8^{\circ }/4$ | $(*4_{1}4{:}2){:}3$ | $(*2_{1}2{:}2{:}2){:}6$ |