# List of space groups

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There are 230 [space groups](/source/Space_group#Table_of_space_groups_in_3_dimensions) in three dimensions, given by a number index, and a full name in [Hermann–Mauguin notation](/source/Hermann%E2%80%93Mauguin_notation), and a short name (international short symbol). The long names are given with spaces for readability. The groups each have a [point group](/source/Point_group) of the unit cell.

## Symbols

In [Hermann–Mauguin notation](/source/Hermann%E2%80%93Mauguin_notation), space groups are named by a symbol combining the [point group](/source/Point_group) identifier with the uppercase letters describing the [lattice type](/source/Bravais_lattice#In_3_dimensions). Translations within the lattice in the form of [screw axes](/source/Screw_axis) and [glide planes](/source/Glide_planes) are also noted, giving a complete crystallographic space group.

These are the [Bravais lattices in three dimensions](/source/Bravais_lattice#In_3_dimensions):

- **P** primitive

- **I** body-centered (from the German *Innenzentriert*)

- **F** face-centered (from the German *Flächenzentriert*)

- **S** base-centered (from the German *Seitenflächenzentriert*), or specifically: - **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](/source/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](/source/Diamond) structure.

- a {\displaystyle a} , b {\displaystyle b} , or c {\displaystyle c} : glide translation along half the lattice vector of this face

- n {\displaystyle n} : glide translation along half the diagonal of this face

- d {\displaystyle d} : glide planes with translation along a quarter of a face diagonal

- e {\displaystyle e} : two glides with the same glide plane and translation along two (different) half-lattice vectors.[note 1]

A gyration point can be replaced by a [screw axis](/source/Screw_axis) denoted by a number, *n*, where the angle of rotation is 360 ∘ n {\displaystyle \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, 21 is a 180° (twofold) rotation followed by a translation of ⁠1/2⁠ of the lattice vector. 31 is a 120° (threefold) rotation followed by a translation of ⁠1/3⁠ 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 n m {\textstyle {\frac {n}{m}}} 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 Γ x y {\displaystyle \Gamma _{x}^{y}} which specifies the Bravais lattice. Here x ∈ { t , m , o , q , r h , h , c } {\displaystyle x\in \{t,m,o,q,rh,h,c\}} is the lattice system, and y ∈ { ∅ , b , v , f } {\displaystyle y\in \{\emptyset ,b,v,f\}} is the centering type.[2]

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 ( 4 m 2 m 2 m {\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} ): the symmorphic space groups are P4/mmm ( P 4 m 2 m 2 m {\displaystyle P{\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} , *36s*) and I4/mmm ( I 4 m 2 m 2 m {\displaystyle 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 ( 4 m 2 m 2 m {\displaystyle {\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 4 m 2 c 2 c {\displaystyle P{\tfrac {4}{m}}{\tfrac {2}{c}}{\tfrac {2}{c}}} , *35h*), P4/nbm ( P 4 n 2 b 2 m {\displaystyle P{\tfrac {4}{n}}{\tfrac {2}{b}}{\tfrac {2}{m}}} , *36h*), P4/nnc ( P 4 n 2 n 2 c {\displaystyle P{\tfrac {4}{n}}{\tfrac {2}{n}}{\tfrac {2}{c}}} , *37h*), and I4/mcm ( I 4 m 2 c 2 m {\displaystyle 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 ( 4 m 2 m 2 m {\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} ): P4/mbm ( P 4 m 2 1 b 2 m {\displaystyle P{\tfrac {4}{m}}{\tfrac {2_{1}}{b}}{\tfrac {2}{m}}} , *54a*), P42/mmc ( P 4 2 m 2 m 2 c {\displaystyle P{\tfrac {4_{2}}{m}}{\tfrac {2}{m}}{\tfrac {2}{c}}} , *60a*), I41/acd ( I 4 1 a 2 c 2 d {\displaystyle 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 Bravais lattice

Triclinic crystal system Number Point group Orbifold Short name Full name Schoenflies Fedorov Shubnikov Fibrifold 1 1 1 {\displaystyle 1} P1 P 1 Γ t C 1 1 {\displaystyle \Gamma _{t}C_{1}^{1}} 1s ( a / b / c ) ⋅ 1 {\displaystyle (a/b/c)\cdot 1} ( ∘ ) {\displaystyle (\circ )} 2 1 × {\displaystyle \times } P1 P 1 Γ t C i 1 {\displaystyle \Gamma _{t}C_{i}^{1}} 2s ( a / b / c ) ⋅ 2 ~ {\displaystyle (a/b/c)\cdot {\tilde {2}}} ( 2222 ) {\displaystyle (2222)}

## List of monoclinic

Monoclinic Bravais lattice Simple (P) Base (S)

Monoclinic crystal system Number Point group Orbifold Short name Full name(s) Schoenflies Fedorov Shubnikov Fibrifold (primary) Fibrifold (secondary) 3 2 22 {\displaystyle 22} P2 P 1 2 1 P 1 1 2 Γ m C 2 1 {\displaystyle \Gamma _{m}C_{2}^{1}} 3s ( b : ( c / a ) ) : 2 {\displaystyle (b:(c/a)):2} ( 2 0 2 0 2 0 2 0 ) {\displaystyle (2_{0}2_{0}2_{0}2_{0})} ( ∗ 0 ∗ 0 ) {\displaystyle ({*}_{0}{*}_{0})} 4 P21 P 1 21 1 P 1 1 21 Γ m C 2 2 {\displaystyle \Gamma _{m}C_{2}^{2}} 1a ( b : ( c / a ) ) : 2 1 {\displaystyle (b:(c/a)):2_{1}} ( 2 1 2 1 2 1 2 1 ) {\displaystyle (2_{1}2_{1}2_{1}2_{1})} ( × ¯ × ¯ ) {\displaystyle ({\bar {\times }}{\bar {\times }})} 5 C2 C 1 2 1 B 1 1 2 Γ m b C 2 3 {\displaystyle \Gamma _{m}^{b}C_{2}^{3}} 4s ( a + b 2 / b : ( c / a ) ) : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right):2} ( 2 0 2 0 2 1 2 1 ) {\displaystyle (2_{0}2_{0}2_{1}2_{1})} ( ∗ 1 ∗ 1 ) {\displaystyle ({*}_{1}{*}_{1})} , ( ∗ × ¯ ) {\displaystyle ({*}{\bar {\times }})} 6 m ∗ {\displaystyle *} Pm P 1 m 1 P 1 1 m Γ m C s 1 {\displaystyle \Gamma _{m}C_{s}^{1}} 5s ( b : ( c / a ) ) ⋅ m {\displaystyle (b:(c/a))\cdot m} [ ∘ 0 ] {\displaystyle [\circ _{0}]} ( ∗ ⋅ ∗ ⋅ ) {\displaystyle ({*}{\cdot }{*}{\cdot })} 7 Pc P 1 c 1 P 1 1 b Γ m C s 2 {\displaystyle \Gamma _{m}C_{s}^{2}} 1h ( b : ( c / a ) ) ⋅ c ~ {\displaystyle (b:(c/a))\cdot {\tilde {c}}} ( ∘ ¯ 0 ) {\displaystyle ({\bar {\circ }}_{0})} ( ∗ : ∗ : ) {\displaystyle ({*}{:}{*}{:})} , ( × × 0 ) {\displaystyle ({\times }{\times }_{0})} 8 Cm C 1 m 1 B 1 1 m Γ m b C s 3 {\displaystyle \Gamma _{m}^{b}C_{s}^{3}} 6s ( a + b 2 / b : ( c / a ) ) ⋅ m {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m} [ ∘ 1 ] {\displaystyle [\circ _{1}]} ( ∗ ⋅ ∗ : ) {\displaystyle ({*}{\cdot }{*}{:})} , ( ∗ ⋅ × ) {\displaystyle ({*}{\cdot }{\times })} 9 Cc C 1 c 1 B 1 1 b Γ m b C s 4 {\displaystyle \Gamma _{m}^{b}C_{s}^{4}} 2h ( a + b 2 / b : ( c / a ) ) ⋅ c ~ {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}} ( ∘ ¯ 1 ) {\displaystyle ({\bar {\circ }}_{1})} ( ∗ : × ) {\displaystyle ({*}{:}{\times })} , ( × × 1 ) {\displaystyle ({\times }{\times }_{1})} 10 2/m 2 ∗ {\displaystyle 2*} P2/m P 1 2/m 1 P 1 1 2/m Γ m C 2 h 1 {\displaystyle \Gamma _{m}C_{2h}^{1}} 7s ( b : ( c / a ) ) ⋅ m : 2 {\displaystyle (b:(c/a))\cdot m:2} [ 2 0 2 0 2 0 2 0 ] {\displaystyle [2_{0}2_{0}2_{0}2_{0}]} ( ∗ 2 ⋅ 22 ⋅ 2 ) {\displaystyle (*2{\cdot }22{\cdot }2)} 11 P21/m P 1 21/m 1 P 1 1 21/m Γ m C 2 h 2 {\displaystyle \Gamma _{m}C_{2h}^{2}} 2a ( b : ( c / a ) ) ⋅ m : 2 1 {\displaystyle (b:(c/a))\cdot m:2_{1}} [ 2 1 2 1 2 1 2 1 ] {\displaystyle [2_{1}2_{1}2_{1}2_{1}]} ( 22 ∗ ⋅ ) {\displaystyle (22{*}{\cdot })} 12 C2/m C 1 2/m 1 B 1 1 2/m Γ m b C 2 h 3 {\displaystyle \Gamma _{m}^{b}C_{2h}^{3}} 8s ( a + b 2 / b : ( c / a ) ) ⋅ m : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m:2} [ 2 0 2 0 2 1 2 1 ] {\displaystyle [2_{0}2_{0}2_{1}2_{1}]} ( ∗ 2 ⋅ 22 : 2 ) {\displaystyle (*2{\cdot }22{:}2)} , ( 2 ∗ ¯ 2 ⋅ 2 ) {\displaystyle (2{\bar {*}}2{\cdot }2)} 13 P2/c P 1 2/c 1 P 1 1 2/b Γ m C 2 h 4 {\displaystyle \Gamma _{m}C_{2h}^{4}} 3h ( b : ( c / a ) ) ⋅ c ~ : 2 {\displaystyle (b:(c/a))\cdot {\tilde {c}}:2} ( 2 0 2 0 22 ) {\displaystyle (2_{0}2_{0}22)} ( ∗ 2 : 22 : 2 ) {\displaystyle (*2{:}22{:}2)} , ( 22 ∗ 0 ) {\displaystyle (22{*}_{0})} 14 P21/c P 1 21/c 1 P 1 1 21/b Γ m C 2 h 5 {\displaystyle \Gamma _{m}C_{2h}^{5}} 3a ( b : ( c / a ) ) ⋅ c ~ : 2 1 {\displaystyle (b:(c/a))\cdot {\tilde {c}}:2_{1}} ( 2 1 2 1 22 ) {\displaystyle (2_{1}2_{1}22)} ( 22 ∗ : ) {\displaystyle (22{*}{:})} , ( 22 × ) {\displaystyle (22{\times })} 15 C2/c C 1 2/c 1 B 1 1 2/b Γ m b C 2 h 6 {\displaystyle \Gamma _{m}^{b}C_{2h}^{6}} 4h ( a + b 2 / b : ( c / a ) ) ⋅ c ~ : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}:2} ( 2 0 2 1 22 ) {\displaystyle (2_{0}2_{1}22)} ( 2 ∗ ¯ 2 : 2 ) {\displaystyle (2{\bar {*}}2{:}2)} , ( 22 ∗ 1 ) {\displaystyle (22{*}_{1})}

## List of orthorhombic

Orthorhombic Bravais lattice Simple (P) Body (I) Face (F) Base (S)

Orthorhombic crystal system Number Point group Orbifold Short name Full name Schoenflies Fedorov Shubnikov Fibrifold (primary) Fibrifold (secondary) 16 222 222 {\displaystyle 222} P222 P 2 2 2 Γ o D 2 1 {\displaystyle \Gamma _{o}D_{2}^{1}} 9s ( c : a : b ) : 2 : 2 {\displaystyle (c:a:b):2:2} ( ∗ 2 0 2 0 2 0 2 0 ) {\displaystyle (*2_{0}2_{0}2_{0}2_{0})} 17 P2221 P 2 2 21 Γ o D 2 2 {\displaystyle \Gamma _{o}D_{2}^{2}} 4a ( c : a : b ) : 2 1 : 2 {\displaystyle (c:a:b):2_{1}:2} ( ∗ 2 1 2 1 2 1 2 1 ) {\displaystyle (*2_{1}2_{1}2_{1}2_{1})} ( 2 0 2 0 ∗ ) {\displaystyle (2_{0}2_{0}{*})} 18 P21212 P 21 21 2 Γ o D 2 3 {\displaystyle \Gamma _{o}D_{2}^{3}} 7a ( c : a : b ) : 2 {\displaystyle (c:a:b):2} 2 1 {\displaystyle 2_{1}} ( 2 0 2 0 × ¯ ) {\displaystyle (2_{0}2_{0}{\bar {\times }})} ( 2 1 2 1 ∗ ) {\displaystyle (2_{1}2_{1}{*})} 19 P212121 P 21 21 21 Γ o D 2 4 {\displaystyle \Gamma _{o}D_{2}^{4}} 8a ( c : a : b ) : 2 1 {\displaystyle (c:a:b):2_{1}} 2 1 {\displaystyle 2_{1}} ( 2 1 2 1 × ¯ ) {\displaystyle (2_{1}2_{1}{\bar {\times }})} 20 C2221 C 2 2 21 Γ o b D 2 5 {\displaystyle \Gamma _{o}^{b}D_{2}^{5}} 5a ( a + b 2 : c : a : b ) : 2 1 : 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):2_{1}:2} ( 2 1 ∗ 2 1 2 1 ) {\displaystyle (2_{1}{*}2_{1}2_{1})} ( 2 0 2 1 ∗ ) {\displaystyle (2_{0}2_{1}{*})} 21 C222 C 2 2 2 Γ o b D 2 6 {\displaystyle \Gamma _{o}^{b}D_{2}^{6}} 10s ( a + b 2 : c : a : b ) : 2 : 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):2:2} ( 2 0 ∗ 2 0 2 0 ) {\displaystyle (2_{0}{*}2_{0}2_{0})} ( ∗ 2 0 2 0 2 1 2 1 ) {\displaystyle (*2_{0}2_{0}2_{1}2_{1})} 22 F222 F 2 2 2 Γ o f D 2 7 {\displaystyle \Gamma _{o}^{f}D_{2}^{7}} 12s ( a + c 2 / b + c 2 / a + b 2 : c : a : b ) : 2 : 2 {\displaystyle \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 ) {\displaystyle (*2_{0}2_{1}2_{0}2_{1})} 23 I222 I 2 2 2 Γ o v D 2 8 {\displaystyle \Gamma _{o}^{v}D_{2}^{8}} 11s ( a + b + c 2 / c : a : b ) : 2 : 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2} ( 2 1 ∗ 2 0 2 0 ) {\displaystyle (2_{1}{*}2_{0}2_{0})} 24 I212121 I 21 21 21 Γ o v D 2 9 {\displaystyle \Gamma _{o}^{v}D_{2}^{9}} 6a ( a + b + c 2 / c : a : b ) : 2 : 2 1 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2_{1}} ( 2 0 ∗ 2 1 2 1 ) {\displaystyle (2_{0}{*}2_{1}2_{1})} 25 mm2 ∗ 22 {\displaystyle *22} Pmm2 P m m 2 Γ o C 2 v 1 {\displaystyle \Gamma _{o}C_{2v}^{1}} 13s ( c : a : b ) : m ⋅ 2 {\displaystyle (c:a:b):m\cdot 2} ( ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ) {\displaystyle (*{\cdot }2{\cdot }2{\cdot }2{\cdot }2)} [ ∗ 0 ⋅ ∗ 0 ⋅ ] {\displaystyle [{*}_{0}{\cdot }{*}_{0}{\cdot }]} 26 Pmc21 P m c 21 Γ o C 2 v 2 {\displaystyle \Gamma _{o}C_{2v}^{2}} 9a ( c : a : b ) : c ~ ⋅ 2 1 {\displaystyle (c:a:b):{\tilde {c}}\cdot 2_{1}} ( ∗ ⋅ 2 : 2 ⋅ 2 : 2 ) {\displaystyle (*{\cdot }2{:}2{\cdot }2{:}2)} ( ∗ ¯ ⋅ ∗ ¯ ⋅ ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}{\cdot })} , [ × 0 × 0 ] {\displaystyle [{\times _{0}}{\times _{0}}]} 27 Pcc2 P c c 2 Γ o C 2 v 3 {\displaystyle \Gamma _{o}C_{2v}^{3}} 5h ( c : a : b ) : c ~ ⋅ 2 {\displaystyle (c:a:b):{\tilde {c}}\cdot 2} ( ∗ : 2 : 2 : 2 : 2 ) {\displaystyle (*{:}2{:}2{:}2{:}2)} ( ∗ ¯ 0 ∗ ¯ 0 ) {\displaystyle ({\bar {*}}_{0}{\bar {*}}_{0})} 28 Pma2 P m a 2 Γ o C 2 v 4 {\displaystyle \Gamma _{o}C_{2v}^{4}} 6h ( c : a : b ) : a ~ ⋅ 2 {\displaystyle (c:a:b):{\tilde {a}}\cdot 2} ( 2 0 2 0 ∗ ⋅ ) {\displaystyle (2_{0}2_{0}{*}{\cdot })} [ ∗ 0 : ∗ 0 : ] {\displaystyle [{*}_{0}{:}{*}_{0}{:}]} , ( ∗ ⋅ ∗ 0 ) {\displaystyle (*{\cdot }{*}_{0})} 29 Pca21 P c a 21 Γ o C 2 v 5 {\displaystyle \Gamma _{o}C_{2v}^{5}} 11a ( c : a : b ) : a ~ ⋅ 2 1 {\displaystyle (c:a:b):{\tilde {a}}\cdot 2_{1}} ( 2 1 2 1 ∗ : ) {\displaystyle (2_{1}2_{1}{*}{:})} ( ∗ ¯ : ∗ ¯ : ) {\displaystyle ({\bar {*}}{:}{\bar {*}}{:})} 30 Pnc2 P n c 2 Γ o C 2 v 6 {\displaystyle \Gamma _{o}C_{2v}^{6}} 7h ( c : a : b ) : c ~ ⊙ 2 {\displaystyle (c:a:b):{\tilde {c}}\odot 2} ( 2 0 2 0 ∗ : ) {\displaystyle (2_{0}2_{0}{*}{:})} ( ∗ ¯ 1 ∗ ¯ 1 ) {\displaystyle ({\bar {*}}_{1}{\bar {*}}_{1})} , ( ∗ 0 × 0 ) {\displaystyle ({*}_{0}{\times }_{0})} 31 Pmn21 P m n 21 Γ o C 2 v 7 {\displaystyle \Gamma _{o}C_{2v}^{7}} 10a ( c : a : b ) : a c ~ ⋅ 2 1 {\displaystyle (c:a:b):{\widetilde {ac}}\cdot 2_{1}} ( 2 1 2 1 ∗ ⋅ ) {\displaystyle (2_{1}2_{1}{*}{\cdot })} ( ∗ ⋅ × ¯ ) {\displaystyle (*{\cdot }{\bar {\times }})} , [ × 0 × 1 ] {\displaystyle [{\times }_{0}{\times }_{1}]} 32 Pba2 P b a 2 Γ o C 2 v 8 {\displaystyle \Gamma _{o}C_{2v}^{8}} 9h ( c : a : b ) : a ~ ⊙ 2 {\displaystyle (c:a:b):{\tilde {a}}\odot 2} ( 2 0 2 0 × 0 ) {\displaystyle (2_{0}2_{0}{\times }_{0})} ( ∗ : ∗ 0 ) {\displaystyle (*{:}{*}_{0})} 33 Pna21 P n a 21 Γ o C 2 v 9 {\displaystyle \Gamma _{o}C_{2v}^{9}} 12a ( c : a : b ) : a ~ ⊙ 2 1 {\displaystyle (c:a:b):{\tilde {a}}\odot 2_{1}} ( 2 1 2 1 × ) {\displaystyle (2_{1}2_{1}{\times })} ( ∗ : × ) {\displaystyle (*{:}{\times })} , ( × × 1 ) {\displaystyle ({\times }{\times }_{1})} 34 Pnn2 P n n 2 Γ o C 2 v 10 {\displaystyle \Gamma _{o}C_{2v}^{10}} 8h ( c : a : b ) : a c ~ ⊙ 2 {\displaystyle (c:a:b):{\widetilde {ac}}\odot 2} ( 2 0 2 0 × 1 ) {\displaystyle (2_{0}2_{0}{\times }_{1})} ( ∗ 0 × 1 ) {\displaystyle (*_{0}{\times }_{1})} 35 Cmm2 C m m 2 Γ o b C 2 v 11 {\displaystyle \Gamma _{o}^{b}C_{2v}^{11}} 14s ( a + b 2 : c : a : b ) : m ⋅ 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2} ( 2 0 ∗ ⋅ 2 ⋅ 2 ) {\displaystyle (2_{0}{*}{\cdot }2{\cdot }2)} [ ∗ 0 ⋅ ∗ 0 : ] {\displaystyle [*_{0}{\cdot }{*}_{0}{:}]} 36 Cmc21 C m c 21 Γ o b C 2 v 12 {\displaystyle \Gamma _{o}^{b}C_{2v}^{12}} 13a ( a + b 2 : c : a : b ) : c ~ ⋅ 2 1 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2_{1}} ( 2 1 ∗ ⋅ 2 : 2 ) {\displaystyle (2_{1}{*}{\cdot }2{:}2)} ( ∗ ¯ ⋅ ∗ ¯ : ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}{:})} , [ × 1 × 1 ] {\displaystyle [{\times }_{1}{\times }_{1}]} 37 Ccc2 C c c 2 Γ o b C 2 v 13 {\displaystyle \Gamma _{o}^{b}C_{2v}^{13}} 10h ( a + b 2 : c : a : b ) : c ~ ⋅ 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2} ( 2 0 ∗ : 2 : 2 ) {\displaystyle (2_{0}{*}{:}2{:}2)} ( ∗ ¯ 0 ∗ ¯ 1 ) {\displaystyle ({\bar {*}}_{0}{\bar {*}}_{1})} 38 Amm2 A m m 2 Γ o b C 2 v 14 {\displaystyle \Gamma _{o}^{b}C_{2v}^{14}} 15s ( b + c 2 / c : a : b ) : m ⋅ 2 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2} ( ∗ ⋅ 2 ⋅ 2 ⋅ 2 : 2 ) {\displaystyle (*{\cdot }2{\cdot }2{\cdot }2{:}2)} [ ∗ 1 ⋅ ∗ 1 ⋅ ] {\displaystyle [{*}_{1}{\cdot }{*}_{1}{\cdot }]} , [ ∗ ⋅ × 0 ] {\displaystyle [*{\cdot }{\times }_{0}]} 39 Aem2 A b m 2 Γ o b C 2 v 15 {\displaystyle \Gamma _{o}^{b}C_{2v}^{15}} 11h ( b + c 2 / c : a : b ) : m ⋅ 2 1 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2_{1}} ( ∗ ⋅ 2 : 2 : 2 : 2 ) {\displaystyle (*{\cdot }2{:}2{:}2{:}2)} [ ∗ 1 : ∗ 1 : ] {\displaystyle [{*}_{1}{:}{*}_{1}{:}]} , ( ∗ ¯ ⋅ ∗ ¯ 0 ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}_{0})} 40 Ama2 A m a 2 Γ o b C 2 v 16 {\displaystyle \Gamma _{o}^{b}C_{2v}^{16}} 12h ( b + c 2 / c : a : b ) : a ~ ⋅ 2 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2} ( 2 0 2 1 ∗ ⋅ ) {\displaystyle (2_{0}2_{1}{*}{\cdot })} ( ∗ ⋅ ∗ 1 ) {\displaystyle (*{\cdot }{*}_{1})} , [ ∗ : × 1 ] {\displaystyle [*{:}{\times }_{1}]} 41 Aea2 A b a 2 Γ o b C 2 v 17 {\displaystyle \Gamma _{o}^{b}C_{2v}^{17}} 13h ( b + c 2 / c : a : b ) : a ~ ⋅ 2 1 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2_{1}} ( 2 0 2 1 ∗ : ) {\displaystyle (2_{0}2_{1}{*}{:})} ( ∗ : ∗ 1 ) {\displaystyle (*{:}{*}_{1})} , ( ∗ ¯ : ∗ ¯ 1 ) {\displaystyle ({\bar {*}}{:}{\bar {*}}_{1})} 42 Fmm2 F m m 2 Γ o f C 2 v 18 {\displaystyle \Gamma _{o}^{f}C_{2v}^{18}} 17s ( a + c 2 / b + c 2 / a + b 2 : c : a : b ) : m ⋅ 2 {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2} ( ∗ ⋅ 2 ⋅ 2 : 2 : 2 ) {\displaystyle (*{\cdot }2{\cdot }2{:}2{:}2)} [ ∗ 1 ⋅ ∗ 1 : ] {\displaystyle [{*}_{1}{\cdot }{*}_{1}{:}]} 43 Fdd2 F d d 2 Γ o f C 2 v 19 {\displaystyle \Gamma _{o}^{f}C_{2v}^{19}} 16h ( a + c 2 / b + c 2 / a + b 2 : c : a : b ) : 1 2 a c ~ ⊙ 2 {\displaystyle \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 × ) {\displaystyle (2_{0}2_{1}{\times })} ( ∗ 1 × ) {\displaystyle ({*}_{1}{\times })} 44 Imm2 I m m 2 Γ o v C 2 v 20 {\displaystyle \Gamma _{o}^{v}C_{2v}^{20}} 16s ( a + b + c 2 / c : a : b ) : m ⋅ 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):m\cdot 2} ( 2 1 ∗ ⋅ 2 ⋅ 2 ) {\displaystyle (2_{1}{*}{\cdot }2{\cdot }2)} [ ∗ ⋅ × 1 ] {\displaystyle [*{\cdot }{\times }_{1}]} 45 Iba2 I b a 2 Γ o v C 2 v 21 {\displaystyle \Gamma _{o}^{v}C_{2v}^{21}} 15h ( a + b + c 2 / c : a : b ) : c ~ ⋅ 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {c}}\cdot 2} ( 2 1 ∗ : 2 : 2 ) {\displaystyle (2_{1}{*}{:}2{:}2)} ( ∗ ¯ : ∗ ¯ 0 ) {\displaystyle ({\bar {*}}{:}{\bar {*}}_{0})} 46 Ima2 I m a 2 Γ o v C 2 v 22 {\displaystyle \Gamma _{o}^{v}C_{2v}^{22}} 14h ( a + b + c 2 / c : a : b ) : a ~ ⋅ 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2} ( 2 0 ∗ ⋅ 2 : 2 ) {\displaystyle (2_{0}{*}{\cdot }2{:}2)} ( ∗ ¯ ⋅ ∗ ¯ 1 ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}_{1})} , [ ∗ : × 0 ] {\displaystyle [*{:}{\times }_{0}]} 47 2/m 2/m 2/m (mmm) ∗ 222 {\displaystyle *222} Pmmm P 2/m 2/m 2/m Γ o D 2 h 1 {\displaystyle \Gamma _{o}D_{2h}^{1}} 18s ( c : a : b ) ⋅ m : 2 ⋅ m {\displaystyle \left(c:a:b\right)\cdot m:2\cdot m} [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]} 48 Pnnn P 2/n 2/n 2/n Γ o D 2 h 2 {\displaystyle \Gamma _{o}D_{2h}^{2}} 19h ( c : a : b ) ⋅ a b ~ : 2 ⊙ a c ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\widetilde {ac}}} ( 2 ∗ ¯ 1 2 0 2 0 ) {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0})} 49 Pccm P 2/c 2/c 2/m Γ o D 2 h 3 {\displaystyle \Gamma _{o}D_{2h}^{3}} 17h ( c : a : b ) ⋅ m : 2 ⋅ c ~ {\displaystyle \left(c:a:b\right)\cdot m:2\cdot {\tilde {c}}} [ ∗ : 2 : 2 : 2 : 2 ] {\displaystyle [*{:}2{:}2{:}2{:}2]} ( ∗ 2 0 2 0 2 ⋅ 2 ) {\displaystyle (*2_{0}2_{0}2{\cdot }2)} 50 Pban P 2/b 2/a 2/n Γ o D 2 h 4 {\displaystyle \Gamma _{o}D_{2h}^{4}} 18h ( c : a : b ) ⋅ a b ~ : 2 ⊙ a ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\tilde {a}}} ( 2 ∗ ¯ 0 2 0 2 0 ) {\displaystyle (2{\bar {*}}_{0}2_{0}2_{0})} ( ∗ 2 0 2 0 2 : 2 ) {\displaystyle (*2_{0}2_{0}2{:}2)} 51 Pmma P 21/m 2/m 2/a Γ o D 2 h 5 {\displaystyle \Gamma _{o}D_{2h}^{5}} 14a ( c : a : b ) ⋅ a ~ : 2 ⋅ m {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\cdot m} [ 2 0 2 0 ∗ ⋅ ] {\displaystyle [2_{0}2_{0}{*}{\cdot }]} [ ∗ ⋅ 2 : 2 ⋅ 2 : 2 ] {\displaystyle [*{\cdot }2{:}2{\cdot }2{:}2]} , [ ∗ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] {\displaystyle [*2{\cdot }2{\cdot }2{\cdot }2]} 52 Pnna P 2/n 21/n 2/a Γ o D 2 h 6 {\displaystyle \Gamma _{o}D_{2h}^{6}} 17a ( c : a : b ) ⋅ a ~ : 2 ⊙ a c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\odot {\widetilde {ac}}} ( 2 0 2 ∗ ¯ 1 ) {\displaystyle (2_{0}2{\bar {*}}_{1})} ( 2 0 ∗ 2 : 2 ) {\displaystyle (2_{0}{*}2{:}2)} , ( 2 ∗ ¯ 2 1 2 1 ) {\displaystyle (2{\bar {*}}2_{1}2_{1})} 53 Pmna P 2/m 2/n 21/a Γ o D 2 h 7 {\displaystyle \Gamma _{o}D_{2h}^{7}} 15a ( c : a : b ) ⋅ a ~ : 2 1 ⋅ a c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\widetilde {ac}}} [ 2 0 2 0 ∗ : ] {\displaystyle [2_{0}2_{0}{*}{:}]} ( ∗ 2 1 2 1 2 ⋅ 2 ) {\displaystyle (*2_{1}2_{1}2{\cdot }2)} , ( 2 0 ∗ 2 ⋅ 2 ) {\displaystyle (2_{0}{*}2{\cdot }2)} 54 Pcca P 21/c 2/c 2/a Γ o D 2 h 8 {\displaystyle \Gamma _{o}D_{2h}^{8}} 16a ( c : a : b ) ⋅ a ~ : 2 ⋅ c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}} ( 2 0 2 ∗ ¯ 0 ) {\displaystyle (2_{0}2{\bar {*}}_{0})} ( ∗ 2 : 2 : 2 : 2 ) {\displaystyle (*2{:}2{:}2{:}2)} , ( ∗ 2 1 2 1 2 : 2 ) {\displaystyle (*2_{1}2_{1}2{:}2)} 55 Pbam P 21/b 21/a 2/m Γ o D 2 h 9 {\displaystyle \Gamma _{o}D_{2h}^{9}} 22a ( c : a : b ) ⋅ m : 2 ⊙ a ~ {\displaystyle \left(c:a:b\right)\cdot m:2\odot {\tilde {a}}} [ 2 0 2 0 × 0 ] {\displaystyle [2_{0}2_{0}{\times }_{0}]} ( ∗ 2 ⋅ 2 : 2 ⋅ 2 ) {\displaystyle (*2{\cdot }2{:}2{\cdot }2)} 56 Pccn P 21/c 21/c 2/n Γ o D 2 h 10 {\displaystyle \Gamma _{o}D_{2h}^{10}} 27a ( c : a : b ) ⋅ a b ~ : 2 ⋅ c ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot {\tilde {c}}} ( 2 ∗ ¯ : 2 : 2 ) {\displaystyle (2{\bar {*}}{:}2{:}2)} ( 2 1 2 ∗ ¯ 0 ) {\displaystyle (2_{1}2{\bar {*}}_{0})} 57 Pbcm P 2/b 21/c 21/m Γ o D 2 h 11 {\displaystyle \Gamma _{o}D_{2h}^{11}} 23a ( c : a : b ) ⋅ m : 2 1 ⊙ c ~ {\displaystyle \left(c:a:b\right)\cdot m:2_{1}\odot {\tilde {c}}} ( 2 0 2 ∗ ¯ ⋅ ) {\displaystyle (2_{0}2{\bar {*}}{\cdot })} ( ∗ 2 : 2 ⋅ 2 : 2 ) {\displaystyle (*2{:}2{\cdot }2{:}2)} , [ 2 1 2 1 ∗ : ] {\displaystyle [2_{1}2_{1}{*}{:}]} 58 Pnnm P 21/n 21/n 2/m Γ o D 2 h 12 {\displaystyle \Gamma _{o}D_{2h}^{12}} 25a ( c : a : b ) ⋅ m : 2 ⊙ a c ~ {\displaystyle \left(c:a:b\right)\cdot m:2\odot {\widetilde {ac}}} [ 2 0 2 0 × 1 ] {\displaystyle [2_{0}2_{0}{\times }_{1}]} ( 2 1 ∗ 2 ⋅ 2 ) {\displaystyle (2_{1}{*}2{\cdot }2)} 59 Pmmn P 21/m 21/m 2/n Γ o D 2 h 13 {\displaystyle \Gamma _{o}D_{2h}^{13}} 24a ( c : a : b ) ⋅ a b ~ : 2 ⋅ m {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot m} ( 2 ∗ ¯ ⋅ 2 ⋅ 2 ) {\displaystyle (2{\bar {*}}{\cdot }2{\cdot }2)} [ 2 1 2 1 ∗ ⋅ ] {\displaystyle [2_{1}2_{1}{*}{\cdot }]} 60 Pbcn P 21/b 2/c 21/n Γ o D 2 h 14 {\displaystyle \Gamma _{o}D_{2h}^{14}} 26a ( c : a : b ) ⋅ a b ~ : 2 1 ⊙ c ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2_{1}\odot {\tilde {c}}} ( 2 0 2 ∗ ¯ : ) {\displaystyle (2_{0}2{\bar {*}}{:})} ( 2 1 ∗ 2 : 2 ) {\displaystyle (2_{1}{*}2{:}2)} , ( 2 1 2 ∗ ¯ 1 ) {\displaystyle (2_{1}2{\bar {*}}_{1})} 61 Pbca P 21/b 21/c 21/a Γ o D 2 h 15 {\displaystyle \Gamma _{o}D_{2h}^{15}} 29a ( c : a : b ) ⋅ a ~ : 2 1 ⊙ c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot {\tilde {c}}} ( 2 1 2 ∗ ¯ : ) {\displaystyle (2_{1}2{\bar {*}}{:})} 62 Pnma P 21/n 21/m 21/a Γ o D 2 h 16 {\displaystyle \Gamma _{o}D_{2h}^{16}} 28a ( c : a : b ) ⋅ a ~ : 2 1 ⊙ m {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot m} ( 2 1 2 ∗ ¯ ⋅ ) {\displaystyle (2_{1}2{\bar {*}}{\cdot })} ( 2 ∗ ¯ ⋅ 2 : 2 ) {\displaystyle (2{\bar {*}}{\cdot }2{:}2)} , [ 2 1 2 1 × ] {\displaystyle [2_{1}2_{1}{\times }]} 63 Cmcm C 2/m 2/c 21/m Γ o b D 2 h 17 {\displaystyle \Gamma _{o}^{b}D_{2h}^{17}} 18a ( a + b 2 : c : a : b ) ⋅ m : 2 1 ⋅ c ~ {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2_{1}\cdot {\tilde {c}}} [ 2 0 2 1 ∗ ⋅ ] {\displaystyle [2_{0}2_{1}{*}{\cdot }]} ( ∗ 2 ⋅ 2 ⋅ 2 : 2 ) {\displaystyle (*2{\cdot }2{\cdot }2{:}2)} , [ 2 1 ∗ ⋅ 2 : 2 ] {\displaystyle [2_{1}{*}{\cdot }2{:}2]} 64 Cmce C 2/m 2/c 21/a Γ o b D 2 h 18 {\displaystyle \Gamma _{o}^{b}D_{2h}^{18}} 19a ( a + b 2 : c : a : b ) ⋅ a ~ : 2 1 ⋅ c ~ {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\tilde {c}}} [ 2 0 2 1 ∗ : ] {\displaystyle [2_{0}2_{1}{*}{:}]} ( ∗ 2 ⋅ 2 : 2 : 2 ) {\displaystyle (*2{\cdot }2{:}2{:}2)} , ( ∗ 2 1 2 ⋅ 2 : 2 ) {\displaystyle (*2_{1}2{\cdot }2{:}2)} 65 Cmmm C 2/m 2/m 2/m Γ o b D 2 h 19 {\displaystyle \Gamma _{o}^{b}D_{2h}^{19}} 19s ( a + b 2 : c : a : b ) ⋅ m : 2 ⋅ m {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m} [ 2 0 ∗ ⋅ 2 ⋅ 2 ] {\displaystyle [2_{0}{*}{\cdot }2{\cdot }2]} [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 : 2 ] {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{:}2]} 66 Cccm C 2/c 2/c 2/m Γ o b D 2 h 20 {\displaystyle \Gamma _{o}^{b}D_{2h}^{20}} 20h ( a + b 2 : c : a : b ) ⋅ m : 2 ⋅ c ~ {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot {\tilde {c}}} [ 2 0 ∗ : 2 : 2 ] {\displaystyle [2_{0}{*}{:}2{:}2]} ( ∗ 2 0 2 1 2 ⋅ 2 ) {\displaystyle (*2_{0}2_{1}2{\cdot }2)} 67 Cmme C 2/m 2/m 2/e Γ o b D 2 h 21 {\displaystyle \Gamma _{o}^{b}D_{2h}^{21}} 21h ( a + b 2 : c : a : b ) ⋅ a ~ : 2 ⋅ m {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot m} ( ∗ 2 0 2 ⋅ 2 ⋅ 2 ) {\displaystyle (*2_{0}2{\cdot }2{\cdot }2)} [ ∗ ⋅ 2 : 2 : 2 : 2 ] {\displaystyle [*{\cdot }2{:}2{:}2{:}2]} 68 Ccce C 2/c 2/c 2/e Γ o b D 2 h 22 {\displaystyle \Gamma _{o}^{b}D_{2h}^{22}} 22h ( a + b 2 : c : a : b ) ⋅ a ~ : 2 ⋅ c ~ {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}} ( ∗ 2 0 2 : 2 : 2 ) {\displaystyle (*2_{0}2{:}2{:}2)} ( ∗ 2 0 2 1 2 : 2 ) {\displaystyle (*2_{0}2_{1}2{:}2)} 69 Fmmm F 2/m 2/m 2/m Γ o f D 2 h 23 {\displaystyle \Gamma _{o}^{f}D_{2h}^{23}} 21s ( a + c 2 / b + c 2 / a + b 2 : c : a : b ) ⋅ m : 2 ⋅ m {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m} [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]} 70 Fddd F 2/d 2/d 2/d Γ o f D 2 h 24 {\displaystyle \Gamma _{o}^{f}D_{2h}^{24}} 24h ( a + c 2 / b + c 2 / a + b 2 : c : a : b ) ⋅ 1 2 a b ~ : 2 ⊙ 1 2 a c ~ {\displaystyle \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 ∗ ¯ 2 0 2 1 ) {\displaystyle (2{\bar {*}}2_{0}2_{1})} 71 Immm I 2/m 2/m 2/m Γ o v D 2 h 25 {\displaystyle \Gamma _{o}^{v}D_{2h}^{25}} 20s ( a + b + c 2 / c : a : b ) ⋅ m : 2 ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot m} [ 2 1 ∗ ⋅ 2 ⋅ 2 ] {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]} 72 Ibam I 2/b 2/a 2/m Γ o v D 2 h 26 {\displaystyle \Gamma _{o}^{v}D_{2h}^{26}} 23h ( a + b + c 2 / c : a : b ) ⋅ m : 2 ⋅ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot {\tilde {c}}} [ 2 1 ∗ : 2 : 2 ] {\displaystyle [2_{1}{*}{:}2{:}2]} ( ∗ 2 0 2 ⋅ 2 : 2 ) {\displaystyle (*2_{0}2{\cdot }2{:}2)} 73 Ibca I 2/b 2/c 2/a Γ o v D 2 h 27 {\displaystyle \Gamma _{o}^{v}D_{2h}^{27}} 21a ( a + b + c 2 / c : a : b ) ⋅ a ~ : 2 ⋅ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}} ( ∗ 2 1 2 : 2 : 2 ) {\displaystyle (*2_{1}2{:}2{:}2)} 74 Imma I 2/m 2/m 2/a Γ o v D 2 h 28 {\displaystyle \Gamma _{o}^{v}D_{2h}^{28}} 20a ( a + b + c 2 / c : a : b ) ⋅ a ~ : 2 ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot m} ( ∗ 2 1 2 ⋅ 2 ⋅ 2 ) {\displaystyle (*2_{1}2{\cdot }2{\cdot }2)} [ 2 0 ∗ ⋅ 2 : 2 ] {\displaystyle [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 {\displaystyle 44} P4 P 4 Γ q C 4 1 {\displaystyle \Gamma _{q}C_{4}^{1}} 22s ( c : a : a ) : 4 {\displaystyle (c:a:a):4} ( 4 0 4 0 2 0 ) {\displaystyle (4_{0}4_{0}2_{0})} 76 P41 P 41 Γ q C 4 2 {\displaystyle \Gamma _{q}C_{4}^{2}} 30a ( c : a : a ) : 4 1 {\displaystyle (c:a:a):4_{1}} ( 4 1 4 1 2 1 ) {\displaystyle (4_{1}4_{1}2_{1})} 77 P42 P 42 Γ q C 4 3 {\displaystyle \Gamma _{q}C_{4}^{3}} 33a ( c : a : a ) : 4 2 {\displaystyle (c:a:a):4_{2}} ( 4 2 4 2 2 0 ) {\displaystyle (4_{2}4_{2}2_{0})} 78 P43 P 43 Γ q C 4 4 {\displaystyle \Gamma _{q}C_{4}^{4}} 31a ( c : a : a ) : 4 3 {\displaystyle (c:a:a):4_{3}} ( 4 1 4 1 2 1 ) {\displaystyle (4_{1}4_{1}2_{1})} 79 I4 I 4 Γ q v C 4 5 {\displaystyle \Gamma _{q}^{v}C_{4}^{5}} 23s ( a + b + c 2 / c : a : a ) : 4 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4} ( 4 2 4 0 2 1 ) {\displaystyle (4_{2}4_{0}2_{1})} 80 I41 I 41 Γ q v C 4 6 {\displaystyle \Gamma _{q}^{v}C_{4}^{6}} 32a ( a + b + c 2 / c : a : a ) : 4 1 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}} ( 4 3 4 1 2 0 ) {\displaystyle (4_{3}4_{1}2_{0})} 81 4 2 × {\displaystyle 2\times } P4 P 4 Γ q S 4 1 {\displaystyle \Gamma _{q}S_{4}^{1}} 26s ( c : a : a ) : 4 ~ {\displaystyle (c:a:a):{\tilde {4}}} ( 442 0 ) {\displaystyle (442_{0})} 82 I4 I 4 Γ q v S 4 2 {\displaystyle \Gamma _{q}^{v}S_{4}^{2}} 27s ( a + b + c 2 / c : a : a ) : 4 ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}} ( 442 1 ) {\displaystyle (442_{1})} 83 4/m 4 ∗ {\displaystyle 4*} P4/m P 4/m Γ q C 4 h 1 {\displaystyle \Gamma _{q}C_{4h}^{1}} 28s ( c : a : a ) ⋅ m : 4 {\displaystyle (c:a:a)\cdot m:4} [ 4 0 4 0 2 0 ] {\displaystyle [4_{0}4_{0}2_{0}]} 84 P42/m P 42/m Γ q C 4 h 2 {\displaystyle \Gamma _{q}C_{4h}^{2}} 41a ( c : a : a ) ⋅ m : 4 2 {\displaystyle (c:a:a)\cdot m:4_{2}} [ 4 2 4 2 2 0 ] {\displaystyle [4_{2}4_{2}2_{0}]} 85 P4/n P 4/n Γ q C 4 h 3 {\displaystyle \Gamma _{q}C_{4h}^{3}} 29h ( c : a : a ) ⋅ a b ~ : 4 {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4} ( 44 0 2 ) {\displaystyle (44_{0}2)} 86 P42/n P 42/n Γ q C 4 h 4 {\displaystyle \Gamma _{q}C_{4h}^{4}} 42a ( c : a : a ) ⋅ a b ~ : 4 2 {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}} ( 44 2 2 ) {\displaystyle (44_{2}2)} 87 I4/m I 4/m Γ q v C 4 h 5 {\displaystyle \Gamma _{q}^{v}C_{4h}^{5}} 29s ( a + b + c 2 / c : a : a ) ⋅ m : 4 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4} [ 4 2 4 0 2 1 ] {\displaystyle [4_{2}4_{0}2_{1}]} 88 I41/a I 41/a Γ q v C 4 h 6 {\displaystyle \Gamma _{q}^{v}C_{4h}^{6}} 40a ( a + b + c 2 / c : a : a ) ⋅ a ~ : 4 1 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}} ( 44 1 2 ) {\displaystyle (44_{1}2)} 89 422 224 {\displaystyle 224} P422 P 4 2 2 Γ q D 4 1 {\displaystyle \Gamma _{q}D_{4}^{1}} 30s ( c : a : a ) : 4 : 2 {\displaystyle (c:a:a):4:2} ( ∗ 4 0 4 0 2 0 ) {\displaystyle (*4_{0}4_{0}2_{0})} 90 P4212 P4212 Γ q D 4 2 {\displaystyle \Gamma _{q}D_{4}^{2}} 43a ( c : a : a ) : 4 {\displaystyle (c:a:a):4} 2 1 {\displaystyle 2_{1}} ( 4 0 ∗ 2 0 ) {\displaystyle (4_{0}{*}2_{0})} 91 P4122 P 41 2 2 Γ q D 4 3 {\displaystyle \Gamma _{q}D_{4}^{3}} 44a ( c : a : a ) : 4 1 : 2 {\displaystyle (c:a:a):4_{1}:2} ( ∗ 4 1 4 1 2 1 ) {\displaystyle (*4_{1}4_{1}2_{1})} 92 P41212 P 41 21 2 Γ q D 4 4 {\displaystyle \Gamma _{q}D_{4}^{4}} 48a ( c : a : a ) : 4 1 {\displaystyle (c:a:a):4_{1}} 2 1 {\displaystyle 2_{1}} ( 4 1 ∗ 2 1 ) {\displaystyle (4_{1}{*}2_{1})} 93 P4222 P 42 2 2 Γ q D 4 5 {\displaystyle \Gamma _{q}D_{4}^{5}} 47a ( c : a : a ) : 4 2 : 2 {\displaystyle (c:a:a):4_{2}:2} ( ∗ 4 2 4 2 2 0 ) {\displaystyle (*4_{2}4_{2}2_{0})} 94 P42212 P 42 21 2 Γ q D 4 6 {\displaystyle \Gamma _{q}D_{4}^{6}} 50a ( c : a : a ) : 4 2 {\displaystyle (c:a:a):4_{2}} 2 1 {\displaystyle 2_{1}} ( 4 2 ∗ 2 0 ) {\displaystyle (4_{2}{*}2_{0})} 95 P4322 P 43 2 2 Γ q D 4 7 {\displaystyle \Gamma _{q}D_{4}^{7}} 45a ( c : a : a ) : 4 3 : 2 {\displaystyle (c:a:a):4_{3}:2} ( ∗ 4 1 4 1 2 1 ) {\displaystyle (*4_{1}4_{1}2_{1})} 96 P43212 P 43 21 2 Γ q D 4 8 {\displaystyle \Gamma _{q}D_{4}^{8}} 49a ( c : a : a ) : 4 3 {\displaystyle (c:a:a):4_{3}} 2 1 {\displaystyle 2_{1}} ( 4 1 ∗ 2 1 ) {\displaystyle (4_{1}{*}2_{1})} 97 I422 I 4 2 2 Γ q v D 4 9 {\displaystyle \Gamma _{q}^{v}D_{4}^{9}} 31s ( a + b + c 2 / c : a : a ) : 4 : 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2} ( ∗ 4 2 4 0 2 1 ) {\displaystyle (*4_{2}4_{0}2_{1})} 98 I4122 I 41 2 2 Γ q v D 4 10 {\displaystyle \Gamma _{q}^{v}D_{4}^{10}} 46a ( a + b + c 2 / c : a : a ) : 4 : 2 1 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2_{1}} ( ∗ 4 3 4 1 2 0 ) {\displaystyle (*4_{3}4_{1}2_{0})} 99 4mm ∗ 44 {\displaystyle *44} P4mm P 4 m m Γ q C 4 v 1 {\displaystyle \Gamma _{q}C_{4v}^{1}} 24s ( c : a : a ) : 4 ⋅ m {\displaystyle (c:a:a):4\cdot m} ( ∗ ⋅ 4 ⋅ 4 ⋅ 2 ) {\displaystyle (*{\cdot }4{\cdot }4{\cdot }2)} 100 P4bm P 4 b m Γ q C 4 v 2 {\displaystyle \Gamma _{q}C_{4v}^{2}} 26h ( c : a : a ) : 4 ⊙ a ~ {\displaystyle (c:a:a):4\odot {\tilde {a}}} ( 4 0 ∗ ⋅ 2 ) {\displaystyle (4_{0}{*}{\cdot }2)} 101 P42cm P 42 c m Γ q C 4 v 3 {\displaystyle \Gamma _{q}C_{4v}^{3}} 37a ( c : a : a ) : 4 2 ⋅ c ~ {\displaystyle (c:a:a):4_{2}\cdot {\tilde {c}}} ( ∗ : 4 ⋅ 4 : 2 ) {\displaystyle (*{:}4{\cdot }4{:}2)} 102 P42nm P 42 n m Γ q C 4 v 4 {\displaystyle \Gamma _{q}C_{4v}^{4}} 38a ( c : a : a ) : 4 2 ⊙ a c ~ {\displaystyle (c:a:a):4_{2}\odot {\widetilde {ac}}} ( 4 2 ∗ ⋅ 2 ) {\displaystyle (4_{2}{*}{\cdot }2)} 103 P4cc P 4 c c Γ q C 4 v 5 {\displaystyle \Gamma _{q}C_{4v}^{5}} 25h ( c : a : a ) : 4 ⋅ c ~ {\displaystyle (c:a:a):4\cdot {\tilde {c}}} ( ∗ : 4 : 4 : 2 ) {\displaystyle (*{:}4{:}4{:}2)} 104 P4nc P 4 n c Γ q C 4 v 6 {\displaystyle \Gamma _{q}C_{4v}^{6}} 27h ( c : a : a ) : 4 ⊙ a c ~ {\displaystyle (c:a:a):4\odot {\widetilde {ac}}} ( 4 0 ∗ : 2 ) {\displaystyle (4_{0}{*}{:}2)} 105 P42mc P 42 m c Γ q C 4 v 7 {\displaystyle \Gamma _{q}C_{4v}^{7}} 36a ( c : a : a ) : 4 2 ⋅ m {\displaystyle (c:a:a):4_{2}\cdot m} ( ∗ ⋅ 4 : 4 ⋅ 2 ) {\displaystyle (*{\cdot }4{:}4{\cdot }2)} 106 P42bc P 42 b c Γ q C 4 v 8 {\displaystyle \Gamma _{q}C_{4v}^{8}} 39a ( c : a : a ) : 4 ⊙ a ~ {\displaystyle (c:a:a):4\odot {\tilde {a}}} ( 4 2 ∗ : 2 ) {\displaystyle (4_{2}{*}{:}2)} 107 I4mm I 4 m m Γ q v C 4 v 9 {\displaystyle \Gamma _{q}^{v}C_{4v}^{9}} 25s ( a + b + c 2 / c : a : a ) : 4 ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot m} ( ∗ ⋅ 4 ⋅ 4 : 2 ) {\displaystyle (*{\cdot }4{\cdot }4{:}2)} 108 I4cm I 4 c m Γ q v C 4 v 10 {\displaystyle \Gamma _{q}^{v}C_{4v}^{10}} 28h ( a + b + c 2 / c : a : a ) : 4 ⋅ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot {\tilde {c}}} ( ∗ ⋅ 4 : 4 : 2 ) {\displaystyle (*{\cdot }4{:}4{:}2)} 109 I41md I 41 m d Γ q v C 4 v 11 {\displaystyle \Gamma _{q}^{v}C_{4v}^{11}} 34a ( a + b + c 2 / c : a : a ) : 4 1 ⊙ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot m} ( 4 1 ∗ ⋅ 2 ) {\displaystyle (4_{1}{*}{\cdot }2)} 110 I41cd I 41 c d Γ q v C 4 v 12 {\displaystyle \Gamma _{q}^{v}C_{4v}^{12}} 35a ( a + b + c 2 / c : a : a ) : 4 1 ⊙ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot {\tilde {c}}} ( 4 1 ∗ : 2 ) {\displaystyle (4_{1}{*}{:}2)} 111 42m 2 ∗ 2 {\displaystyle 2{*}2} P42m P 4 2 m Γ q D 2 d 1 {\displaystyle \Gamma _{q}D_{2d}^{1}} 32s ( c : a : a ) : 4 ~ : 2 {\displaystyle (c:a:a):{\tilde {4}}:2} ( ∗ 4 ⋅ 42 0 ) {\displaystyle (*4{\cdot }42_{0})} 112 P42c P 4 2 c Γ q D 2 d 2 {\displaystyle \Gamma _{q}D_{2d}^{2}} 30h ( c : a : a ) : 4 ~ {\displaystyle (c:a:a):{\tilde {4}}} 2 {\displaystyle 2} ( ∗ 4 : 42 0 ) {\displaystyle (*4{:}42_{0})} 113 P421m P 4 21 m Γ q D 2 d 3 {\displaystyle \Gamma _{q}D_{2d}^{3}} 52a ( c : a : a ) : 4 ~ ⋅ a b ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {ab}}} ( 4 ∗ ¯ ⋅ 2 ) {\displaystyle (4{\bar {*}}{\cdot }2)} 114 P421c P 4 21 c Γ q D 2 d 4 {\displaystyle \Gamma _{q}D_{2d}^{4}} 53a ( c : a : a ) : 4 ~ ⋅ a b c ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {abc}}} ( 4 ∗ ¯ : 2 ) {\displaystyle (4{\bar {*}}{:}2)} 115 P4m2 P 4 m 2 Γ q D 2 d 5 {\displaystyle \Gamma _{q}D_{2d}^{5}} 33s ( c : a : a ) : 4 ~ ⋅ m {\displaystyle (c:a:a):{\tilde {4}}\cdot m} ( ∗ ⋅ 44 ⋅ 2 ) {\displaystyle (*{\cdot }44{\cdot }2)} 116 P4c2 P 4 c 2 Γ q D 2 d 6 {\displaystyle \Gamma _{q}D_{2d}^{6}} 31h ( c : a : a ) : 4 ~ ⋅ c ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\tilde {c}}} ( ∗ : 44 : 2 ) {\displaystyle (*{:}44{:}2)} 117 P4b2 P 4 b 2 Γ q D 2 d 7 {\displaystyle \Gamma _{q}D_{2d}^{7}} 32h ( c : a : a ) : 4 ~ ⊙ a ~ {\displaystyle (c:a:a):{\tilde {4}}\odot {\tilde {a}}} ( 4 ∗ ¯ 0 2 0 ) {\displaystyle (4{\bar {*}}_{0}2_{0})} 118 P4n2 P 4 n 2 Γ q D 2 d 8 {\displaystyle \Gamma _{q}D_{2d}^{8}} 33h ( c : a : a ) : 4 ~ ⋅ a c ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {ac}}} ( 4 ∗ ¯ 1 2 0 ) {\displaystyle (4{\bar {*}}_{1}2_{0})} 119 I4m2 I 4 m 2 Γ q v D 2 d 9 {\displaystyle \Gamma _{q}^{v}D_{2d}^{9}} 35s ( a + b + c 2 / c : a : a ) : 4 ~ ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot m} ( ∗ 4 ⋅ 42 1 ) {\displaystyle (*4{\cdot }42_{1})} 120 I4c2 I 4 c 2 Γ q v D 2 d 10 {\displaystyle \Gamma _{q}^{v}D_{2d}^{10}} 34h ( a + b + c 2 / c : a : a ) : 4 ~ ⋅ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot {\tilde {c}}} ( ∗ 4 : 42 1 ) {\displaystyle (*4{:}42_{1})} 121 I42m I 4 2 m Γ q v D 2 d 11 {\displaystyle \Gamma _{q}^{v}D_{2d}^{11}} 34s ( a + b + c 2 / c : a : a ) : 4 ~ : 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}:2} ( ∗ ⋅ 44 : 2 ) {\displaystyle (*{\cdot }44{:}2)} 122 I42d I 4 2 d Γ q v D 2 d 12 {\displaystyle \Gamma _{q}^{v}D_{2d}^{12}} 51a ( a + b + c 2 / c : a : a ) : 4 ~ ⊙ 1 2 a b c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\odot {\tfrac {1}{2}}{\widetilde {abc}}} ( 4 ∗ ¯ 2 1 ) {\displaystyle (4{\bar {*}}2_{1})} 123 4/m 2/m 2/m (4/mmm) ∗ 224 {\displaystyle *224} P4/mmm P 4/m 2/m 2/m Γ q D 4 h 1 {\displaystyle \Gamma _{q}D_{4h}^{1}} 36s ( c : a : a ) ⋅ m : 4 ⋅ m {\displaystyle (c:a:a)\cdot m:4\cdot m} [ ∗ ⋅ 4 ⋅ 4 ⋅ 2 ] {\displaystyle [*{\cdot }4{\cdot }4{\cdot }2]} 124 P4/mcc P 4/m 2/c 2/c Γ q D 4 h 2 {\displaystyle \Gamma _{q}D_{4h}^{2}} 35h ( c : a : a ) ⋅ m : 4 ⋅ c ~ {\displaystyle (c:a:a)\cdot m:4\cdot {\tilde {c}}} [ ∗ : 4 : 4 : 2 ] {\displaystyle [*{:}4{:}4{:}2]} 125 P4/nbm P 4/n 2/b 2/m Γ q D 4 h 3 {\displaystyle \Gamma _{q}D_{4h}^{3}} 36h ( c : a : a ) ⋅ a b ~ : 4 ⊙ a ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\odot {\tilde {a}}} ( ∗ 4 0 4 ⋅ 2 ) {\displaystyle (*4_{0}4{\cdot }2)} 126 P4/nnc P 4/n 2/n 2/c Γ q D 4 h 4 {\displaystyle \Gamma _{q}D_{4h}^{4}} 37h ( c : a : a ) ⋅ a b ~ : 4 ⊙ a c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\odot {\widetilde {ac}}} ( ∗ 4 0 4 : 2 ) {\displaystyle (*4_{0}4{:}2)} 127 P4/mbm P 4/m 21/b 2/m Γ q D 4 h 5 {\displaystyle \Gamma _{q}D_{4h}^{5}} 54a ( c : a : a ) ⋅ m : 4 ⊙ a ~ {\displaystyle (c:a:a)\cdot m:4\odot {\tilde {a}}} [ 4 0 ∗ ⋅ 2 ] {\displaystyle [4_{0}{*}{\cdot }2]} 128 P4/mnc P 4/m 21/n 2/c Γ q D 4 h 6 {\displaystyle \Gamma _{q}D_{4h}^{6}} 56a ( c : a : a ) ⋅ m : 4 ⊙ a c ~ {\displaystyle (c:a:a)\cdot m:4\odot {\widetilde {ac}}} [ 4 0 ∗ : 2 ] {\displaystyle [4_{0}{*}{:}2]} 129 P4/nmm P 4/n 21/m 2/m Γ q D 4 h 7 {\displaystyle \Gamma _{q}D_{4h}^{7}} 55a ( c : a : a ) ⋅ a b ~ : 4 ⋅ m {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\cdot m} ( ∗ 4 ⋅ 4 ⋅ 2 ) {\displaystyle (*4{\cdot }4{\cdot }2)} 130 P4/ncc P 4/n 21/c 2/c Γ q D 4 h 8 {\displaystyle \Gamma _{q}D_{4h}^{8}} 57a ( c : a : a ) ⋅ a b ~ : 4 ⋅ c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\cdot {\tilde {c}}} ( ∗ 4 : 4 : 2 ) {\displaystyle (*4{:}4{:}2)} 131 P42/mmc P 42/m 2/m 2/c Γ q D 4 h 9 {\displaystyle \Gamma _{q}D_{4h}^{9}} 60a ( c : a : a ) ⋅ m : 4 2 ⋅ m {\displaystyle (c:a:a)\cdot m:4_{2}\cdot m} [ ∗ ⋅ 4 : 4 ⋅ 2 ] {\displaystyle [*{\cdot }4{:}4{\cdot }2]} 132 P42/mcm P 42/m 2/c 2/m Γ q D 4 h 10 {\displaystyle \Gamma _{q}D_{4h}^{10}} 61a ( c : a : a ) ⋅ m : 4 2 ⋅ c ~ {\displaystyle (c:a:a)\cdot m:4_{2}\cdot {\tilde {c}}} [ ∗ : 4 ⋅ 4 : 2 ] {\displaystyle [*{:}4{\cdot }4{:}2]} 133 P42/nbc P 42/n 2/b 2/c Γ q D 4 h 11 {\displaystyle \Gamma _{q}D_{4h}^{11}} 63a ( c : a : a ) ⋅ a b ~ : 4 2 ⊙ a ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\tilde {a}}} ( ∗ 4 2 4 : 2 ) {\displaystyle (*4_{2}4{:}2)} 134 P42/nnm P 42/n 2/n 2/m Γ q D 4 h 12 {\displaystyle \Gamma _{q}D_{4h}^{12}} 62a ( c : a : a ) ⋅ a b ~ : 4 2 ⊙ a c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\widetilde {ac}}} ( ∗ 4 2 4 ⋅ 2 ) {\displaystyle (*4_{2}4{\cdot }2)} 135 P42/mbc P 42/m 21/b 2/c Γ q D 4 h 13 {\displaystyle \Gamma _{q}D_{4h}^{13}} 66a ( c : a : a ) ⋅ m : 4 2 ⊙ a ~ {\displaystyle (c:a:a)\cdot m:4_{2}\odot {\tilde {a}}} [ 4 2 ∗ : 2 ] {\displaystyle [4_{2}{*}{:}2]} 136 P42/mnm P 42/m 21/n 2/m Γ q D 4 h 14 {\displaystyle \Gamma _{q}D_{4h}^{14}} 65a ( c : a : a ) ⋅ m : 4 2 ⊙ a c ~ {\displaystyle (c:a:a)\cdot m:4_{2}\odot {\widetilde {ac}}} [ 4 2 ∗ ⋅ 2 ] {\displaystyle [4_{2}{*}{\cdot }2]} 137 P42/nmc P 42/n 21/m 2/c Γ q D 4 h 15 {\displaystyle \Gamma _{q}D_{4h}^{15}} 67a ( c : a : a ) ⋅ a b ~ : 4 2 ⋅ m {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot m} ( ∗ 4 ⋅ 4 : 2 ) {\displaystyle (*4{\cdot }4{:}2)} 138 P42/ncm P 42/n 21/c 2/m Γ q D 4 h 16 {\displaystyle \Gamma _{q}D_{4h}^{16}} 65a ( c : a : a ) ⋅ a b ~ : 4 2 ⋅ c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot {\tilde {c}}} ( ∗ 4 : 4 ⋅ 2 ) {\displaystyle (*4{:}4{\cdot }2)} 139 I4/mmm I 4/m 2/m 2/m Γ q v D 4 h 17 {\displaystyle \Gamma _{q}^{v}D_{4h}^{17}} 37s ( a + b + c 2 / c : a : a ) ⋅ m : 4 ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot m} [ ∗ ⋅ 4 ⋅ 4 : 2 ] {\displaystyle [*{\cdot }4{\cdot }4{:}2]} 140 I4/mcm I 4/m 2/c 2/m Γ q v D 4 h 18 {\displaystyle \Gamma _{q}^{v}D_{4h}^{18}} 38h ( a + b + c 2 / c : a : a ) ⋅ m : 4 ⋅ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot {\tilde {c}}} [ ∗ ⋅ 4 : 4 : 2 ] {\displaystyle [*{\cdot }4{:}4{:}2]} 141 I41/amd I 41/a 2/m 2/d Γ q v D 4 h 19 {\displaystyle \Gamma _{q}^{v}D_{4h}^{19}} 59a ( a + b + c 2 / c : a : a ) ⋅ a ~ : 4 1 ⊙ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot m} ( ∗ 4 1 4 ⋅ 2 ) {\displaystyle (*4_{1}4{\cdot }2)} 142 I41/acd I 41/a 2/c 2/d Γ q v D 4 h 20 {\displaystyle \Gamma _{q}^{v}D_{4h}^{20}} 58a ( a + b + c 2 / c : a : a ) ⋅ a ~ : 4 1 ⊙ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot {\tilde {c}}} ( ∗ 4 1 4 : 2 ) {\displaystyle (*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 {\displaystyle 33} P3 P 3 Γ h C 3 1 {\displaystyle \Gamma _{h}C_{3}^{1}} 38s ( c : ( a / a ) ) : 3 {\displaystyle (c:(a/a)):3} ( 3 0 3 0 3 0 ) {\displaystyle (3_{0}3_{0}3_{0})} 144 P31 P 31 Γ h C 3 2 {\displaystyle \Gamma _{h}C_{3}^{2}} 68a ( c : ( a / a ) ) : 3 1 {\displaystyle (c:(a/a)):3_{1}} ( 3 1 3 1 3 1 ) {\displaystyle (3_{1}3_{1}3_{1})} 145 P32 P 32 Γ h C 3 3 {\displaystyle \Gamma _{h}C_{3}^{3}} 69a ( c : ( a / a ) ) : 3 2 {\displaystyle (c:(a/a)):3_{2}} ( 3 1 3 1 3 1 ) {\displaystyle (3_{1}3_{1}3_{1})} 146 R3 R 3 Γ r h C 3 4 {\displaystyle \Gamma _{rh}C_{3}^{4}} 39s ( a / a / a ) / 3 {\displaystyle (a/a/a)/3} ( 3 0 3 1 3 2 ) {\displaystyle (3_{0}3_{1}3_{2})} 147 3 3 × {\displaystyle 3\times } P3 P 3 Γ h C 3 i 1 {\displaystyle \Gamma _{h}C_{3i}^{1}} 51s ( c : ( a / a ) ) : 6 ~ {\displaystyle (c:(a/a)):{\tilde {6}}} ( 63 0 2 ) {\displaystyle (63_{0}2)} 148 R3 R 3 Γ r h C 3 i 2 {\displaystyle \Gamma _{rh}C_{3i}^{2}} 52s ( a / a / a ) / 6 ~ {\displaystyle (a/a/a)/{\tilde {6}}} ( 63 1 2 ) {\displaystyle (63_{1}2)} 149 32 223 {\displaystyle 223} P312 P 3 1 2 Γ h D 3 1 {\displaystyle \Gamma _{h}D_{3}^{1}} 45s ( c : ( a / a ) ) : 2 : 3 {\displaystyle (c:(a/a)):2:3} ( ∗ 3 0 3 0 3 0 ) {\displaystyle (*3_{0}3_{0}3_{0})} 150 P321 P 3 2 1 Γ h D 3 2 {\displaystyle \Gamma _{h}D_{3}^{2}} 44s ( c : ( a / a ) ) ⋅ 2 : 3 {\displaystyle (c:(a/a))\cdot 2:3} ( 3 0 ∗ 3 0 ) {\displaystyle (3_{0}{*}3_{0})} 151 P3112 P 31 1 2 Γ h D 3 3 {\displaystyle \Gamma _{h}D_{3}^{3}} 72a ( c : ( a / a ) ) : 2 : 3 1 {\displaystyle (c:(a/a)):2:3_{1}} ( ∗ 3 1 3 1 3 1 ) {\displaystyle (*3_{1}3_{1}3_{1})} 152 P3121 P 31 2 1 Γ h D 3 4 {\displaystyle \Gamma _{h}D_{3}^{4}} 70a ( c : ( a / a ) ) ⋅ 2 : 3 1 {\displaystyle (c:(a/a))\cdot 2:3_{1}} ( 3 1 ∗ 3 1 ) {\displaystyle (3_{1}{*}3_{1})} 153 P3212 P 32 1 2 Γ h D 3 5 {\displaystyle \Gamma _{h}D_{3}^{5}} 73a ( c : ( a / a ) ) : 2 : 3 2 {\displaystyle (c:(a/a)):2:3_{2}} ( ∗ 3 1 3 1 3 1 ) {\displaystyle (*3_{1}3_{1}3_{1})} 154 P3221 P 32 2 1 Γ h D 3 6 {\displaystyle \Gamma _{h}D_{3}^{6}} 71a ( c : ( a / a ) ) ⋅ 2 : 3 2 {\displaystyle (c:(a/a))\cdot 2:3_{2}} ( 3 1 ∗ 3 1 ) {\displaystyle (3_{1}{*}3_{1})} 155 R32 R 3 2 Γ r h D 3 7 {\displaystyle \Gamma _{rh}D_{3}^{7}} 46s ( a / a / a ) / 3 : 2 {\displaystyle (a/a/a)/3:2} ( ∗ 3 0 3 1 3 2 ) {\displaystyle (*3_{0}3_{1}3_{2})} 156 3m ∗ 33 {\displaystyle *33} P3m1 P 3 m 1 Γ h C 3 v 1 {\displaystyle \Gamma _{h}C_{3v}^{1}} 40s ( c : ( a / a ) ) : m ⋅ 3 {\displaystyle (c:(a/a)):m\cdot 3} ( ∗ ⋅ 3 ⋅ 3 ⋅ 3 ) {\displaystyle (*{\cdot }3{\cdot }3{\cdot }3)} 157 P31m P 3 1 m Γ h C 3 v 2 {\displaystyle \Gamma _{h}C_{3v}^{2}} 41s ( c : ( a / a ) ) ⋅ m ⋅ 3 {\displaystyle (c:(a/a))\cdot m\cdot 3} ( 3 0 ∗ ⋅ 3 ) {\displaystyle (3_{0}{*}{\cdot }3)} 158 P3c1 P 3 c 1 Γ h C 3 v 3 {\displaystyle \Gamma _{h}C_{3v}^{3}} 39h ( c : ( a / a ) ) : c ~ : 3 {\displaystyle (c:(a/a)):{\tilde {c}}:3} ( ∗ : 3 : 3 : 3 ) {\displaystyle (*{:}3{:}3{:}3)} 159 P31c P 3 1 c Γ h C 3 v 4 {\displaystyle \Gamma _{h}C_{3v}^{4}} 40h ( c : ( a / a ) ) ⋅ c ~ : 3 {\displaystyle (c:(a/a))\cdot {\tilde {c}}:3} ( 3 0 ∗ : 3 ) {\displaystyle (3_{0}{*}{:}3)} 160 R3m R 3 m Γ r h C 3 v 5 {\displaystyle \Gamma _{rh}C_{3v}^{5}} 42s ( a / a / a ) / 3 ⋅ m {\displaystyle (a/a/a)/3\cdot m} ( 3 1 ∗ ⋅ 3 ) {\displaystyle (3_{1}{*}{\cdot }3)} 161 R3c R 3 c Γ r h C 3 v 6 {\displaystyle \Gamma _{rh}C_{3v}^{6}} 41h ( a / a / a ) / 3 ⋅ c ~ {\displaystyle (a/a/a)/3\cdot {\tilde {c}}} ( 3 1 ∗ : 3 ) {\displaystyle (3_{1}{*}{:}3)} 162 3 2/m (3m) 2 ∗ 3 {\displaystyle 2{*}3} P31m P 3 1 2/m Γ h D 3 d 1 {\displaystyle \Gamma _{h}D_{3d}^{1}} 56s ( c : ( a / a ) ) ⋅ m ⋅ 6 ~ {\displaystyle (c:(a/a))\cdot m\cdot {\tilde {6}}} ( ∗ ⋅ 63 0 2 ) {\displaystyle (*{\cdot }63_{0}2)} 163 P31c P 3 1 2/c Γ h D 3 d 2 {\displaystyle \Gamma _{h}D_{3d}^{2}} 46h ( c : ( a / a ) ) ⋅ c ~ ⋅ 6 ~ {\displaystyle (c:(a/a))\cdot {\tilde {c}}\cdot {\tilde {6}}} ( ∗ : 63 0 2 ) {\displaystyle (*{:}63_{0}2)} 164 P3m1 P 3 2/m 1 Γ h D 3 d 3 {\displaystyle \Gamma _{h}D_{3d}^{3}} 55s ( c : ( a / a ) ) : m ⋅ 6 ~ {\displaystyle (c:(a/a)):m\cdot {\tilde {6}}} ( ∗ 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*6{\cdot }3{\cdot }2)} 165 P3c1 P 3 2/c 1 Γ h D 3 d 4 {\displaystyle \Gamma _{h}D_{3d}^{4}} 45h ( c : ( a / a ) ) : c ~ ⋅ 6 ~ {\displaystyle (c:(a/a)):{\tilde {c}}\cdot {\tilde {6}}} ( ∗ 6 : 3 : 2 ) {\displaystyle (*6{:}3{:}2)} 166 R3m R 3 2/m Γ r h D 3 d 5 {\displaystyle \Gamma _{rh}D_{3d}^{5}} 57s ( a / a / a ) / 6 ~ ⋅ m {\displaystyle (a/a/a)/{\tilde {6}}\cdot m} ( ∗ ⋅ 63 1 2 ) {\displaystyle (*{\cdot }63_{1}2)} 167 R3c R 3 2/c Γ r h D 3 d 6 {\displaystyle \Gamma _{rh}D_{3d}^{6}} 47h ( a / a / a ) / 6 ~ ⋅ c ~ {\displaystyle (a/a/a)/{\tilde {6}}\cdot {\tilde {c}}} ( ∗ : 63 1 2 ) {\displaystyle (*{:}63_{1}2)}

## List of hexagonal

Hexagonal Bravais lattice

Hexagonal crystal system Number Point group Orbifold Short name Full name Schoenflies Fedorov Shubnikov Fibrifold 168 6 66 {\displaystyle 66} P6 P 6 Γ h C 6 1 {\displaystyle \Gamma _{h}C_{6}^{1}} 49s ( c : ( a / a ) ) : 6 {\displaystyle (c:(a/a)):6} ( 6 0 3 0 2 0 ) {\displaystyle (6_{0}3_{0}2_{0})} 169 P61 P 61 Γ h C 6 2 {\displaystyle \Gamma _{h}C_{6}^{2}} 74a ( c : ( a / a ) ) : 6 1 {\displaystyle (c:(a/a)):6_{1}} ( 6 1 3 1 2 1 ) {\displaystyle (6_{1}3_{1}2_{1})} 170 P65 P 65 Γ h C 6 3 {\displaystyle \Gamma _{h}C_{6}^{3}} 75a ( c : ( a / a ) ) : 6 5 {\displaystyle (c:(a/a)):6_{5}} ( 6 1 3 1 2 1 ) {\displaystyle (6_{1}3_{1}2_{1})} 171 P62 P 62 Γ h C 6 4 {\displaystyle \Gamma _{h}C_{6}^{4}} 76a ( c : ( a / a ) ) : 6 2 {\displaystyle (c:(a/a)):6_{2}} ( 6 2 3 2 2 0 ) {\displaystyle (6_{2}3_{2}2_{0})} 172 P64 P 64 Γ h C 6 5 {\displaystyle \Gamma _{h}C_{6}^{5}} 77a ( c : ( a / a ) ) : 6 4 {\displaystyle (c:(a/a)):6_{4}} ( 6 2 3 2 2 0 ) {\displaystyle (6_{2}3_{2}2_{0})} 173 P63 P 63 Γ h C 6 6 {\displaystyle \Gamma _{h}C_{6}^{6}} 78a ( c : ( a / a ) ) : 6 3 {\displaystyle (c:(a/a)):6_{3}} ( 6 3 3 0 2 1 ) {\displaystyle (6_{3}3_{0}2_{1})} 174 6 3 ∗ {\displaystyle 3*} P6 P 6 Γ h C 3 h 1 {\displaystyle \Gamma _{h}C_{3h}^{1}} 43s ( c : ( a / a ) ) : 3 : m {\displaystyle (c:(a/a)):3:m} [ 3 0 3 0 3 0 ] {\displaystyle [3_{0}3_{0}3_{0}]} 175 6/m 6 ∗ {\displaystyle 6*} P6/m P 6/m Γ h C 6 h 1 {\displaystyle \Gamma _{h}C_{6h}^{1}} 53s ( c : ( a / a ) ) ⋅ m : 6 {\displaystyle (c:(a/a))\cdot m:6} [ 6 0 3 0 2 0 ] {\displaystyle [6_{0}3_{0}2_{0}]} 176 P63/m P 63/m Γ h C 6 h 2 {\displaystyle \Gamma _{h}C_{6h}^{2}} 81a ( c : ( a / a ) ) ⋅ m : 6 3 {\displaystyle (c:(a/a))\cdot m:6_{3}} [ 6 3 3 0 2 1 ] {\displaystyle [6_{3}3_{0}2_{1}]} 177 622 226 {\displaystyle 226} P622 P 6 2 2 Γ h D 6 1 {\displaystyle \Gamma _{h}D_{6}^{1}} 54s ( c : ( a / a ) ) ⋅ 2 : 6 {\displaystyle (c:(a/a))\cdot 2:6} ( ∗ 6 0 3 0 2 0 ) {\displaystyle (*6_{0}3_{0}2_{0})} 178 P6122 P 61 2 2 Γ h D 6 2 {\displaystyle \Gamma _{h}D_{6}^{2}} 82a ( c : ( a / a ) ) ⋅ 2 : 6 1 {\displaystyle (c:(a/a))\cdot 2:6_{1}} ( ∗ 6 1 3 1 2 1 ) {\displaystyle (*6_{1}3_{1}2_{1})} 179 P6522 P 65 2 2 Γ h D 6 3 {\displaystyle \Gamma _{h}D_{6}^{3}} 83a ( c : ( a / a ) ) ⋅ 2 : 6 5 {\displaystyle (c:(a/a))\cdot 2:6_{5}} ( ∗ 6 1 3 1 2 1 ) {\displaystyle (*6_{1}3_{1}2_{1})} 180 P6222 P 62 2 2 Γ h D 6 4 {\displaystyle \Gamma _{h}D_{6}^{4}} 84a ( c : ( a / a ) ) ⋅ 2 : 6 2 {\displaystyle (c:(a/a))\cdot 2:6_{2}} ( ∗ 6 2 3 2 2 0 ) {\displaystyle (*6_{2}3_{2}2_{0})} 181 P6422 P 64 2 2 Γ h D 6 5 {\displaystyle \Gamma _{h}D_{6}^{5}} 85a ( c : ( a / a ) ) ⋅ 2 : 6 4 {\displaystyle (c:(a/a))\cdot 2:6_{4}} ( ∗ 6 2 3 2 2 0 ) {\displaystyle (*6_{2}3_{2}2_{0})} 182 P6322 P 63 2 2 Γ h D 6 6 {\displaystyle \Gamma _{h}D_{6}^{6}} 86a ( c : ( a / a ) ) ⋅ 2 : 6 3 {\displaystyle (c:(a/a))\cdot 2:6_{3}} ( ∗ 6 3 3 0 2 1 ) {\displaystyle (*6_{3}3_{0}2_{1})} 183 6mm ∗ 66 {\displaystyle *66} P6mm P 6 m m Γ h C 6 v 1 {\displaystyle \Gamma _{h}C_{6v}^{1}} 50s ( c : ( a / a ) ) : m ⋅ 6 {\displaystyle (c:(a/a)):m\cdot 6} ( ∗ ⋅ 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*{\cdot }6{\cdot }3{\cdot }2)} 184 P6cc P 6 c c Γ h C 6 v 2 {\displaystyle \Gamma _{h}C_{6v}^{2}} 44h ( c : ( a / a ) ) : c ~ ⋅ 6 {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6} ( ∗ : 6 : 3 : 2 ) {\displaystyle (*{:}6{:}3{:}2)} 185 P63cm P 63 c m Γ h C 6 v 3 {\displaystyle \Gamma _{h}C_{6v}^{3}} 80a ( c : ( a / a ) ) : c ~ ⋅ 6 3 {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6_{3}} ( ∗ ⋅ 6 : 3 : 2 ) {\displaystyle (*{\cdot }6{:}3{:}2)} 186 P63mc P 63 m c Γ h C 6 v 4 {\displaystyle \Gamma _{h}C_{6v}^{4}} 79a ( c : ( a / a ) ) : m ⋅ 6 3 {\displaystyle (c:(a/a)):m\cdot 6_{3}} ( ∗ : 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*{:}6{\cdot }3{\cdot }2)} 187 6m2 ∗ 223 {\displaystyle *223} P6m2 P 6 m 2 Γ h D 3 h 1 {\displaystyle \Gamma _{h}D_{3h}^{1}} 48s ( c : ( a / a ) ) : m ⋅ 3 : m {\displaystyle (c:(a/a)):m\cdot 3:m} [ ∗ ⋅ 3 ⋅ 3 ⋅ 3 ] {\displaystyle [*{\cdot }3{\cdot }3{\cdot }3]} 188 P6c2 P 6 c 2 Γ h D 3 h 2 {\displaystyle \Gamma _{h}D_{3h}^{2}} 43h ( c : ( a / a ) ) : c ~ ⋅ 3 : m {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 3:m} [ ∗ : 3 : 3 : 3 ] {\displaystyle [*{:}3{:}3{:}3]} 189 P62m P 6 2 m Γ h D 3 h 3 {\displaystyle \Gamma _{h}D_{3h}^{3}} 47s ( c : ( a / a ) ) ⋅ m : 3 ⋅ m {\displaystyle (c:(a/a))\cdot m:3\cdot m} [ 3 0 ∗ ⋅ 3 ] {\displaystyle [3_{0}{*}{\cdot }3]} 190 P62c P 6 2 c Γ h D 3 h 4 {\displaystyle \Gamma _{h}D_{3h}^{4}} 42h ( c : ( a / a ) ) ⋅ m : 3 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:3\cdot {\tilde {c}}} [ 3 0 ∗ : 3 ] {\displaystyle [3_{0}{*}{:}3]} 191 6/m 2/m 2/m (6/mmm) ∗ 226 {\displaystyle *226} P6/mmm P 6/m 2/m 2/m Γ h D 6 h 1 {\displaystyle \Gamma _{h}D_{6h}^{1}} 58s ( c : ( a / a ) ) ⋅ m : 6 ⋅ m {\displaystyle (c:(a/a))\cdot m:6\cdot m} [ ∗ ⋅ 6 ⋅ 3 ⋅ 2 ] {\displaystyle [*{\cdot }6{\cdot }3{\cdot }2]} 192 P6/mcc P 6/m 2/c 2/c Γ h D 6 h 2 {\displaystyle \Gamma _{h}D_{6h}^{2}} 48h ( c : ( a / a ) ) ⋅ m : 6 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:6\cdot {\tilde {c}}} [ ∗ : 6 : 3 : 2 ] {\displaystyle [*{:}6{:}3{:}2]} 193 P63/mcm P 63/m 2/c 2/m Γ h D 6 h 3 {\displaystyle \Gamma _{h}D_{6h}^{3}} 87a ( c : ( a / a ) ) ⋅ m : 6 3 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:6_{3}\cdot {\tilde {c}}} [ ∗ ⋅ 6 : 3 : 2 ] {\displaystyle [*{\cdot }6{:}3{:}2]} 194 P63/mmc P 63/m 2/m 2/c Γ h D 6 h 4 {\displaystyle \Gamma _{h}D_{6h}^{4}} 88a ( c : ( a / a ) ) ⋅ m : 6 3 ⋅ m {\displaystyle (c:(a/a))\cdot m:6_{3}\cdot m} [ ∗ : 6 ⋅ 3 ⋅ 2 ] {\displaystyle [*{:}6{\cdot }3{\cdot }2]}

## List of cubic

Cubic Bravais lattice Simple (P) Body centered (I) Face centered (F)

Example cubic structures

		- (221) [Caesium chloride](/source/Caesium_chloride). Different colors for the two atom types.

		- (216) [Sphalerite](/source/Sphalerite)

		- (223) [Weaire–Phelan structure](/source/Weaire%E2%80%93Phelan_structure)

Cubic crystal system Number Point group Orbifold Short name Full name Schoenflies Fedorov Shubnikov Conway Fibrifold (preserving z {\displaystyle z} ) Fibrifold (preserving x {\displaystyle x} , y {\displaystyle y} , z {\displaystyle z} ) 195 23 332 {\displaystyle 332} P23 P 2 3 Γ c T 1 {\displaystyle \Gamma _{c}T^{1}} 59s ( a : a : a ) : 2 / 3 {\displaystyle \left(a:a:a\right):2/3} 2 ∘ {\displaystyle 2^{\circ }} ( ∗ 2 0 2 0 2 0 2 0 ) : 3 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}3} ( ∗ 2 0 2 0 2 0 2 0 ) : 3 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}3} 196 F23 F 2 3 Γ c f T 2 {\displaystyle \Gamma _{c}^{f}T^{2}} 61s ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 2 / 3 {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):2/3} 1 ∘ {\displaystyle 1^{\circ }} ( ∗ 2 0 2 1 2 0 2 1 ) : 3 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}3} ( ∗ 2 0 2 1 2 0 2 1 ) : 3 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}3} 197 I23 I 2 3 Γ c v T 3 {\displaystyle \Gamma _{c}^{v}T^{3}} 60s ( a + b + c 2 / a : a : a ) : 2 / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):2/3} 4 ∘ ∘ {\displaystyle 4^{\circ \circ }} ( 2 1 ∗ 2 0 2 0 ) : 3 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}3} ( 2 1 ∗ 2 0 2 0 ) : 3 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}3} 198 P213 P 21 3 Γ c T 4 {\displaystyle \Gamma _{c}T^{4}} 89a ( a : a : a ) : 2 1 / 3 {\displaystyle \left(a:a:a\right):2_{1}/3} 1 ∘ / 4 {\displaystyle 1^{\circ }/4} ( 2 1 2 1 × ¯ ) : 3 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}3} ( 2 1 2 1 × ¯ ) : 3 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}3} 199 I213 I 21 3 Γ c v T 5 {\displaystyle \Gamma _{c}^{v}T^{5}} 90a ( a + b + c 2 / a : a : a ) : 2 1 / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):2_{1}/3} 2 ∘ / 4 {\displaystyle 2^{\circ }/4} ( 2 0 ∗ 2 1 2 1 ) : 3 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}3} ( 2 0 ∗ 2 1 2 1 ) : 3 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}3} 200 2/m 3 (m3) 3 ∗ 2 {\displaystyle 3{*}2} Pm3 P 2/m 3 Γ c T h 1 {\displaystyle \Gamma _{c}T_{h}^{1}} 62s ( a : a : a ) ⋅ m / 6 ~ {\displaystyle \left(a:a:a\right)\cdot m/{\tilde {6}}} 4 − {\displaystyle 4^{-}} [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3} [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3} 201 Pn3 P 2/n 3 Γ c T h 2 {\displaystyle \Gamma _{c}T_{h}^{2}} 49h ( a : a : a ) ⋅ a b ~ / 6 ~ {\displaystyle \left(a:a:a\right)\cdot {\widetilde {ab}}/{\tilde {6}}} 4 ∘ + {\displaystyle 4^{\circ +}} ( 2 ∗ ¯ 1 2 0 2 0 ) : 3 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}3} ( 2 ∗ ¯ 1 2 0 2 0 ) : 3 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}3} 202 Fm3 F 2/m 3 Γ c f T h 3 {\displaystyle \Gamma _{c}^{f}T_{h}^{3}} 64s ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) ⋅ m / 6 ~ {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right)\cdot m/{\tilde {6}}} 2 − {\displaystyle 2^{-}} [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}3} [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}3} 203 Fd3 F 2/d 3 Γ c f T h 4 {\displaystyle \Gamma _{c}^{f}T_{h}^{4}} 50h ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) ⋅ 1 2 a b ~ / 6 ~ {\displaystyle \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 ∘ + {\displaystyle 2^{\circ +}} ( 2 ∗ ¯ 2 0 2 1 ) : 3 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}3} ( 2 ∗ ¯ 2 0 2 1 ) : 3 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}3} 204 Im3 I 2/m 3 Γ c v T h 5 {\displaystyle \Gamma _{c}^{v}T_{h}^{5}} 63s ( a + b + c 2 / a : a : a ) ⋅ m / 6 ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot m/{\tilde {6}}} 8 − ∘ {\displaystyle 8^{-\circ }} [ 2 1 ∗ ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}3} [ 2 1 ∗ ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}3} 205 Pa3 P 21/a 3 Γ c T h 6 {\displaystyle \Gamma _{c}T_{h}^{6}} 91a ( a : a : a ) ⋅ a ~ / 6 ~ {\displaystyle \left(a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}} 2 − / 4 {\displaystyle 2^{-}/4} ( 2 1 2 ∗ ¯ : ) : 3 {\displaystyle (2_{1}2{\bar {*}}{:}){:}3} ( 2 1 2 ∗ ¯ : ) : 3 {\displaystyle (2_{1}2{\bar {*}}{:}){:}3} 206 Ia3 I 21/a 3 Γ c v T h 7 {\displaystyle \Gamma _{c}^{v}T_{h}^{7}} 92a ( a + b + c 2 / a : a : a ) ⋅ a ~ / 6 ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}} 4 − / 4 {\displaystyle 4^{-}/4} ( ∗ 2 1 2 : 2 : 2 ) : 3 {\displaystyle (*2_{1}2{:}2{:}2){:}3} ( ∗ 2 1 2 : 2 : 2 ) : 3 {\displaystyle (*2_{1}2{:}2{:}2){:}3} 207 432 432 {\displaystyle 432} P432 P 4 3 2 Γ c O 1 {\displaystyle \Gamma _{c}O^{1}} 68s ( a : a : a ) : 4 / 3 {\displaystyle \left(a:a:a\right):4/3} 4 ∘ − {\displaystyle 4^{\circ -}} ( ∗ 4 0 4 0 2 0 ) : 3 {\displaystyle (*4_{0}4_{0}2_{0}){:}3} ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} 208 P4232 P 42 3 2 Γ c O 2 {\displaystyle \Gamma _{c}O^{2}} 98a ( a : a : a ) : 4 2 / / 3 {\displaystyle \left(a:a:a\right):4_{2}//3} 4 + {\displaystyle 4^{+}} ( ∗ 4 2 4 2 2 0 ) : 3 {\displaystyle (*4_{2}4_{2}2_{0}){:}3} ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} 209 F432 F 4 3 2 Γ c f O 3 {\displaystyle \Gamma _{c}^{f}O^{3}} 70s ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 / 3 {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/3} 2 ∘ − {\displaystyle 2^{\circ -}} ( ∗ 4 2 4 0 2 1 ) : 3 {\displaystyle (*4_{2}4_{0}2_{1}){:}3} ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} 210 F4132 F 41 3 2 Γ c f O 4 {\displaystyle \Gamma _{c}^{f}O^{4}} 97a ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 1 / / 3 {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//3} 2 + {\displaystyle 2^{+}} ( ∗ 4 3 4 1 2 0 ) : 3 {\displaystyle (*4_{3}4_{1}2_{0}){:}3} ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} 211 I432 I 4 3 2 Γ c v O 5 {\displaystyle \Gamma _{c}^{v}O^{5}} 69s ( a + b + c 2 / a : a : a ) : 4 / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):4/3} 8 + ∘ {\displaystyle 8^{+\circ }} ( 4 2 4 0 2 1 ) : 3 {\displaystyle (4_{2}4_{0}2_{1}){:}3} ( 2 1 ∗ 2 0 2 0 ) : 6 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}6} 212 P4332 P 43 3 2 Γ c O 6 {\displaystyle \Gamma _{c}O^{6}} 94a ( a : a : a ) : 4 3 / / 3 {\displaystyle \left(a:a:a\right):4_{3}//3} 2 + / 4 {\displaystyle 2^{+}/4} ( 4 1 ∗ 2 1 ) : 3 {\displaystyle (4_{1}{*}2_{1}){:}3} ( 2 1 2 1 × ¯ ) : 6 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}6} 213 P4132 P 41 3 2 Γ c O 7 {\displaystyle \Gamma _{c}O^{7}} 95a ( a : a : a ) : 4 1 / / 3 {\displaystyle \left(a:a:a\right):4_{1}//3} 2 + / 4 {\displaystyle 2^{+}/4} ( 4 1 ∗ 2 1 ) : 3 {\displaystyle (4_{1}{*}2_{1}){:}3} ( 2 1 2 1 × ¯ ) : 6 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}6} 214 I4132 I 41 3 2 Γ c v O 8 {\displaystyle \Gamma _{c}^{v}O^{8}} 96a ( a + b + c 2 / : a : a : a ) : 4 1 / / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/:a:a:a\right):4_{1}//3} 4 + / 4 {\displaystyle 4^{+}/4} ( ∗ 4 3 4 1 2 0 ) : 3 {\displaystyle (*4_{3}4_{1}2_{0}){:}3} ( 2 0 ∗ 2 1 2 1 ) : 6 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}6} 215 43m ∗ 332 {\displaystyle *332} P43m P 4 3 m Γ c T d 1 {\displaystyle \Gamma _{c}T_{d}^{1}} 65s ( a : a : a ) : 4 ~ / 3 {\displaystyle \left(a:a:a\right):{\tilde {4}}/3} 2 ∘ : 2 {\displaystyle 2^{\circ }{:}2} ( ∗ 4 ⋅ 42 0 ) : 3 {\displaystyle (*4{\cdot }42_{0}){:}3} ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} 216 F43m F 4 3 m Γ c f T d 2 {\displaystyle \Gamma _{c}^{f}T_{d}^{2}} 67s ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 ~ / 3 {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}/3} 1 ∘ : 2 {\displaystyle 1^{\circ }{:}2} ( ∗ 4 ⋅ 42 1 ) : 3 {\displaystyle (*4{\cdot }42_{1}){:}3} ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} 217 I43m I 4 3 m Γ c v T d 3 {\displaystyle \Gamma _{c}^{v}T_{d}^{3}} 66s ( a + b + c 2 / a : a : a ) : 4 ~ / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}/3} 4 ∘ : 2 {\displaystyle 4^{\circ }{:}2} ( ∗ ⋅ 44 : 2 ) : 3 {\displaystyle (*{\cdot }44{:}2){:}3} ( 2 1 ∗ 2 0 2 0 ) : 6 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}6} 218 P43n P 4 3 n Γ c T d 4 {\displaystyle \Gamma _{c}T_{d}^{4}} 51h ( a : a : a ) : 4 ~ / / 3 {\displaystyle \left(a:a:a\right):{\tilde {4}}//3} 4 ∘ {\displaystyle 4^{\circ }} ( ∗ 4 : 42 0 ) : 3 {\displaystyle (*4{:}42_{0}){:}3} ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} 219 F43c F 4 3 c Γ c f T d 5 {\displaystyle \Gamma _{c}^{f}T_{d}^{5}} 52h ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 ~ / / 3 {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}//3} 2 ∘ ∘ {\displaystyle 2^{\circ \circ }} ( ∗ 4 : 42 1 ) : 3 {\displaystyle (*4{:}42_{1}){:}3} ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} 220 I43d I 4 3 d Γ c v T d 6 {\displaystyle \Gamma _{c}^{v}T_{d}^{6}} 93a ( a + b + c 2 / a : a : a ) : 4 ~ / / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}//3} 4 ∘ / 4 {\displaystyle 4^{\circ }/4} ( 4 ∗ ¯ 2 1 ) : 3 {\displaystyle (4{\bar {*}}2_{1}){:}3} ( 2 0 ∗ 2 1 2 1 ) : 6 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}6} 221 4/m 3 2/m (m3m) ∗ 432 {\displaystyle *432} Pm3m P 4/m 3 2/m Γ c O h 1 {\displaystyle \Gamma _{c}O_{h}^{1}} 71s ( a : a : a ) : 4 / 6 ~ ⋅ m {\displaystyle \left(a:a:a\right):4/{\tilde {6}}\cdot m} 4 − : 2 {\displaystyle 4^{-}{:}2} [ ∗ ⋅ 4 ⋅ 4 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }4{\cdot }4{\cdot }2]{:}3} [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6} 222 Pn3n P 4/n 3 2/n Γ c O h 2 {\displaystyle \Gamma _{c}O_{h}^{2}} 53h ( a : a : a ) : 4 / 6 ~ ⋅ a b c ~ {\displaystyle \left(a:a:a\right):4/{\tilde {6}}\cdot {\widetilde {abc}}} 8 ∘ ∘ {\displaystyle 8^{\circ \circ }} ( ∗ 4 0 4 : 2 ) : 3 {\displaystyle (*4_{0}4{:}2){:}3} ( 2 ∗ ¯ 1 2 0 2 0 ) : 6 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}6} 223 Pm3n P 42/m 3 2/n Γ c O h 3 {\displaystyle \Gamma _{c}O_{h}^{3}} 102a ( a : a : a ) : 4 2 / / 6 ~ ⋅ a b c ~ {\displaystyle \left(a:a:a\right):4_{2}//{\tilde {6}}\cdot {\widetilde {abc}}} 8 ∘ {\displaystyle 8^{\circ }} [ ∗ ⋅ 4 : 4 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }4{:}4{\cdot }2]{:}3} [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6} 224 Pn3m P 42/n 3 2/m Γ c O h 4 {\displaystyle \Gamma _{c}O_{h}^{4}} 103a ( a : a : a ) : 4 2 / / 6 ~ ⋅ m {\displaystyle \left(a:a:a\right):4_{2}//{\tilde {6}}\cdot m} 4 + : 2 {\displaystyle 4^{+}{:}2} ( ∗ 4 2 4 ⋅ 2 ) : 3 {\displaystyle (*4_{2}4{\cdot }2){:}3} ( 2 ∗ ¯ 1 2 0 2 0 ) : 6 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}6} 225 Fm3m F 4/m 3 2/m Γ c f O h 5 {\displaystyle \Gamma _{c}^{f}O_{h}^{5}} 73s ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 / 6 ~ ⋅ m {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot m} 2 − : 2 {\displaystyle 2^{-}{:}2} [ ∗ ⋅ 4 ⋅ 4 : 2 ] : 3 {\displaystyle [*{\cdot }4{\cdot }4{:}2]{:}3} [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}6} 226 Fm3c F 4/m 3 2/c Γ c f O h 6 {\displaystyle \Gamma _{c}^{f}O_{h}^{6}} 54h ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 / 6 ~ ⋅ c ~ {\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot {\tilde {c}}} 4 − − {\displaystyle 4^{--}} [ ∗ ⋅ 4 : 4 : 2 ] : 3 {\displaystyle [*{\cdot }4{:}4{:}2]{:}3} [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}6} 227 Fd3m F 41/d 3 2/m Γ c f O h 7 {\displaystyle \Gamma _{c}^{f}O_{h}^{7}} 100a ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 1 / / 6 ~ ⋅ m {\displaystyle \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 {\displaystyle 2^{+}{:}2} ( ∗ 4 1 4 ⋅ 2 ) : 3 {\displaystyle (*4_{1}4{\cdot }2){:}3} ( 2 ∗ ¯ 2 0 2 1 ) : 6 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}6} 228 Fd3c F 41/d 3 2/c Γ c f O h 8 {\displaystyle \Gamma _{c}^{f}O_{h}^{8}} 101a ( a + c 2 / b + c 2 / a + b 2 : a : a : a ) : 4 1 / / 6 ~ ⋅ c ~ {\displaystyle \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 + + {\displaystyle 4^{++}} ( ∗ 4 1 4 : 2 ) : 3 {\displaystyle (*4_{1}4{:}2){:}3} ( 2 ∗ ¯ 2 0 2 1 ) : 6 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}6} 229 Im3m I 4/m 3 2/m Γ c v O h 9 {\displaystyle \Gamma _{c}^{v}O_{h}^{9}} 72s ( a + b + c 2 / a : a : a ) : 4 / 6 ~ ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):4/{\tilde {6}}\cdot m} 8 ∘ : 2 {\displaystyle 8^{\circ }{:}2} [ ∗ ⋅ 4 ⋅ 4 : 2 ] : 3 {\displaystyle [*{\cdot }4{\cdot }4{:}2]{:}3} [ 2 1 ∗ ⋅ 2 ⋅ 2 ] : 6 {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}6} 230 Ia3d I 41/a 3 2/d Γ c v O h 10 {\displaystyle \Gamma _{c}^{v}O_{h}^{10}} 99a ( a + b + c 2 / a : a : a ) : 4 1 / / 6 ~ ⋅ 1 2 a b c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):4_{1}//{\tilde {6}}\cdot {\tfrac {1}{2}}{\widetilde {abc}}} 8 ∘ / 4 {\displaystyle 8^{\circ }/4} ( ∗ 4 1 4 : 2 ) : 3 {\displaystyle (*4_{1}4{:}2){:}3} ( ∗ 2 1 2 : 2 : 2 ) : 6 {\displaystyle (*2_{1}2{:}2{:}2){:}6}

## Notes

1. **[^](#cite_ref-e_2-0)** The symbol e {\displaystyle e} was introduced by the [IUCR](/source/International_Union_of_Crystallography) in 1992. Prior to this, the space groups Aem2 (No. 39), Aea2 (No. 41), Cmce (No. 64), Cmme (No. 67), and Ccce (No. 68) were known as Abm2 (No. 39), Aba2 (No. 41), Cmca (No. 64), Cmma (No. 67), and Ccca (No. 68) respectively. Historical literature may refer to the old names, but their meaning is unchanged.[1]

## References

1. **[^](#cite_ref-1)** de Wolff, P. M.; Billiet, Y.; Donnay, J. D. H.; Fischer, W.; Galiulin, R. B.; Glazer, A. M.; Hahn, T.; Senechal, M.; Shoemaker, D. P.; Wondratschek, H.; Wilson, A. J. C.; Abrahams, S. C. (1992-09-01). ["Symbols for symmetry elements and symmetry operations. Final report of the IUCr Ad-Hoc Committee on the Nomenclature of Symmetry"](https://doi.org/10.1107%2Fs0108767392003428). *Acta Crystallographica Section A*. **48** (5): 727–732. [Bibcode](/source/Bibcode_(identifier)):[1992AcCrA..48..727D](https://ui.adsabs.harvard.edu/abs/1992AcCrA..48..727D). [doi](/source/Doi_(identifier)):[10.1107/s0108767392003428](https://doi.org/10.1107%2Fs0108767392003428). [ISSN](/source/ISSN_(identifier)) [0108-7673](https://search.worldcat.org/issn/0108-7673).

1. **[^](#cite_ref-3)** Bradley, C. J.; Cracknell, A. P. (2010). *The mathematical theory of symmetry in solids: representation theory for point groups and space groups*. Oxford New York: Clarendon Press. pp. 127–134. [ISBN](/source/ISBN_(identifier)) [978-0-19-958258-7](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-958258-7). [OCLC](/source/OCLC_(identifier)) [859155300](https://search.worldcat.org/oclc/859155300).

## External links

Wikimedia Commons has media related to [Space groups](https://commons.wikimedia.org/wiki/Category:Space_groups).

- [International Union of Crystallography](https://www.iucr.org/)

- [Point Groups and Bravais Lattices](http://neon.mems.cmu.edu/degraef/pointgroups/)

- [Full list of 230 crystallographic space groups](http://img.chem.ucl.ac.uk/sgp/mainmenu.htm)

- [Conway et al. on fibrifold notation](https://www.emis.de/journals/BAG/vol.42/no.2/b42h2con.pdf)

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