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)
  • 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, 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.

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.

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
NumberPoint groupOrbifoldShort nameFull nameSchoenfliesFedorovShubnikovFibrifold
111 {\displaystyle 1}P1P 1Γ t C 1 1 {\displaystyle \Gamma _{t}C_{1}^{1}}1s( a / b / c ) ⋅ 1 {\displaystyle (a/b/c)\cdot 1}( ∘ ) {\displaystyle (\circ )}
21× {\displaystyle \times }P1P 1Γ 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
NumberPoint groupOrbifoldShort nameFull name(s)SchoenfliesFedorovShubnikovFibrifold (primary)Fibrifold (secondary)
3222 {\displaystyle 22}P2P 1 2 1P 1 1 2Γ 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})}
4P21P 1 21 1P 1 1 21Γ 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 }})}
5C2C 1 2 1B 1 1 2Γ 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 }})}
6m∗ {\displaystyle *}PmP 1 m 1P 1 1 mΓ 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 })}
7PcP 1 c 1P 1 1 bΓ 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})}
8CmC 1 m 1B 1 1 mΓ 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 })}
9CcC 1 c 1B 1 1 bΓ 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})}
102/m2 ∗ {\displaystyle 2*}P2/mP 1 2/m 1P 1 1 2/mΓ 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)}
11P21/mP 1 21/m 1P 1 1 21/mΓ 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 })}
12C2/mC 1 2/m 1B 1 1 2/mΓ 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)}
13P2/cP 1 2/c 1P 1 1 2/bΓ 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})}
14P21/cP 1 21/c 1P 1 1 21/bΓ 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 })}
15C2/cC 1 2/c 1B 1 1 2/bΓ 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
NumberPoint groupOrbifoldShort nameFull nameSchoenfliesFedorovShubnikovFibrifold (primary)Fibrifold (secondary)
16222222 {\displaystyle 222}P222P 2 2 2Γ 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})}
17P2221P 2 2 21Γ 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}{*})}
18P21212P 21 21 2Γ 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}{*})}
19P212121P 21 21 21Γ 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 }})}
20C2221C 2 2 21Γ 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}{*})}
21C222C 2 2 2Γ 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})}
22F222F 2 2 2Γ 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})}
23I222I 2 2 2Γ 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})}
24I212121I 21 21 21Γ 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})}
25mm2∗ 22 {\displaystyle *22}Pmm2P m m 2Γ 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 }]}
26Pmc21P m c 21Γ 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}}]}
27Pcc2P c c 2Γ 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})}
28Pma2P m a 2Γ 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})}
29Pca21P c a 21Γ 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 {*}}{:})}
30Pnc2P n c 2Γ 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})}
31Pmn21P m n 21Γ 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}]}
32Pba2P b a 2Γ 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})}
33Pna21P n a 21Γ 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})}
34Pnn2P n n 2Γ 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})}
35Cmm2C m m 2Γ 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}{:}]}
36Cmc21C m c 21Γ 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}]}
37Ccc2C c c 2Γ 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})}
38Amm2A m m 2Γ 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}]}
39Aem2A b m 2Γ 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})}
40Ama2A m a 2Γ 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}]}
41Aea2A b a 2Γ 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})}
42Fmm2F m m 2Γ 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}{:}]}
43Fdd2F d d 2Γ 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 })}
44Imm2I m m 2Γ 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}]}
45Iba2I b a 2Γ 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})}
46Ima2I m a 2Γ 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}]}
472/m 2/m 2/m (mmm)∗ 222 {\displaystyle *222}PmmmP 2/m 2/m 2/mΓ 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]}
48PnnnP 2/n 2/n 2/nΓ 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})}
49PccmP 2/c 2/c 2/mΓ 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)}
50PbanP 2/b 2/a 2/nΓ 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)}
51PmmaP 21/m 2/m 2/aΓ 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]}
52PnnaP 2/n 21/n 2/aΓ 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})}
53PmnaP 2/m 2/n 21/aΓ 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)}
54PccaP 21/c 2/c 2/aΓ 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)}
55PbamP 21/b 21/a 2/mΓ 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)}
56PccnP 21/c 21/c 2/nΓ 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})}
57PbcmP 2/b 21/c 21/mΓ 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}{*}{:}]}
58PnnmP 21/n 21/n 2/mΓ 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)}
59PmmnP 21/m 21/m 2/nΓ 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 }]}
60PbcnP 21/b 2/c 21/nΓ 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})}
61PbcaP 21/b 21/c 21/aΓ 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 {*}}{:})}
62PnmaP 21/n 21/m 21/aΓ 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 }]}
63CmcmC 2/m 2/c 21/mΓ 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]}
64CmceC 2/m 2/c 21/aΓ 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)}
65CmmmC 2/m 2/m 2/mΓ 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]}
66CccmC 2/c 2/c 2/mΓ 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)}
67CmmeC 2/m 2/m 2/eΓ 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]}
68CcceC 2/c 2/c 2/eΓ 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)}
69FmmmF 2/m 2/m 2/mΓ 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]}
70FdddF 2/d 2/d 2/dΓ 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})}
71ImmmI 2/m 2/m 2/mΓ 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]}
72IbamI 2/b 2/a 2/mΓ 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)}
73IbcaI 2/b 2/c 2/aΓ 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)}
74ImmaI 2/m 2/m 2/aΓ 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
NumberPoint groupOrbifoldShort nameFull nameSchoenfliesFedorovShubnikovFibrifold
75444 {\displaystyle 44}P4P 4Γ 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})}
76P41P 41Γ 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})}
77P42P 42Γ 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})}
78P43P 43Γ 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})}
79I4I 4Γ 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})}
80I41I 41Γ 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})}
8142 × {\displaystyle 2\times }P4P 4Γ 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})}
82I4I 4Γ 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})}
834/m4 ∗ {\displaystyle 4*}P4/mP 4/mΓ 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}]}
84P42/mP 42/mΓ 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}]}
85P4/nP 4/nΓ 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)}
86P42/nP 42/nΓ 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)}
87I4/mI 4/mΓ 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}]}
88I41/aI 41/aΓ 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)}
89422224 {\displaystyle 224}P422P 4 2 2Γ 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})}
90P4212P4212Γ 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})}
91P4122P 41 2 2Γ 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})}
92P41212P 41 21 2Γ 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})}
93P4222P 42 2 2Γ 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})}
94P42212P 42 21 2Γ 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})}
95P4322P 43 2 2Γ 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})}
96P43212P 43 21 2Γ 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})}
97I422I 4 2 2Γ 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})}
98I4122I 41 2 2Γ 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})}
994mm∗ 44 {\displaystyle *44}P4mmP 4 m mΓ 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)}
100P4bmP 4 b mΓ 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)}
101P42cmP 42 c mΓ 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)}
102P42nmP 42 n mΓ 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)}
103P4ccP 4 c cΓ 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)}
104P4ncP 4 n cΓ 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)}
105P42mcP 42 m cΓ 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)}
106P42bcP 42 b cΓ 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)}
107I4mmI 4 m mΓ 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)}
108I4cmI 4 c mΓ 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)}
109I41mdI 41 m dΓ 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)}
110I41cdI 41 c dΓ 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)}
11142m2 ∗ 2 {\displaystyle 2{*}2}P42mP 4 2 mΓ 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})}
112P42cP 4 2 cΓ 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})}
113P421mP 4 21 mΓ 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)}
114P421cP 4 21 cΓ 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)}
115P4m2P 4 m 2Γ 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)}
116P4c2P 4 c 2Γ 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)}
117P4b2P 4 b 2Γ 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})}
118P4n2P 4 n 2Γ 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})}
119I4m2I 4 m 2Γ 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})}
120I4c2I 4 c 2Γ 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})}
121I42mI 4 2 mΓ 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)}
122I42dI 4 2 dΓ 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})}
1234/m 2/m 2/m (4/mmm)∗ 224 {\displaystyle *224}P4/mmmP 4/m 2/m 2/mΓ 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]}
124P4/mccP 4/m 2/c 2/cΓ 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]}
125P4/nbmP 4/n 2/b 2/mΓ 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)}
126P4/nncP 4/n 2/n 2/cΓ 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)}
127P4/mbmP 4/m 21/b 2/mΓ 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]}
128P4/mncP 4/m 21/n 2/cΓ 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]}
129P4/nmmP 4/n 21/m 2/mΓ 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)}
130P4/nccP 4/n 21/c 2/cΓ 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)}
131P42/mmcP 42/m 2/m 2/cΓ 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]}
132P42/mcmP 42/m 2/c 2/mΓ 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]}
133P42/nbcP 42/n 2/b 2/cΓ 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)}
134P42/nnmP 42/n 2/n 2/mΓ 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)}
135P42/mbcP 42/m 21/b 2/cΓ 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]}
136P42/mnmP 42/m 21/n 2/mΓ 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]}
137P42/nmcP 42/n 21/m 2/cΓ 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)}
138P42/ncmP 42/n 21/c 2/mΓ 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)}
139I4/mmmI 4/m 2/m 2/mΓ 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]}
140I4/mcmI 4/m 2/c 2/mΓ 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]}
141I41/amdI 41/a 2/m 2/dΓ 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)}
142I41/acdI 41/a 2/c 2/dΓ 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
NumberPoint groupOrbifoldShort nameFull nameSchoenfliesFedorovShubnikovFibrifold
143333 {\displaystyle 33}P3P 3Γ 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})}
144P31P 31Γ 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})}
145P32P 32Γ 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})}
146R3R 3Γ 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})}
14733 × {\displaystyle 3\times }P3P 3Γ 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)}
148R3R 3Γ 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)}
14932223 {\displaystyle 223}P312P 3 1 2Γ 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})}
150P321P 3 2 1Γ 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})}
151P3112P 31 1 2Γ 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})}
152P3121P 31 2 1Γ 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})}
153P3212P 32 1 2Γ 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})}
154P3221P 32 2 1Γ 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})}
155R32R 3 2Γ 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})}
1563m∗ 33 {\displaystyle *33}P3m1P 3 m 1Γ 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)}
157P31mP 3 1 mΓ 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)}
158P3c1P 3 c 1Γ 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)}
159P31cP 3 1 cΓ 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)}
160R3mR 3 mΓ 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)}
161R3cR 3 cΓ 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)}
1623 2/m (3m)2 ∗ 3 {\displaystyle 2{*}3}P31mP 3 1 2/mΓ 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)}
163P31cP 3 1 2/cΓ 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)}
164P3m1P 3 2/m 1Γ 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)}
165P3c1P 3 2/c 1Γ 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)}
166R3mR 3 2/mΓ 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)}
167R3cR 3 2/cΓ 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
NumberPoint groupOrbifoldShort nameFull nameSchoenfliesFedorovShubnikovFibrifold
168666 {\displaystyle 66}P6P 6Γ 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})}
169P61P 61Γ 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})}
170P65P 65Γ 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})}
171P62P 62Γ 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})}
172P64P 64Γ 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})}
173P63P 63Γ 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})}
17463 ∗ {\displaystyle 3*}P6P 6Γ 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}]}
1756/m6 ∗ {\displaystyle 6*}P6/mP 6/mΓ 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}]}
176P63/mP 63/mΓ 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}]}
177622226 {\displaystyle 226}P622P 6 2 2Γ 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})}
178P6122P 61 2 2Γ 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})}
179P6522P 65 2 2Γ 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})}
180P6222P 62 2 2Γ 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})}
181P6422P 64 2 2Γ 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})}
182P6322P 63 2 2Γ 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})}
1836mm∗ 66 {\displaystyle *66}P6mmP 6 m mΓ 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)}
184P6ccP 6 c cΓ 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)}
185P63cmP 63 c mΓ 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)}
186P63mcP 63 m cΓ 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)}
1876m2∗ 223 {\displaystyle *223}P6m2P 6 m 2Γ 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]}
188P6c2P 6 c 2Γ 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]}
189P62mP 6 2 mΓ 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]}
190P62cP 6 2 cΓ 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]}
1916/m 2/m 2/m (6/mmm)∗ 226 {\displaystyle *226}P6/mmmP 6/m 2/m 2/mΓ 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]}
192P6/mccP 6/m 2/c 2/cΓ 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]}
193P63/mcmP 63/m 2/c 2/mΓ 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]}
194P63/mmcP 63/m 2/m 2/cΓ 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)
Cubic crystal system
NumberPoint groupOrbifoldShort nameFull nameSchoenfliesFedorovShubnikovConwayFibrifold (preserving z {\displaystyle z})Fibrifold (preserving x {\displaystyle x}, y {\displaystyle y}, z {\displaystyle z})
19523332 {\displaystyle 332}P23P 2 3Γ 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}
196F23F 2 3Γ 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}
197I23I 2 3Γ 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}
198P213P 21 3Γ 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}
199I213I 21 3Γ 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}
2002/m 3 (m3)3 ∗ 2 {\displaystyle 3{*}2}Pm3P 2/m 3Γ 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}
201Pn3P 2/n 3Γ 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}
202Fm3F 2/m 3Γ 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}
203Fd3F 2/d 3Γ 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}
204Im3I 2/m 3Γ 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}
205Pa3P 21/a 3Γ 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}
206Ia3I 21/a 3Γ 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}
207432432 {\displaystyle 432}P432P 4 3 2Γ 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}
208P4232P 42 3 2Γ 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}
209F432F 4 3 2Γ 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}
210F4132F 41 3 2Γ 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}
211I432I 4 3 2Γ 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}
212P4332P 43 3 2Γ 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}
213P4132P 41 3 2Γ 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}
214I4132I 41 3 2Γ 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}
21543m∗ 332 {\displaystyle *332}P43mP 4 3 mΓ 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}
216F43mF 4 3 mΓ 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}
217I43mI 4 3 mΓ 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}
218P43nP 4 3 nΓ 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}
219F43cF 4 3 cΓ 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}
220I43dI 4 3 dΓ 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}
2214/m 3 2/m (m3m)∗ 432 {\displaystyle *432}Pm3mP 4/m 3 2/mΓ 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}
222Pn3nP 4/n 3 2/nΓ 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}
223Pm3nP 42/m 3 2/nΓ 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}
224Pn3mP 42/n 3 2/mΓ 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}
225Fm3mF 4/m 3 2/mΓ 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}
226Fm3cF 4/m 3 2/cΓ 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}
227Fd3mF 41/d 3 2/mΓ 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}
228Fd3cF 41/d 3 2/cΓ 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}
229Im3mI 4/m 3 2/mΓ 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}
230Ia3dI 41/a 3 2/dΓ 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