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 {\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.1
A gyration point can be replaced by a 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| 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 (C) |
|---|---|
| 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 (A or C) |
|---|---|---|---|
| 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 {\displaystyle {\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} | ∗ 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) |
|---|---|
| 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 | ∗ 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) |
|---|---|
| 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 | 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| 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 | ∗ 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) |
|---|---|---|
| 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 | 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 | ∗ 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
External links
Wikimedia Commons has media related to Space groups.- International Union of Crystallography
- Point Groups and Bravais Lattices
- Full list of 230 crystallographic space groups
- Conway et al. on fibrifold notation
References
The symbol e {\displaystyle e} was introduced by the IUCR 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] /wiki/International_Union_of_Crystallography ↩
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 978-0-19-958258-7. OCLC 859155300. 978-0-19-958258-7 ↩