List of space groups

<h2 id="symbols">Symbols</h2>
In <a href="/facts/Hermann%E2%80%93Mauguin_notation/NGHDFXKC">Hermann–Mauguin notation</a>, space groups are named by a symbol combining the <a href="/facts/Point_group/41NSqUN6">point group</a> identifier with the uppercase letters describing the <a href="/facts/Bravais_lattice/7gQKTsXk">lattice type</a>. Translations within the lattice in the form of <a href="/facts/Screw_axis/Cos1gnJb">screw axes</a> and <a href="/facts/Glide_planes/Nggu4E1X">glide planes</a> are also noted, giving a complete crystallographic space group.
These are the <a href="/facts/Bravais_lattice/7gQKTsXk">Bravais lattices in three dimensions</a>:

<ul><li>P primitive</li>
<li>I body centered (from the German Innenzentriert)</li>
<li>F face centered (from the German Flächenzentriert)</li>
<li>A centered on A faces only</li>
<li>B centered on B faces only</li>
<li>C centered on C faces only</li>
<li>R rhombohedral</li></ul>
A reflection plane m within the point groups can be replaced by a <a href="/facts/Glide_plane/Nggu4E1X">glide plane</a>, 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 <a href="/facts/Diamond/IBUdnd1y">diamond</a> structure.

<ul><li>
 
 
 
 a
 
 
 {\displaystyle a}
 
, 
 
 
 
 b
 
 
 {\displaystyle b}
 
, or 
 
 
 
 c
 
 
 {\displaystyle c}
 
: glide translation along half the lattice vector of this face</li>
<li>
 
 
 
 n
 
 
 {\displaystyle n}
 
: glide translation along half the diagonal of this face</li>
<li>
 
 
 
 d
 
 
 {\displaystyle d}
 
: glide planes with translation along a quarter of a face diagonal</li>
<li>
 
 
 
 e
 
 
 {\displaystyle e}
 
: two glides with the same glide plane and translation along two (different) half-lattice vectors.<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a></li></ul>
A gyration point can be replaced by a <a href="/facts/Screw_axis/Cos1gnJb">screw axis</a> 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.<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a>
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.

<h3>Symmorphic</h3>
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).

<h3>Hemisymmorphic</h3>
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).

<h3>Asymmorphic</h3>
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.

<h2 id="list-of-triclinic">List of triclinic</h2>
Triclinic Bravais lattice<table><tbody><tr><td></td></tr></tbody></table>
<a href="/facts/Triclinic_crystal_system/Y6yEdqfN">Triclinic crystal system</a><table><tbody><tr><th>Number</th><th><a href="/facts/Point_group/41NSqUN6">Point group</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></th><th>Short name</th><th>Full name</th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies</a></th><th><a href="/facts/Evgraf_Fedorov/fPqQhHMn">Fedorov</a></th><th><a href="/facts/Shubnikov_group/bCtqSDhI">Shubnikov</a></th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a></th></tr><tr><td>1</td><td>1</td><td> 1 {\displaystyle 1} </td><td>P1</td><td>P 1</td><td> Γ t C 1 1 {\displaystyle \Gamma _{t}C_{1}^{1}} </td><td>1s</td><td> ( a / b / c ) ⋅ 1 {\displaystyle (a/b/c)\cdot 1} </td><td> ( ∘ ) {\displaystyle (\circ )} </td></tr><tr><td>2</td><td>1</td><td> × {\displaystyle \times } </td><td>P1</td><td>P 1</td><td> Γ t C i 1 {\displaystyle \Gamma _{t}C_{i}^{1}} </td><td>2s</td><td> ( a / b / c ) ⋅ 2 ~ {\displaystyle (a/b/c)\cdot {\tilde {2}}} </td><td> ( 2222 ) {\displaystyle (2222)} </td></tr></tbody></table>
<h2 id="list-of-monoclinic">List of monoclinic</h2>
Monoclinic Bravais lattice<table><tbody><tr><th>Simple (P)</th><th>Base (C)</th></tr><tr><td></td><td></td></tr></tbody></table>
<a href="/facts/Monoclinic_crystal_system/5PCwXvzX">Monoclinic crystal system</a><table><tbody><tr><th>Number</th><th><a href="/facts/Point_group/41NSqUN6">Point group</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></th><th>Short name</th><th colspan="2">Full name(s)</th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies</a></th><th><a href="/facts/Evgraf_Fedorov/fPqQhHMn">Fedorov</a></th><th><a href="/facts/Shubnikov_group/bCtqSDhI">Shubnikov</a></th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a> (primary)</th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a> (secondary)</th></tr><tr><td>3</td><td rowspan="3">2</td><td rowspan="3"> 22 {\displaystyle 22} </td><td>P2</td><td>P 1 2 1</td><td>P 1 1 2</td><td> Γ m C 2 1 {\displaystyle \Gamma _{m}C_{2}^{1}} </td><td>3s</td><td> ( b : ( c / a ) ) : 2 {\displaystyle (b:(c/a)):2} </td><td> ( 2 0 2 0 2 0 2 0 ) {\displaystyle (2_{0}2_{0}2_{0}2_{0})} </td><td> ( ∗ 0 ∗ 0 ) {\displaystyle ({*}_{0}{*}_{0})} </td></tr><tr><td>4</td><td>P21</td><td>P 1 21 1</td><td>P 1 1 21</td><td> Γ m C 2 2 {\displaystyle \Gamma _{m}C_{2}^{2}} </td><td>1a</td><td> ( b : ( c / a ) ) : 2 1 {\displaystyle (b:(c/a)):2_{1}} </td><td> ( 2 1 2 1 2 1 2 1 ) {\displaystyle (2_{1}2_{1}2_{1}2_{1})} </td><td> ( × ¯ × ¯ ) {\displaystyle ({\bar {\times }}{\bar {\times }})} </td></tr><tr><td>5</td><td>C2</td><td>C 1 2 1</td><td>B 1 1 2</td><td> Γ m b C 2 3 {\displaystyle \Gamma _{m}^{b}C_{2}^{3}} </td><td>4s</td><td> ( a + b 2 / b : ( c / a ) ) : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right):2} </td><td> ( 2 0 2 0 2 1 2 1 ) {\displaystyle (2_{0}2_{0}2_{1}2_{1})} </td><td> ( ∗ 1 ∗ 1 ) {\displaystyle ({*}_{1}{*}_{1})} , ( ∗ × ¯ ) {\displaystyle ({*}{\bar {\times }})} </td></tr><tr><td>6</td><td rowspan="4">m</td><td rowspan="4"> ∗ {\displaystyle *} </td><td>Pm</td><td>P 1 m 1</td><td>P 1 1 m</td><td> Γ m C s 1 {\displaystyle \Gamma _{m}C_{s}^{1}} </td><td>5s</td><td> ( b : ( c / a ) ) ⋅ m {\displaystyle (b:(c/a))\cdot m} </td><td> [ ∘ 0 ] {\displaystyle [\circ _{0}]} </td><td> ( ∗ ⋅ ∗ ⋅ ) {\displaystyle ({*}{\cdot }{*}{\cdot })} </td></tr><tr><td>7</td><td>Pc</td><td>P 1 c 1</td><td>P 1 1 b</td><td> Γ m C s 2 {\displaystyle \Gamma _{m}C_{s}^{2}} </td><td>1h</td><td> ( b : ( c / a ) ) ⋅ c ~ {\displaystyle (b:(c/a))\cdot {\tilde {c}}} </td><td> ( ∘ ¯ 0 ) {\displaystyle ({\bar {\circ }}_{0})} </td><td> ( ∗ : ∗ : ) {\displaystyle ({*}{:}{*}{:})} , ( × × 0 ) {\displaystyle ({\times }{\times }_{0})} </td></tr><tr><td>8</td><td>Cm</td><td>C 1 m 1</td><td>B 1 1 m</td><td> Γ m b C s 3 {\displaystyle \Gamma _{m}^{b}C_{s}^{3}} </td><td>6s</td><td> ( a + b 2 / b : ( c / a ) ) ⋅ m {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m} </td><td> [ ∘ 1 ] {\displaystyle [\circ _{1}]} </td><td> ( ∗ ⋅ ∗ : ) {\displaystyle ({*}{\cdot }{*}{:})} , ( ∗ ⋅ × ) {\displaystyle ({*}{\cdot }{\times })} </td></tr><tr><td>9</td><td>Cc</td><td>C 1 c 1</td><td>B 1 1 b</td><td> Γ m b C s 4 {\displaystyle \Gamma _{m}^{b}C_{s}^{4}} </td><td>2h</td><td> ( a + b 2 / b : ( c / a ) ) ⋅ c ~ {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}} </td><td> ( ∘ ¯ 1 ) {\displaystyle ({\bar {\circ }}_{1})} </td><td> ( ∗ : × ) {\displaystyle ({*}{:}{\times })} , ( × × 1 ) {\displaystyle ({\times }{\times }_{1})} </td></tr><tr><td>10</td><td rowspan="6">2/m</td><td rowspan="6"> 2 ∗ {\displaystyle 2*} </td><td>P2/m</td><td>P 1 2/m 1</td><td>P 1 1 2/m</td><td> Γ m C 2 h 1 {\displaystyle \Gamma _{m}C_{2h}^{1}} </td><td>7s</td><td> ( b : ( c / a ) ) ⋅ m : 2 {\displaystyle (b:(c/a))\cdot m:2} </td><td> [ 2 0 2 0 2 0 2 0 ] {\displaystyle [2_{0}2_{0}2_{0}2_{0}]} </td><td> [ ∗ 2 ⋅ 22 ⋅ 2 ) {\displaystyle [*2{\cdot }22{\cdot }2)} </td></tr><tr><td>11</td><td>P21/m</td><td>P 1 21/m 1</td><td>P 1 1 21/m</td><td> Γ m C 2 h 2 {\displaystyle \Gamma _{m}C_{2h}^{2}} </td><td>2a</td><td> ( b : ( c / a ) ) ⋅ m : 2 1 {\displaystyle (b:(c/a))\cdot m:2_{1}} </td><td> [ 2 1 2 1 2 1 2 1 ] {\displaystyle [2_{1}2_{1}2_{1}2_{1}]} </td><td> ( 22 ∗ ⋅ ) {\displaystyle (22{*}{\cdot })} </td></tr><tr><td>12</td><td>C2/m</td><td>C 1 2/m 1</td><td>B 1 1 2/m</td><td> Γ m b C 2 h 3 {\displaystyle \Gamma _{m}^{b}C_{2h}^{3}} </td><td>8s</td><td> ( a + b 2 / b : ( c / a ) ) ⋅ m : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m:2} </td><td> [ 2 0 2 0 2 1 2 1 ] {\displaystyle [2_{0}2_{0}2_{1}2_{1}]} </td><td> ( ∗ 2 ⋅ 22 : 2 ) {\displaystyle (*2{\cdot }22{:}2)} , ( 2 ∗ ¯ 2 ⋅ 2 ) {\displaystyle (2{\bar {*}}2{\cdot }2)} </td></tr><tr><td>13</td><td>P2/c</td><td>P 1 2/c 1</td><td>P 1 1 2/b</td><td> Γ m C 2 h 4 {\displaystyle \Gamma _{m}C_{2h}^{4}} </td><td>3h</td><td> ( b : ( c / a ) ) ⋅ c ~ : 2 {\displaystyle (b:(c/a))\cdot {\tilde {c}}:2} </td><td> ( 2 0 2 0 22 ) {\displaystyle (2_{0}2_{0}22)} </td><td> ( ∗ 2 : 22 : 2 ) {\displaystyle (*2{:}22{:}2)} , ( 22 ∗ 0 ) {\displaystyle (22{*}_{0})} </td></tr><tr><td>14</td><td>P21/c</td><td>P 1 21/c 1</td><td>P 1 1 21/b</td><td> Γ m C 2 h 5 {\displaystyle \Gamma _{m}C_{2h}^{5}} </td><td>3a</td><td> ( b : ( c / a ) ) ⋅ c ~ : 2 1 {\displaystyle (b:(c/a))\cdot {\tilde {c}}:2_{1}} </td><td> ( 2 1 2 1 22 ) {\displaystyle (2_{1}2_{1}22)} </td><td> ( 22 ∗ : ) {\displaystyle (22{*}{:})} , ( 22 × ) {\displaystyle (22{\times })} </td></tr><tr><td>15</td><td>C2/c</td><td>C 1 2/c 1</td><td>B 1 1 2/b</td><td> Γ m b C 2 h 6 {\displaystyle \Gamma _{m}^{b}C_{2h}^{6}} </td><td>4h</td><td> ( a + b 2 / b : ( c / a ) ) ⋅ c ~ : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}:2} </td><td> ( 2 0 2 1 22 ) {\displaystyle (2_{0}2_{1}22)} </td><td> ( 2 ∗ ¯ 2 : 2 ) {\displaystyle (2{\bar {*}}2{:}2)} , ( 22 ∗ 1 ) {\displaystyle (22{*}_{1})} </td></tr></tbody></table>
<h2 id="list-of-orthorhombic">List of orthorhombic</h2>
Orthorhombic Bravais lattice<table><tbody><tr><th>Simple (P)</th><th>Body (I)</th><th>Face (F)</th><th>Base (A or C)</th></tr><tr><td></td><td></td><td></td><td></td></tr></tbody></table>
<a href="/facts/Orthorhombic_crystal_system/3zo4F8P0">Orthorhombic crystal system</a><table><tbody><tr><th>Number</th><th><a href="/facts/Point_group/41NSqUN6">Point group</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></th><th>Short name</th><th>Full name</th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies</a></th><th><a href="/facts/Evgraf_Fedorov/fPqQhHMn">Fedorov</a></th><th><a href="/facts/Shubnikov_group/bCtqSDhI">Shubnikov</a></th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a> (primary)</th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a> (secondary)</th></tr><tr><td>16</td><td rowspan="9">222</td><td rowspan="9"> 222 {\displaystyle 222} </td><td>P222</td><td>P 2 2 2</td><td> Γ o D 2 1 {\displaystyle \Gamma _{o}D_{2}^{1}} </td><td>9s</td><td> ( c : a : b ) : 2 : 2 {\displaystyle (c:a:b):2:2} </td><td> ( ∗ 2 0 2 0 2 0 2 0 ) {\displaystyle (*2_{0}2_{0}2_{0}2_{0})} </td><td></td></tr><tr><td>17</td><td>P2221</td><td>P 2 2 21</td><td> Γ o D 2 2 {\displaystyle \Gamma _{o}D_{2}^{2}} </td><td>4a</td><td> ( c : a : b ) : 2 1 : 2 {\displaystyle (c:a:b):2_{1}:2} </td><td> ( ∗ 2 1 2 1 2 1 2 1 ) {\displaystyle (*2_{1}2_{1}2_{1}2_{1})} </td><td> ( 2 0 2 0 ∗ ) {\displaystyle (2_{0}2_{0}{*})} </td></tr><tr><td>18</td><td>P21212</td><td>P 21 21 2</td><td> Γ o D 2 3 {\displaystyle \Gamma _{o}D_{2}^{3}} </td><td>7a</td><td> ( c : a : b ) : 2 {\displaystyle (c:a:b):2} 2 1 {\displaystyle 2_{1}} </td><td> ( 2 0 2 0 × ¯ ) {\displaystyle (2_{0}2_{0}{\bar {\times }})} </td><td> ( 2 1 2 1 ∗ ) {\displaystyle (2_{1}2_{1}{*})} </td></tr><tr><td>19</td><td>P212121</td><td>P 21 21 21</td><td> Γ o D 2 4 {\displaystyle \Gamma _{o}D_{2}^{4}} </td><td>8a</td><td> ( c : a : b ) : 2 1 {\displaystyle (c:a:b):2_{1}} 2 1 {\displaystyle 2_{1}} </td><td> ( 2 1 2 1 × ¯ ) {\displaystyle (2_{1}2_{1}{\bar {\times }})} </td><td></td></tr><tr><td>20</td><td>C2221</td><td>C 2 2 21</td><td> Γ o b D 2 5 {\displaystyle \Gamma _{o}^{b}D_{2}^{5}} </td><td>5a</td><td> ( a + b 2 : c : a : b ) : 2 1 : 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):2_{1}:2} </td><td> ( 2 1 ∗ 2 1 2 1 ) {\displaystyle (2_{1}{*}2_{1}2_{1})} </td><td> ( 2 0 2 1 ∗ ) {\displaystyle (2_{0}2_{1}{*})} </td></tr><tr><td>21</td><td>C222</td><td>C 2 2 2</td><td> Γ o b D 2 6 {\displaystyle \Gamma _{o}^{b}D_{2}^{6}} </td><td>10s</td><td> ( a + b 2 : c : a : b ) : 2 : 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):2:2} </td><td> ( 2 0 ∗ 2 0 2 0 ) {\displaystyle (2_{0}{*}2_{0}2_{0})} </td><td> ( ∗ 2 0 2 0 2 1 2 1 ) {\displaystyle (*2_{0}2_{0}2_{1}2_{1})} </td></tr><tr><td>22</td><td>F222</td><td>F 2 2 2</td><td> Γ o f D 2 7 {\displaystyle \Gamma _{o}^{f}D_{2}^{7}} </td><td>12s</td><td> ( 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} </td><td> ( ∗ 2 0 2 1 2 0 2 1 ) {\displaystyle (*2_{0}2_{1}2_{0}2_{1})} </td><td></td></tr><tr><td>23</td><td>I222</td><td>I 2 2 2</td><td> Γ o v D 2 8 {\displaystyle \Gamma _{o}^{v}D_{2}^{8}} </td><td>11s</td><td> ( a + b + c 2 / c : a : b ) : 2 : 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2} </td><td> ( 2 1 ∗ 2 0 2 0 ) {\displaystyle (2_{1}{*}2_{0}2_{0})} </td><td></td></tr><tr><td>24</td><td>I212121</td><td>I 21 21 21</td><td> Γ o v D 2 9 {\displaystyle \Gamma _{o}^{v}D_{2}^{9}} </td><td>6a</td><td> ( a + b + c 2 / c : a : b ) : 2 : 2 1 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2_{1}} </td><td> ( 2 0 ∗ 2 1 2 1 ) {\displaystyle (2_{0}{*}2_{1}2_{1})} </td><td></td></tr><tr><td>25</td><td rowspan="22">mm2</td><td rowspan="22"> ∗ 22 {\displaystyle *22} </td><td>Pmm2</td><td>P m m 2</td><td> Γ o C 2 v 1 {\displaystyle \Gamma _{o}C_{2v}^{1}} </td><td>13s</td><td> ( c : a : b ) : m ⋅ 2 {\displaystyle (c:a:b):m\cdot 2} </td><td> ( ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ) {\displaystyle (*{\cdot }2{\cdot }2{\cdot }2{\cdot }2)} </td><td> [ ∗ 0 ⋅ ∗ 0 ⋅ ] {\displaystyle [{*}_{0}{\cdot }{*}_{0}{\cdot }]} </td></tr><tr><td>26</td><td>Pmc21</td><td>P m c 21</td><td> Γ o C 2 v 2 {\displaystyle \Gamma _{o}C_{2v}^{2}} </td><td>9a</td><td> ( c : a : b ) : c ~ ⋅ 2 1 {\displaystyle (c:a:b):{\tilde {c}}\cdot 2_{1}} </td><td> ( ∗ ⋅ 2 : 2 ⋅ 2 : 2 ) {\displaystyle (*{\cdot }2{:}2{\cdot }2{:}2)} </td><td> ( ∗ ¯ ⋅ ∗ ¯ ⋅ ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}{\cdot })} , [ × 0 × 0 ] {\displaystyle [{\times _{0}}{\times _{0}}]} </td></tr><tr><td>27</td><td>Pcc2</td><td>P c c 2</td><td> Γ o C 2 v 3 {\displaystyle \Gamma _{o}C_{2v}^{3}} </td><td>5h</td><td> ( c : a : b ) : c ~ ⋅ 2 {\displaystyle (c:a:b):{\tilde {c}}\cdot 2} </td><td> ( ∗ : 2 : 2 : 2 : 2 ) {\displaystyle (*{:}2{:}2{:}2{:}2)} </td><td> ( ∗ ¯ 0 ∗ ¯ 0 ) {\displaystyle ({\bar {*}}_{0}{\bar {*}}_{0})} </td></tr><tr><td>28</td><td>Pma2</td><td>P m a 2</td><td> Γ o C 2 v 4 {\displaystyle \Gamma _{o}C_{2v}^{4}} </td><td>6h</td><td> ( c : a : b ) : a ~ ⋅ 2 {\displaystyle (c:a:b):{\tilde {a}}\cdot 2} </td><td> ( 2 0 2 0 ∗ ⋅ ) {\displaystyle (2_{0}2_{0}{*}{\cdot })} </td><td> [ ∗ 0 : ∗ 0 : ] {\displaystyle [{*}_{0}{:}{*}_{0}{:}]} , ( ∗ ⋅ ∗ 0 ) {\displaystyle (*{\cdot }{*}_{0})} </td></tr><tr><td>29</td><td>Pca21</td><td>P c a 21</td><td> Γ o C 2 v 5 {\displaystyle \Gamma _{o}C_{2v}^{5}} </td><td>11a</td><td> ( c : a : b ) : a ~ ⋅ 2 1 {\displaystyle (c:a:b):{\tilde {a}}\cdot 2_{1}} </td><td> ( 2 1 2 1 ∗ : ) {\displaystyle (2_{1}2_{1}{*}{:})} </td><td> ( ∗ ¯ : ∗ ¯ : ) {\displaystyle ({\bar {*}}{:}{\bar {*}}{:})} </td></tr><tr><td>30</td><td>Pnc2</td><td>P n c 2</td><td> Γ o C 2 v 6 {\displaystyle \Gamma _{o}C_{2v}^{6}} </td><td>7h</td><td> ( c : a : b ) : c ~ ⊙ 2 {\displaystyle (c:a:b):{\tilde {c}}\odot 2} </td><td> ( 2 0 2 0 ∗ : ) {\displaystyle (2_{0}2_{0}{*}{:})} </td><td> ( ∗ ¯ 1 ∗ ¯ 1 ) {\displaystyle ({\bar {*}}_{1}{\bar {*}}_{1})} , ( ∗ 0 × 0 ) {\displaystyle ({*}_{0}{\times }_{0})} </td></tr><tr><td>31</td><td>Pmn21</td><td>P m n 21</td><td> Γ o C 2 v 7 {\displaystyle \Gamma _{o}C_{2v}^{7}} </td><td>10a</td><td> ( c : a : b ) : a c ~ ⋅ 2 1 {\displaystyle (c:a:b):{\widetilde {ac}}\cdot 2_{1}} </td><td> ( 2 1 2 1 ∗ ⋅ ) {\displaystyle (2_{1}2_{1}{*}{\cdot })} </td><td> ( ∗ ⋅ × ¯ ) {\displaystyle (*{\cdot }{\bar {\times }})} , [ × 0 × 1 ] {\displaystyle [{\times }_{0}{\times }_{1}]} </td></tr><tr><td>32</td><td>Pba2</td><td>P b a 2</td><td> Γ o C 2 v 8 {\displaystyle \Gamma _{o}C_{2v}^{8}} </td><td>9h</td><td> ( c : a : b ) : a ~ ⊙ 2 {\displaystyle (c:a:b):{\tilde {a}}\odot 2} </td><td> ( 2 0 2 0 × 0 ) {\displaystyle (2_{0}2_{0}{\times }_{0})} </td><td> ( ∗ : ∗ 0 ) {\displaystyle (*{:}{*}_{0})} </td></tr><tr><td>33</td><td>Pna21</td><td>P n a 21</td><td> Γ o C 2 v 9 {\displaystyle \Gamma _{o}C_{2v}^{9}} </td><td>12a</td><td> ( c : a : b ) : a ~ ⊙ 2 1 {\displaystyle (c:a:b):{\tilde {a}}\odot 2_{1}} </td><td> ( 2 1 2 1 × ) {\displaystyle (2_{1}2_{1}{\times })} </td><td> ( ∗ : × ) {\displaystyle (*{:}{\times })} , ( × × 1 ) {\displaystyle ({\times }{\times }_{1})} </td></tr><tr><td>34</td><td>Pnn2</td><td>P n n 2</td><td> Γ o C 2 v 10 {\displaystyle \Gamma _{o}C_{2v}^{10}} </td><td>8h</td><td> ( c : a : b ) : a c ~ ⊙ 2 {\displaystyle (c:a:b):{\widetilde {ac}}\odot 2} </td><td> ( 2 0 2 0 × 1 ) {\displaystyle (2_{0}2_{0}{\times }_{1})} </td><td> ( ∗ 0 × 1 ) {\displaystyle (*_{0}{\times }_{1})} </td></tr><tr><td>35</td><td>Cmm2</td><td>C m m 2</td><td> Γ o b C 2 v 11 {\displaystyle \Gamma _{o}^{b}C_{2v}^{11}} </td><td>14s</td><td> ( a + b 2 : c : a : b ) : m ⋅ 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2} </td><td> ( 2 0 ∗ ⋅ 2 ⋅ 2 ) {\displaystyle (2_{0}{*}{\cdot }2{\cdot }2)} </td><td> [ ∗ 0 ⋅ ∗ 0 : ] {\displaystyle [*_{0}{\cdot }{*}_{0}{:}]} </td></tr><tr><td>36</td><td>Cmc21</td><td>C m c 21</td><td> Γ o b C 2 v 12 {\displaystyle \Gamma _{o}^{b}C_{2v}^{12}} </td><td>13a</td><td> ( a + b 2 : c : a : b ) : c ~ ⋅ 2 1 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2_{1}} </td><td> ( 2 1 ∗ ⋅ 2 : 2 ) {\displaystyle (2_{1}{*}{\cdot }2{:}2)} </td><td> ( ∗ ¯ ⋅ ∗ ¯ : ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}{:})} , [ × 1 × 1 ] {\displaystyle [{\times }_{1}{\times }_{1}]} </td></tr><tr><td>37</td><td>Ccc2</td><td>C c c 2</td><td> Γ o b C 2 v 13 {\displaystyle \Gamma _{o}^{b}C_{2v}^{13}} </td><td>10h</td><td> ( a + b 2 : c : a : b ) : c ~ ⋅ 2 {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2} </td><td> ( 2 0 ∗ : 2 : 2 ) {\displaystyle (2_{0}{*}{:}2{:}2)} </td><td> ( ∗ ¯ 0 ∗ ¯ 1 ) {\displaystyle ({\bar {*}}_{0}{\bar {*}}_{1})} </td></tr><tr><td>38</td><td>Amm2</td><td>A m m 2</td><td> Γ o b C 2 v 14 {\displaystyle \Gamma _{o}^{b}C_{2v}^{14}} </td><td>15s</td><td> ( b + c 2 / c : a : b ) : m ⋅ 2 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2} </td><td> ( ∗ ⋅ 2 ⋅ 2 ⋅ 2 : 2 ) {\displaystyle (*{\cdot }2{\cdot }2{\cdot }2{:}2)} </td><td> [ ∗ 1 ⋅ ∗ 1 ⋅ ] {\displaystyle [{*}_{1}{\cdot }{*}_{1}{\cdot }]} , [ ∗ ⋅ × 0 ] {\displaystyle [*{\cdot }{\times }_{0}]} </td></tr><tr><td>39</td><td>Aem2</td><td>A b m 2</td><td> Γ o b C 2 v 15 {\displaystyle \Gamma _{o}^{b}C_{2v}^{15}} </td><td>11h</td><td> ( b + c 2 / c : a : b ) : m ⋅ 2 1 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2_{1}} </td><td> ( ∗ ⋅ 2 : 2 : 2 : 2 ) {\displaystyle (*{\cdot }2{:}2{:}2{:}2)} </td><td> [ ∗ 1 : ∗ 1 : ] {\displaystyle [{*}_{1}{:}{*}_{1}{:}]} , ( ∗ ¯ ⋅ ∗ ¯ 0 ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}_{0})} </td></tr><tr><td>40</td><td>Ama2</td><td>A m a 2</td><td> Γ o b C 2 v 16 {\displaystyle \Gamma _{o}^{b}C_{2v}^{16}} </td><td>12h</td><td> ( b + c 2 / c : a : b ) : a ~ ⋅ 2 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2} </td><td> ( 2 0 2 1 ∗ ⋅ ) {\displaystyle (2_{0}2_{1}{*}{\cdot })} </td><td> ( ∗ ⋅ ∗ 1 ) {\displaystyle (*{\cdot }{*}_{1})} , [ ∗ : × 1 ] {\displaystyle [*{:}{\times }_{1}]} </td></tr><tr><td>41</td><td>Aea2</td><td>A b a 2</td><td> Γ o b C 2 v 17 {\displaystyle \Gamma _{o}^{b}C_{2v}^{17}} </td><td>13h</td><td> ( b + c 2 / c : a : b ) : a ~ ⋅ 2 1 {\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2_{1}} </td><td> ( 2 0 2 1 ∗ : ) {\displaystyle (2_{0}2_{1}{*}{:})} </td><td> ( ∗ : ∗ 1 ) {\displaystyle (*{:}{*}_{1})} , ( ∗ ¯ : ∗ ¯ 1 ) {\displaystyle ({\bar {*}}{:}{\bar {*}}_{1})} </td></tr><tr><td>42</td><td>Fmm2</td><td>F m m 2</td><td> Γ o f C 2 v 18 {\displaystyle \Gamma _{o}^{f}C_{2v}^{18}} </td><td>17s</td><td> ( 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} </td><td> ( ∗ ⋅ 2 ⋅ 2 : 2 : 2 ) {\displaystyle (*{\cdot }2{\cdot }2{:}2{:}2)} </td><td> [ ∗ 1 ⋅ ∗ 1 : ] {\displaystyle [{*}_{1}{\cdot }{*}_{1}{:}]} </td></tr><tr><td>43</td><td>Fdd2</td><td>F d d 2</td><td> Γ o f C 2 v 19 {\displaystyle \Gamma _{o}^{f}C_{2v}^{19}} </td><td>16h</td><td> ( 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} </td><td> ( 2 0 2 1 × ) {\displaystyle (2_{0}2_{1}{\times })} </td><td> ( ∗ 1 × ) {\displaystyle ({*}_{1}{\times })} </td></tr><tr><td>44</td><td>Imm2</td><td>I m m 2</td><td> Γ o v C 2 v 20 {\displaystyle \Gamma _{o}^{v}C_{2v}^{20}} </td><td>16s</td><td> ( a + b + c 2 / c : a : b ) : m ⋅ 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):m\cdot 2} </td><td> ( 2 1 ∗ ⋅ 2 ⋅ 2 ) {\displaystyle (2_{1}{*}{\cdot }2{\cdot }2)} </td><td> [ ∗ ⋅ × 1 ] {\displaystyle [*{\cdot }{\times }_{1}]} </td></tr><tr><td>45</td><td>Iba2</td><td>I b a 2</td><td> Γ o v C 2 v 21 {\displaystyle \Gamma _{o}^{v}C_{2v}^{21}} </td><td>15h</td><td> ( a + b + c 2 / c : a : b ) : c ~ ⋅ 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {c}}\cdot 2} </td><td> ( 2 1 ∗ : 2 : 2 ) {\displaystyle (2_{1}{*}{:}2{:}2)} </td><td> ( ∗ ¯ : ∗ ¯ 0 ) {\displaystyle ({\bar {*}}{:}{\bar {*}}_{0})} </td></tr><tr><td>46</td><td>Ima2</td><td>I m a 2</td><td> Γ o v C 2 v 22 {\displaystyle \Gamma _{o}^{v}C_{2v}^{22}} </td><td>14h</td><td> ( a + b + c 2 / c : a : b ) : a ~ ⋅ 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2} </td><td> ( 2 0 ∗ ⋅ 2 : 2 ) {\displaystyle (2_{0}{*}{\cdot }2{:}2)} </td><td> ( ∗ ¯ ⋅ ∗ ¯ 1 ) {\displaystyle ({\bar {*}}{\cdot }{\bar {*}}_{1})} , [ ∗ : × 0 ] {\displaystyle [*{:}{\times }_{0}]} </td></tr><tr><td>47</td><td rowspan="28"> 2 m 2 m 2 m {\displaystyle {\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} </td><td rowspan="28"> ∗ 222 {\displaystyle *222} </td><td>Pmmm</td><td>P 2/m 2/m 2/m</td><td> Γ o D 2 h 1 {\displaystyle \Gamma _{o}D_{2h}^{1}} </td><td>18s</td><td> ( c : a : b ) ⋅ m : 2 ⋅ m {\displaystyle \left(c:a:b\right)\cdot m:2\cdot m} </td><td> [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]} </td><td></td></tr><tr><td>48</td><td>Pnnn</td><td>P 2/n 2/n 2/n</td><td> Γ o D 2 h 2 {\displaystyle \Gamma _{o}D_{2h}^{2}} </td><td>19h</td><td> ( c : a : b ) ⋅ a b ~ : 2 ⊙ a c ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\widetilde {ac}}} </td><td> ( 2 ∗ ¯ 1 2 0 2 0 ) {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0})} </td><td></td></tr><tr><td>49</td><td>Pccm</td><td>P 2/c 2/c 2/m</td><td> Γ o D 2 h 3 {\displaystyle \Gamma _{o}D_{2h}^{3}} </td><td>17h</td><td> ( c : a : b ) ⋅ m : 2 ⋅ c ~ {\displaystyle \left(c:a:b\right)\cdot m:2\cdot {\tilde {c}}} </td><td> [ ∗ : 2 : 2 : 2 : 2 ] {\displaystyle [*{:}2{:}2{:}2{:}2]} </td><td> ( ∗ 2 0 2 0 2 ⋅ 2 ) {\displaystyle (*2_{0}2_{0}2{\cdot }2)} </td></tr><tr><td>50</td><td>Pban</td><td>P 2/b 2/a 2/n</td><td> Γ o D 2 h 4 {\displaystyle \Gamma _{o}D_{2h}^{4}} </td><td>18h</td><td> ( c : a : b ) ⋅ a b ~ : 2 ⊙ a ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\tilde {a}}} </td><td> ( 2 ∗ ¯ 0 2 0 2 0 ) {\displaystyle (2{\bar {*}}_{0}2_{0}2_{0})} </td><td> ( ∗ 2 0 2 0 2 : 2 ) {\displaystyle (*2_{0}2_{0}2{:}2)} </td></tr><tr><td>51</td><td>Pmma</td><td>P 21/m 2/m 2/a</td><td> Γ o D 2 h 5 {\displaystyle \Gamma _{o}D_{2h}^{5}} </td><td>14a</td><td> ( c : a : b ) ⋅ a ~ : 2 ⋅ m {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\cdot m} </td><td> [ 2 0 2 0 ∗ ⋅ ] {\displaystyle [2_{0}2_{0}{*}{\cdot }]} </td><td> [ ∗ ⋅ 2 : 2 ⋅ 2 : 2 ] {\displaystyle [*{\cdot }2{:}2{\cdot }2{:}2]} , [ ∗ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] {\displaystyle [*2{\cdot }2{\cdot }2{\cdot }2]} </td></tr><tr><td>52</td><td>Pnna</td><td>P 2/n 21/n 2/a</td><td> Γ o D 2 h 6 {\displaystyle \Gamma _{o}D_{2h}^{6}} </td><td>17a</td><td> ( c : a : b ) ⋅ a ~ : 2 ⊙ a c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\odot {\widetilde {ac}}} </td><td> ( 2 0 2 ∗ ¯ 1 ) {\displaystyle (2_{0}2{\bar {*}}_{1})} </td><td> ( 2 0 ∗ 2 : 2 ) {\displaystyle (2_{0}{*}2{:}2)} , ( 2 ∗ ¯ 2 1 2 1 ) {\displaystyle (2{\bar {*}}2_{1}2_{1})} </td></tr><tr><td>53</td><td>Pmna</td><td>P 2/m 2/n 21/a</td><td> Γ o D 2 h 7 {\displaystyle \Gamma _{o}D_{2h}^{7}} </td><td>15a</td><td> ( c : a : b ) ⋅ a ~ : 2 1 ⋅ a c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\widetilde {ac}}} </td><td> [ 2 0 2 0 ∗ : ] {\displaystyle [2_{0}2_{0}{*}{:}]} </td><td> ( ∗ 2 1 2 1 2 ⋅ 2 ) {\displaystyle (*2_{1}2_{1}2{\cdot }2)} , ( 2 0 ∗ 2 ⋅ 2 ) {\displaystyle (2_{0}{*}2{\cdot }2)} </td></tr><tr><td>54</td><td>Pcca</td><td>P 21/c 2/c 2/a</td><td> Γ o D 2 h 8 {\displaystyle \Gamma _{o}D_{2h}^{8}} </td><td>16a</td><td> ( c : a : b ) ⋅ a ~ : 2 ⋅ c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}} </td><td> ( 2 0 2 ∗ ¯ 0 ) {\displaystyle (2_{0}2{\bar {*}}_{0})} </td><td> ( ∗ 2 : 2 : 2 : 2 ) {\displaystyle (*2{:}2{:}2{:}2)} , ( ∗ 2 1 2 1 2 : 2 ) {\displaystyle (*2_{1}2_{1}2{:}2)} </td></tr><tr><td>55</td><td>Pbam</td><td>P 21/b 21/a 2/m</td><td> Γ o D 2 h 9 {\displaystyle \Gamma _{o}D_{2h}^{9}} </td><td>22a</td><td> ( c : a : b ) ⋅ m : 2 ⊙ a ~ {\displaystyle \left(c:a:b\right)\cdot m:2\odot {\tilde {a}}} </td><td> [ 2 0 2 0 × 0 ] {\displaystyle [2_{0}2_{0}{\times }_{0}]} </td><td> ( ∗ 2 ⋅ 2 : 2 ⋅ 2 ) {\displaystyle (*2{\cdot }2{:}2{\cdot }2)} </td></tr><tr><td>56</td><td>Pccn</td><td>P 21/c 21/c 2/n</td><td> Γ o D 2 h 10 {\displaystyle \Gamma _{o}D_{2h}^{10}} </td><td>27a</td><td> ( c : a : b ) ⋅ a b ~ : 2 ⋅ c ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot {\tilde {c}}} </td><td> ( 2 ∗ ¯ : 2 : 2 ) {\displaystyle (2{\bar {*}}{:}2{:}2)} </td><td> ( 2 1 2 ∗ ¯ 0 ) {\displaystyle (2_{1}2{\bar {*}}_{0})} </td></tr><tr><td>57</td><td>Pbcm</td><td>P 2/b 21/c 21/m</td><td> Γ o D 2 h 11 {\displaystyle \Gamma _{o}D_{2h}^{11}} </td><td>23a</td><td> ( c : a : b ) ⋅ m : 2 1 ⊙ c ~ {\displaystyle \left(c:a:b\right)\cdot m:2_{1}\odot {\tilde {c}}} </td><td> ( 2 0 2 ∗ ¯ ⋅ ) {\displaystyle (2_{0}2{\bar {*}}{\cdot })} </td><td> ( ∗ 2 : 2 ⋅ 2 : 2 ) {\displaystyle (*2{:}2{\cdot }2{:}2)} , [ 2 1 2 1 ∗ : ] {\displaystyle [2_{1}2_{1}{*}{:}]} </td></tr><tr><td>58</td><td>Pnnm</td><td>P 21/n 21/n 2/m</td><td> Γ o D 2 h 12 {\displaystyle \Gamma _{o}D_{2h}^{12}} </td><td>25a</td><td> ( c : a : b ) ⋅ m : 2 ⊙ a c ~ {\displaystyle \left(c:a:b\right)\cdot m:2\odot {\widetilde {ac}}} </td><td> [ 2 0 2 0 × 1 ] {\displaystyle [2_{0}2_{0}{\times }_{1}]} </td><td> ( 2 1 ∗ 2 ⋅ 2 ) {\displaystyle (2_{1}{*}2{\cdot }2)} </td></tr><tr><td>59</td><td>Pmmn</td><td>P 21/m 21/m 2/n</td><td> Γ o D 2 h 13 {\displaystyle \Gamma _{o}D_{2h}^{13}} </td><td>24a</td><td> ( c : a : b ) ⋅ a b ~ : 2 ⋅ m {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot m} </td><td> ( 2 ∗ ¯ ⋅ 2 ⋅ 2 ) {\displaystyle (2{\bar {*}}{\cdot }2{\cdot }2)} </td><td> [ 2 1 2 1 ∗ ⋅ ] {\displaystyle [2_{1}2_{1}{*}{\cdot }]} </td></tr><tr><td>60</td><td>Pbcn</td><td>P 21/b 2/c 21/n</td><td> Γ o D 2 h 14 {\displaystyle \Gamma _{o}D_{2h}^{14}} </td><td>26a</td><td> ( c : a : b ) ⋅ a b ~ : 2 1 ⊙ c ~ {\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2_{1}\odot {\tilde {c}}} </td><td> ( 2 0 2 ∗ ¯ : ) {\displaystyle (2_{0}2{\bar {*}}{:})} </td><td> ( 2 1 ∗ 2 : 2 ) {\displaystyle (2_{1}{*}2{:}2)} , ( 2 1 2 ∗ ¯ 1 ) {\displaystyle (2_{1}2{\bar {*}}_{1})} </td></tr><tr><td>61</td><td>Pbca</td><td>P 21/b 21/c 21/a</td><td> Γ o D 2 h 15 {\displaystyle \Gamma _{o}D_{2h}^{15}} </td><td>29a</td><td> ( c : a : b ) ⋅ a ~ : 2 1 ⊙ c ~ {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot {\tilde {c}}} </td><td> ( 2 1 2 ∗ ¯ : ) {\displaystyle (2_{1}2{\bar {*}}{:})} </td><td></td></tr><tr><td>62</td><td>Pnma</td><td>P 21/n 21/m 21/a</td><td> Γ o D 2 h 16 {\displaystyle \Gamma _{o}D_{2h}^{16}} </td><td>28a</td><td> ( c : a : b ) ⋅ a ~ : 2 1 ⊙ m {\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot m} </td><td> ( 2 1 2 ∗ ¯ ⋅ ) {\displaystyle (2_{1}2{\bar {*}}{\cdot })} </td><td> ( 2 ∗ ¯ ⋅ 2 : 2 ) {\displaystyle (2{\bar {*}}{\cdot }2{:}2)} , [ 2 1 2 1 × ] {\displaystyle [2_{1}2_{1}{\times }]} </td></tr><tr><td>63</td><td>Cmcm</td><td>C 2/m 2/c 21/m</td><td> Γ o b D 2 h 17 {\displaystyle \Gamma _{o}^{b}D_{2h}^{17}} </td><td>18a</td><td> ( 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}}} </td><td> [ 2 0 2 1 ∗ ⋅ ] {\displaystyle [2_{0}2_{1}{*}{\cdot }]} </td><td> ( ∗ 2 ⋅ 2 ⋅ 2 : 2 ) {\displaystyle (*2{\cdot }2{\cdot }2{:}2)} , [ 2 1 ∗ ⋅ 2 : 2 ] {\displaystyle [2_{1}{*}{\cdot }2{:}2]} </td></tr><tr><td>64</td><td>Cmce</td><td>C 2/m 2/c 21/a</td><td> Γ o b D 2 h 18 {\displaystyle \Gamma _{o}^{b}D_{2h}^{18}} </td><td>19a</td><td> ( 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}}} </td><td> [ 2 0 2 1 ∗ : ] {\displaystyle [2_{0}2_{1}{*}{:}]} </td><td> ( ∗ 2 ⋅ 2 : 2 : 2 ) {\displaystyle (*2{\cdot }2{:}2{:}2)} , ( ∗ 2 1 2 ⋅ 2 : 2 ) {\displaystyle (*2_{1}2{\cdot }2{:}2)} </td></tr><tr><td>65</td><td>Cmmm</td><td>C 2/m 2/m 2/m</td><td> Γ o b D 2 h 19 {\displaystyle \Gamma _{o}^{b}D_{2h}^{19}} </td><td>19s</td><td> ( a + b 2 : c : a : b ) ⋅ m : 2 ⋅ m {\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m} </td><td> [ 2 0 ∗ ⋅ 2 ⋅ 2 ] {\displaystyle [2_{0}{*}{\cdot }2{\cdot }2]} </td><td> [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 : 2 ] {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{:}2]} </td></tr><tr><td>66</td><td>Cccm</td><td>C 2/c 2/c 2/m</td><td> Γ o b D 2 h 20 {\displaystyle \Gamma _{o}^{b}D_{2h}^{20}} </td><td>20h</td><td> ( 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}}} </td><td> [ 2 0 ∗ : 2 : 2 ] {\displaystyle [2_{0}{*}{:}2{:}2]} </td><td> ( ∗ 2 0 2 1 2 ⋅ 2 ) {\displaystyle (*2_{0}2_{1}2{\cdot }2)} </td></tr><tr><td>67</td><td>Cmme</td><td>C 2/m 2/m 2/e</td><td> Γ o b D 2 h 21 {\displaystyle \Gamma _{o}^{b}D_{2h}^{21}} </td><td>21h</td><td> ( 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} </td><td> ( ∗ 2 0 2 ⋅ 2 ⋅ 2 ) {\displaystyle (*2_{0}2{\cdot }2{\cdot }2)} </td><td> [ ∗ ⋅ 2 : 2 : 2 : 2 ] {\displaystyle [*{\cdot }2{:}2{:}2{:}2]} </td></tr><tr><td>68</td><td>Ccce</td><td>C 2/c 2/c 2/e</td><td> Γ o b D 2 h 22 {\displaystyle \Gamma _{o}^{b}D_{2h}^{22}} </td><td>22h</td><td> ( 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}}} </td><td> ( ∗ 2 0 2 : 2 : 2 ) {\displaystyle (*2_{0}2{:}2{:}2)} </td><td> ( ∗ 2 0 2 1 2 : 2 ) {\displaystyle (*2_{0}2_{1}2{:}2)} </td></tr><tr><td>69</td><td>Fmmm</td><td>F 2/m 2/m 2/m</td><td> Γ o f D 2 h 23 {\displaystyle \Gamma _{o}^{f}D_{2h}^{23}} </td><td>21s</td><td> ( 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} </td><td> [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]} </td><td></td></tr><tr><td>70</td><td>Fddd</td><td>F 2/d 2/d 2/d</td><td> Γ o f D 2 h 24 {\displaystyle \Gamma _{o}^{f}D_{2h}^{24}} </td><td>24h</td><td> ( 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}}} </td><td> ( 2 ∗ ¯ 2 0 2 1 ) {\displaystyle (2{\bar {*}}2_{0}2_{1})} </td><td></td></tr><tr><td>71</td><td>Immm</td><td>I 2/m 2/m 2/m</td><td> Γ o v D 2 h 25 {\displaystyle \Gamma _{o}^{v}D_{2h}^{25}} </td><td>20s</td><td> ( 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} </td><td> [ 2 1 ∗ ⋅ 2 ⋅ 2 ] {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]} </td><td></td></tr><tr><td>72</td><td>Ibam</td><td>I 2/b 2/a 2/m</td><td> Γ o v D 2 h 26 {\displaystyle \Gamma _{o}^{v}D_{2h}^{26}} </td><td>23h</td><td> ( 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}}} </td><td> [ 2 1 ∗ : 2 : 2 ] {\displaystyle [2_{1}{*}{:}2{:}2]} </td><td> ( ∗ 2 0 2 ⋅ 2 : 2 ) {\displaystyle (*2_{0}2{\cdot }2{:}2)} </td></tr><tr><td>73</td><td>Ibca</td><td>I 2/b 2/c 2/a</td><td> Γ o v D 2 h 27 {\displaystyle \Gamma _{o}^{v}D_{2h}^{27}} </td><td>21a</td><td> ( 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}}} </td><td> ( ∗ 2 1 2 : 2 : 2 ) {\displaystyle (*2_{1}2{:}2{:}2)} </td><td></td></tr><tr><td>74</td><td>Imma</td><td>I 2/m 2/m 2/a</td><td> Γ o v D 2 h 28 {\displaystyle \Gamma _{o}^{v}D_{2h}^{28}} </td><td>20a</td><td> ( 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} </td><td> ( ∗ 2 1 2 ⋅ 2 ⋅ 2 ) {\displaystyle (*2_{1}2{\cdot }2{\cdot }2)} </td><td> [ 2 0 ∗ ⋅ 2 : 2 ] {\displaystyle [2_{0}{*}{\cdot }2{:}2]} </td></tr></tbody></table>
<h2 id="list-of-tetragonal">List of tetragonal</h2>
Tetragonal Bravais lattice<table><tbody><tr><th>Simple (P)</th><th>Body (I)</th></tr><tr><td></td><td></td></tr></tbody></table>
<a href="/facts/Tetragonal_crystal_system/12Aop255">Tetragonal crystal system</a><table><tbody><tr><th>Number</th><th><a href="/facts/Point_group/41NSqUN6">Point group</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></th><th>Short name</th><th>Full name</th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies</a></th><th><a href="/facts/Evgraf_Fedorov/fPqQhHMn">Fedorov</a></th><th><a href="/facts/Shubnikov_group/bCtqSDhI">Shubnikov</a></th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a></th></tr><tr><td>75</td><td rowspan="6">4</td><td rowspan="6"> 44 {\displaystyle 44} </td><td>P4</td><td>P 4</td><td> Γ q C 4 1 {\displaystyle \Gamma _{q}C_{4}^{1}} </td><td>22s</td><td> ( c : a : a ) : 4 {\displaystyle (c:a:a):4} </td><td> ( 4 0 4 0 2 0 ) {\displaystyle (4_{0}4_{0}2_{0})} </td></tr><tr><td>76</td><td>P41</td><td>P 41</td><td> Γ q C 4 2 {\displaystyle \Gamma _{q}C_{4}^{2}} </td><td>30a</td><td> ( c : a : a ) : 4 1 {\displaystyle (c:a:a):4_{1}} </td><td> ( 4 1 4 1 2 1 ) {\displaystyle (4_{1}4_{1}2_{1})} </td></tr><tr><td>77</td><td>P42</td><td>P 42</td><td> Γ q C 4 3 {\displaystyle \Gamma _{q}C_{4}^{3}} </td><td>33a</td><td> ( c : a : a ) : 4 2 {\displaystyle (c:a:a):4_{2}} </td><td> ( 4 2 4 2 2 0 ) {\displaystyle (4_{2}4_{2}2_{0})} </td></tr><tr><td>78</td><td>P43</td><td>P 43</td><td> Γ q C 4 4 {\displaystyle \Gamma _{q}C_{4}^{4}} </td><td>31a</td><td> ( c : a : a ) : 4 3 {\displaystyle (c:a:a):4_{3}} </td><td> ( 4 1 4 1 2 1 ) {\displaystyle (4_{1}4_{1}2_{1})} </td></tr><tr><td>79</td><td>I4</td><td>I 4</td><td> Γ q v C 4 5 {\displaystyle \Gamma _{q}^{v}C_{4}^{5}} </td><td>23s</td><td> ( a + b + c 2 / c : a : a ) : 4 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4} </td><td> ( 4 2 4 0 2 1 ) {\displaystyle (4_{2}4_{0}2_{1})} </td></tr><tr><td>80</td><td>I41</td><td>I 41</td><td> Γ q v C 4 6 {\displaystyle \Gamma _{q}^{v}C_{4}^{6}} </td><td>32a</td><td> ( a + b + c 2 / c : a : a ) : 4 1 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}} </td><td> ( 4 3 4 1 2 0 ) {\displaystyle (4_{3}4_{1}2_{0})} </td></tr><tr><td>81</td><td rowspan="2">4</td><td rowspan="2"> 2 × {\displaystyle 2\times } </td><td>P4</td><td>P 4</td><td> Γ q S 4 1 {\displaystyle \Gamma _{q}S_{4}^{1}} </td><td>26s</td><td> ( c : a : a ) : 4 ~ {\displaystyle (c:a:a):{\tilde {4}}} </td><td> ( 442 0 ) {\displaystyle (442_{0})} </td></tr><tr><td>82</td><td>I4</td><td>I 4</td><td> Γ q v S 4 2 {\displaystyle \Gamma _{q}^{v}S_{4}^{2}} </td><td>27s</td><td> ( a + b + c 2 / c : a : a ) : 4 ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}} </td><td> ( 442 1 ) {\displaystyle (442_{1})} </td></tr><tr><td>83</td><td rowspan="6">4/m</td><td rowspan="6"> 4 ∗ {\displaystyle 4*} </td><td>P4/m</td><td>P 4/m</td><td> Γ q C 4 h 1 {\displaystyle \Gamma _{q}C_{4h}^{1}} </td><td>28s</td><td> ( c : a : a ) ⋅ m : 4 {\displaystyle (c:a:a)\cdot m:4} </td><td> [ 4 0 4 0 2 0 ] {\displaystyle [4_{0}4_{0}2_{0}]} </td></tr><tr><td>84</td><td>P42/m</td><td>P 42/m</td><td> Γ q C 4 h 2 {\displaystyle \Gamma _{q}C_{4h}^{2}} </td><td>41a</td><td> ( c : a : a ) ⋅ m : 4 2 {\displaystyle (c:a:a)\cdot m:4_{2}} </td><td> [ 4 2 4 2 2 0 ] {\displaystyle [4_{2}4_{2}2_{0}]} </td></tr><tr><td>85</td><td>P4/n</td><td>P 4/n</td><td> Γ q C 4 h 3 {\displaystyle \Gamma _{q}C_{4h}^{3}} </td><td>29h</td><td> ( c : a : a ) ⋅ a b ~ : 4 {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4} </td><td> ( 44 0 2 ) {\displaystyle (44_{0}2)} </td></tr><tr><td>86</td><td>P42/n</td><td>P 42/n</td><td> Γ q C 4 h 4 {\displaystyle \Gamma _{q}C_{4h}^{4}} </td><td>42a</td><td> ( c : a : a ) ⋅ a b ~ : 4 2 {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}} </td><td> ( 44 2 2 ) {\displaystyle (44_{2}2)} </td></tr><tr><td>87</td><td>I4/m</td><td>I 4/m</td><td> Γ q v C 4 h 5 {\displaystyle \Gamma _{q}^{v}C_{4h}^{5}} </td><td>29s</td><td> ( a + b + c 2 / c : a : a ) ⋅ m : 4 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4} </td><td> [ 4 2 4 0 2 1 ] {\displaystyle [4_{2}4_{0}2_{1}]} </td></tr><tr><td>88</td><td>I41/a</td><td>I 41/a</td><td> Γ q v C 4 h 6 {\displaystyle \Gamma _{q}^{v}C_{4h}^{6}} </td><td>40a</td><td> ( 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}} </td><td> ( 44 1 2 ) {\displaystyle (44_{1}2)} </td></tr><tr><td>89</td><td rowspan="10">422</td><td rowspan="10"> 224 {\displaystyle 224} </td><td>P422</td><td>P 4 2 2</td><td> Γ q D 4 1 {\displaystyle \Gamma _{q}D_{4}^{1}} </td><td>30s</td><td> ( c : a : a ) : 4 : 2 {\displaystyle (c:a:a):4:2} </td><td> ( ∗ 4 0 4 0 2 0 ) {\displaystyle (*4_{0}4_{0}2_{0})} </td></tr><tr><td>90</td><td>P4212</td><td>P4212</td><td> Γ q D 4 2 {\displaystyle \Gamma _{q}D_{4}^{2}} </td><td>43a</td><td> ( c : a : a ) : 4 {\displaystyle (c:a:a):4} 2 1 {\displaystyle 2_{1}} </td><td> ( 4 0 ∗ 2 0 ) {\displaystyle (4_{0}{*}2_{0})} </td></tr><tr><td>91</td><td>P4122</td><td>P 41 2 2</td><td> Γ q D 4 3 {\displaystyle \Gamma _{q}D_{4}^{3}} </td><td>44a</td><td> ( c : a : a ) : 4 1 : 2 {\displaystyle (c:a:a):4_{1}:2} </td><td> ( ∗ 4 1 4 1 2 1 ) {\displaystyle (*4_{1}4_{1}2_{1})} </td></tr><tr><td>92</td><td>P41212</td><td>P 41 21 2</td><td> Γ q D 4 4 {\displaystyle \Gamma _{q}D_{4}^{4}} </td><td>48a</td><td> ( c : a : a ) : 4 1 {\displaystyle (c:a:a):4_{1}} 2 1 {\displaystyle 2_{1}} </td><td> ( 4 1 ∗ 2 1 ) {\displaystyle (4_{1}{*}2_{1})} </td></tr><tr><td>93</td><td>P4222</td><td>P 42 2 2</td><td> Γ q D 4 5 {\displaystyle \Gamma _{q}D_{4}^{5}} </td><td>47a</td><td> ( c : a : a ) : 4 2 : 2 {\displaystyle (c:a:a):4_{2}:2} </td><td> ( ∗ 4 2 4 2 2 0 ) {\displaystyle (*4_{2}4_{2}2_{0})} </td></tr><tr><td>94</td><td>P42212</td><td>P 42 21 2</td><td> Γ q D 4 6 {\displaystyle \Gamma _{q}D_{4}^{6}} </td><td>50a</td><td> ( c : a : a ) : 4 2 {\displaystyle (c:a:a):4_{2}} 2 1 {\displaystyle 2_{1}} </td><td> ( 4 2 ∗ 2 0 ) {\displaystyle (4_{2}{*}2_{0})} </td></tr><tr><td>95</td><td>P4322</td><td>P 43 2 2</td><td> Γ q D 4 7 {\displaystyle \Gamma _{q}D_{4}^{7}} </td><td>45a</td><td> ( c : a : a ) : 4 3 : 2 {\displaystyle (c:a:a):4_{3}:2} </td><td> ( ∗ 4 1 4 1 2 1 ) {\displaystyle (*4_{1}4_{1}2_{1})} </td></tr><tr><td>96</td><td>P43212</td><td>P 43 21 2</td><td> Γ q D 4 8 {\displaystyle \Gamma _{q}D_{4}^{8}} </td><td>49a</td><td> ( c : a : a ) : 4 3 {\displaystyle (c:a:a):4_{3}} 2 1 {\displaystyle 2_{1}} </td><td> ( 4 1 ∗ 2 1 ) {\displaystyle (4_{1}{*}2_{1})} </td></tr><tr><td>97</td><td>I422</td><td>I 4 2 2</td><td> Γ q v D 4 9 {\displaystyle \Gamma _{q}^{v}D_{4}^{9}} </td><td>31s</td><td> ( a + b + c 2 / c : a : a ) : 4 : 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2} </td><td> ( ∗ 4 2 4 0 2 1 ) {\displaystyle (*4_{2}4_{0}2_{1})} </td></tr><tr><td>98</td><td>I4122</td><td>I 41 2 2</td><td> Γ q v D 4 10 {\displaystyle \Gamma _{q}^{v}D_{4}^{10}} </td><td>46a</td><td> ( a + b + c 2 / c : a : a ) : 4 : 2 1 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2_{1}} </td><td> ( ∗ 4 3 4 1 2 0 ) {\displaystyle (*4_{3}4_{1}2_{0})} </td></tr><tr><td>99</td><td rowspan="12">4mm</td><td rowspan="12"> ∗ 44 {\displaystyle *44} </td><td>P4mm</td><td>P 4 m m</td><td> Γ q C 4 v 1 {\displaystyle \Gamma _{q}C_{4v}^{1}} </td><td>24s</td><td> ( c : a : a ) : 4 ⋅ m {\displaystyle (c:a:a):4\cdot m} </td><td> ( ∗ ⋅ 4 ⋅ 4 ⋅ 2 ) {\displaystyle (*{\cdot }4{\cdot }4{\cdot }2)} </td></tr><tr><td>100</td><td>P4bm</td><td>P 4 b m</td><td> Γ q C 4 v 2 {\displaystyle \Gamma _{q}C_{4v}^{2}} </td><td>26h</td><td> ( c : a : a ) : 4 ⊙ a ~ {\displaystyle (c:a:a):4\odot {\tilde {a}}} </td><td> ( 4 0 ∗ ⋅ 2 ) {\displaystyle (4_{0}{*}{\cdot }2)} </td></tr><tr><td>101</td><td>P42cm</td><td>P 42 c m</td><td> Γ q C 4 v 3 {\displaystyle \Gamma _{q}C_{4v}^{3}} </td><td>37a</td><td> ( c : a : a ) : 4 2 ⋅ c ~ {\displaystyle (c:a:a):4_{2}\cdot {\tilde {c}}} </td><td> ( ∗ : 4 ⋅ 4 : 2 ) {\displaystyle (*{:}4{\cdot }4{:}2)} </td></tr><tr><td>102</td><td>P42nm</td><td>P 42 n m</td><td> Γ q C 4 v 4 {\displaystyle \Gamma _{q}C_{4v}^{4}} </td><td>38a</td><td> ( c : a : a ) : 4 2 ⊙ a c ~ {\displaystyle (c:a:a):4_{2}\odot {\widetilde {ac}}} </td><td> ( 4 2 ∗ ⋅ 2 ) {\displaystyle (4_{2}{*}{\cdot }2)} </td></tr><tr><td>103</td><td>P4cc</td><td>P 4 c c</td><td> Γ q C 4 v 5 {\displaystyle \Gamma _{q}C_{4v}^{5}} </td><td>25h</td><td> ( c : a : a ) : 4 ⋅ c ~ {\displaystyle (c:a:a):4\cdot {\tilde {c}}} </td><td> ( ∗ : 4 : 4 : 2 ) {\displaystyle (*{:}4{:}4{:}2)} </td></tr><tr><td>104</td><td>P4nc</td><td>P 4 n c</td><td> Γ q C 4 v 6 {\displaystyle \Gamma _{q}C_{4v}^{6}} </td><td>27h</td><td> ( c : a : a ) : 4 ⊙ a c ~ {\displaystyle (c:a:a):4\odot {\widetilde {ac}}} </td><td> ( 4 0 ∗ : 2 ) {\displaystyle (4_{0}{*}{:}2)} </td></tr><tr><td>105</td><td>P42mc</td><td>P 42 m c</td><td> Γ q C 4 v 7 {\displaystyle \Gamma _{q}C_{4v}^{7}} </td><td>36a</td><td> ( c : a : a ) : 4 2 ⋅ m {\displaystyle (c:a:a):4_{2}\cdot m} </td><td> ( ∗ ⋅ 4 : 4 ⋅ 2 ) {\displaystyle (*{\cdot }4{:}4{\cdot }2)} </td></tr><tr><td>106</td><td>P42bc</td><td>P 42 b c</td><td> Γ q C 4 v 8 {\displaystyle \Gamma _{q}C_{4v}^{8}} </td><td>39a</td><td> ( c : a : a ) : 4 ⊙ a ~ {\displaystyle (c:a:a):4\odot {\tilde {a}}} </td><td> ( 4 2 ∗ : 2 ) {\displaystyle (4_{2}{*}{:}2)} </td></tr><tr><td>107</td><td>I4mm</td><td>I 4 m m</td><td> Γ q v C 4 v 9 {\displaystyle \Gamma _{q}^{v}C_{4v}^{9}} </td><td>25s</td><td> ( a + b + c 2 / c : a : a ) : 4 ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot m} </td><td> ( ∗ ⋅ 4 ⋅ 4 : 2 ) {\displaystyle (*{\cdot }4{\cdot }4{:}2)} </td></tr><tr><td>108</td><td>I4cm</td><td>I 4 c m</td><td> Γ q v C 4 v 10 {\displaystyle \Gamma _{q}^{v}C_{4v}^{10}} </td><td>28h</td><td> ( a + b + c 2 / c : a : a ) : 4 ⋅ c ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot {\tilde {c}}} </td><td> ( ∗ ⋅ 4 : 4 : 2 ) {\displaystyle (*{\cdot }4{:}4{:}2)} </td></tr><tr><td>109</td><td>I41md</td><td>I 41 m d</td><td> Γ q v C 4 v 11 {\displaystyle \Gamma _{q}^{v}C_{4v}^{11}} </td><td>34a</td><td> ( 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} </td><td> ( 4 1 ∗ ⋅ 2 ) {\displaystyle (4_{1}{*}{\cdot }2)} </td></tr><tr><td>110</td><td>I41cd</td><td>I 41 c d</td><td> Γ q v C 4 v 12 {\displaystyle \Gamma _{q}^{v}C_{4v}^{12}} </td><td>35a</td><td> ( 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}}} </td><td> ( 4 1 ∗ : 2 ) {\displaystyle (4_{1}{*}{:}2)} </td></tr><tr><td>111</td><td rowspan="12">42m</td><td rowspan="12"> 2 ∗ 2 {\displaystyle 2{*}2} </td><td>P42m</td><td>P 4 2 m</td><td> Γ q D 2 d 1 {\displaystyle \Gamma _{q}D_{2d}^{1}} </td><td>32s</td><td> ( c : a : a ) : 4 ~ : 2 {\displaystyle (c:a:a):{\tilde {4}}:2} </td><td> ( ∗ 4 ⋅ 42 0 ) {\displaystyle (*4{\cdot }42_{0})} </td></tr><tr><td>112</td><td>P42c</td><td>P 4 2 c</td><td> Γ q D 2 d 2 {\displaystyle \Gamma _{q}D_{2d}^{2}} </td><td>30h</td><td> ( c : a : a ) : 4 ~ {\displaystyle (c:a:a):{\tilde {4}}} 2 {\displaystyle 2} </td><td> ( ∗ 4 : 42 0 ) {\displaystyle (*4{:}42_{0})} </td></tr><tr><td>113</td><td>P421m</td><td>P 4 21 m</td><td> Γ q D 2 d 3 {\displaystyle \Gamma _{q}D_{2d}^{3}} </td><td>52a</td><td> ( c : a : a ) : 4 ~ ⋅ a b ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {ab}}} </td><td> ( 4 ∗ ¯ ⋅ 2 ) {\displaystyle (4{\bar {*}}{\cdot }2)} </td></tr><tr><td>114</td><td>P421c</td><td>P 4 21 c</td><td> Γ q D 2 d 4 {\displaystyle \Gamma _{q}D_{2d}^{4}} </td><td>53a</td><td> ( c : a : a ) : 4 ~ ⋅ a b c ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {abc}}} </td><td> ( 4 ∗ ¯ : 2 ) {\displaystyle (4{\bar {*}}{:}2)} </td></tr><tr><td>115</td><td>P4m2</td><td>P 4 m 2</td><td> Γ q D 2 d 5 {\displaystyle \Gamma _{q}D_{2d}^{5}} </td><td>33s</td><td> ( c : a : a ) : 4 ~ ⋅ m {\displaystyle (c:a:a):{\tilde {4}}\cdot m} </td><td> ( ∗ ⋅ 44 ⋅ 2 ) {\displaystyle (*{\cdot }44{\cdot }2)} </td></tr><tr><td>116</td><td>P4c2</td><td>P 4 c 2</td><td> Γ q D 2 d 6 {\displaystyle \Gamma _{q}D_{2d}^{6}} </td><td>31h</td><td> ( c : a : a ) : 4 ~ ⋅ c ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\tilde {c}}} </td><td> ( ∗ : 44 : 2 ) {\displaystyle (*{:}44{:}2)} </td></tr><tr><td>117</td><td>P4b2</td><td>P 4 b 2</td><td> Γ q D 2 d 7 {\displaystyle \Gamma _{q}D_{2d}^{7}} </td><td>32h</td><td> ( c : a : a ) : 4 ~ ⊙ a ~ {\displaystyle (c:a:a):{\tilde {4}}\odot {\tilde {a}}} </td><td> ( 4 ∗ ¯ 0 2 0 ) {\displaystyle (4{\bar {*}}_{0}2_{0})} </td></tr><tr><td>118</td><td>P4n2</td><td>P 4 n 2</td><td> Γ q D 2 d 8 {\displaystyle \Gamma _{q}D_{2d}^{8}} </td><td>33h</td><td> ( c : a : a ) : 4 ~ ⋅ a c ~ {\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {ac}}} </td><td> ( 4 ∗ ¯ 1 2 0 ) {\displaystyle (4{\bar {*}}_{1}2_{0})} </td></tr><tr><td>119</td><td>I4m2</td><td>I 4 m 2</td><td> Γ q v D 2 d 9 {\displaystyle \Gamma _{q}^{v}D_{2d}^{9}} </td><td>35s</td><td> ( a + b + c 2 / c : a : a ) : 4 ~ ⋅ m {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot m} </td><td> ( ∗ 4 ⋅ 42 1 ) {\displaystyle (*4{\cdot }42_{1})} </td></tr><tr><td>120</td><td>I4c2</td><td>I 4 c 2</td><td> Γ q v D 2 d 10 {\displaystyle \Gamma _{q}^{v}D_{2d}^{10}} </td><td>34h</td><td> ( 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}}} </td><td> ( ∗ 4 : 42 1 ) {\displaystyle (*4{:}42_{1})} </td></tr><tr><td>121</td><td>I42m</td><td>I 4 2 m</td><td> Γ q v D 2 d 11 {\displaystyle \Gamma _{q}^{v}D_{2d}^{11}} </td><td>34s</td><td> ( a + b + c 2 / c : a : a ) : 4 ~ : 2 {\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}:2} </td><td> ( ∗ ⋅ 44 : 2 ) {\displaystyle (*{\cdot }44{:}2)} </td></tr><tr><td>122</td><td>I42d</td><td>I 4 2 d</td><td> Γ q v D 2 d 12 {\displaystyle \Gamma _{q}^{v}D_{2d}^{12}} </td><td>51a</td><td> ( 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}}} </td><td> ( 4 ∗ ¯ 2 1 ) {\displaystyle (4{\bar {*}}2_{1})} </td></tr><tr><td>123</td><td rowspan="20">4/m 2/m 2/m</td><td rowspan="20"> ∗ 224 {\displaystyle *224} </td><td>P4/mmm</td><td>P 4/m 2/m 2/m</td><td> Γ q D 4 h 1 {\displaystyle \Gamma _{q}D_{4h}^{1}} </td><td>36s</td><td> ( c : a : a ) ⋅ m : 4 ⋅ m {\displaystyle (c:a:a)\cdot m:4\cdot m} </td><td> [ ∗ ⋅ 4 ⋅ 4 ⋅ 2 ] {\displaystyle [*{\cdot }4{\cdot }4{\cdot }2]} </td></tr><tr><td>124</td><td>P4/mcc</td><td>P 4/m 2/c 2/c</td><td> Γ q D 4 h 2 {\displaystyle \Gamma _{q}D_{4h}^{2}} </td><td>35h</td><td> ( c : a : a ) ⋅ m : 4 ⋅ c ~ {\displaystyle (c:a:a)\cdot m:4\cdot {\tilde {c}}} </td><td> [ ∗ : 4 : 4 : 2 ] {\displaystyle [*{:}4{:}4{:}2]} </td></tr><tr><td>125</td><td>P4/nbm</td><td>P 4/n 2/b 2/m</td><td> Γ q D 4 h 3 {\displaystyle \Gamma _{q}D_{4h}^{3}} </td><td>36h</td><td> ( c : a : a ) ⋅ a b ~ : 4 ⊙ a ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\odot {\tilde {a}}} </td><td> ( ∗ 4 0 4 ⋅ 2 ) {\displaystyle (*4_{0}4{\cdot }2)} </td></tr><tr><td>126</td><td>P4/nnc</td><td>P 4/n 2/n 2/c</td><td> Γ q D 4 h 4 {\displaystyle \Gamma _{q}D_{4h}^{4}} </td><td>37h</td><td> ( c : a : a ) ⋅ a b ~ : 4 ⊙ a c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\odot {\widetilde {ac}}} </td><td> ( ∗ 4 0 4 : 2 ) {\displaystyle (*4_{0}4{:}2)} </td></tr><tr><td>127</td><td>P4/mbm</td><td>P 4/m 21/b 2/m</td><td> Γ q D 4 h 5 {\displaystyle \Gamma _{q}D_{4h}^{5}} </td><td>54a</td><td> ( c : a : a ) ⋅ m : 4 ⊙ a ~ {\displaystyle (c:a:a)\cdot m:4\odot {\tilde {a}}} </td><td> [ 4 0 ∗ ⋅ 2 ] {\displaystyle [4_{0}{*}{\cdot }2]} </td></tr><tr><td>128</td><td>P4/mnc</td><td>P 4/m 21/n 2/c</td><td> Γ q D 4 h 6 {\displaystyle \Gamma _{q}D_{4h}^{6}} </td><td>56a</td><td> ( c : a : a ) ⋅ m : 4 ⊙ a c ~ {\displaystyle (c:a:a)\cdot m:4\odot {\widetilde {ac}}} </td><td> [ 4 0 ∗ : 2 ] {\displaystyle [4_{0}{*}{:}2]} </td></tr><tr><td>129</td><td>P4/nmm</td><td>P 4/n 21/m 2/m</td><td> Γ q D 4 h 7 {\displaystyle \Gamma _{q}D_{4h}^{7}} </td><td>55a</td><td> ( c : a : a ) ⋅ a b ~ : 4 ⋅ m {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\cdot m} </td><td> ( ∗ 4 ⋅ 4 ⋅ 2 ) {\displaystyle (*4{\cdot }4{\cdot }2)} </td></tr><tr><td>130</td><td>P4/ncc</td><td>P 4/n 21/c 2/c</td><td> Γ q D 4 h 8 {\displaystyle \Gamma _{q}D_{4h}^{8}} </td><td>57a</td><td> ( c : a : a ) ⋅ a b ~ : 4 ⋅ c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\cdot {\tilde {c}}} </td><td> ( ∗ 4 : 4 : 2 ) {\displaystyle (*4{:}4{:}2)} </td></tr><tr><td>131</td><td>P42/mmc</td><td>P 42/m 2/m 2/c</td><td> Γ q D 4 h 9 {\displaystyle \Gamma _{q}D_{4h}^{9}} </td><td>60a</td><td> ( c : a : a ) ⋅ m : 4 2 ⋅ m {\displaystyle (c:a:a)\cdot m:4_{2}\cdot m} </td><td> [ ∗ ⋅ 4 : 4 ⋅ 2 ] {\displaystyle [*{\cdot }4{:}4{\cdot }2]} </td></tr><tr><td>132</td><td>P42/mcm</td><td>P 42/m 2/c 2/m</td><td> Γ q D 4 h 10 {\displaystyle \Gamma _{q}D_{4h}^{10}} </td><td>61a</td><td> ( c : a : a ) ⋅ m : 4 2 ⋅ c ~ {\displaystyle (c:a:a)\cdot m:4_{2}\cdot {\tilde {c}}} </td><td> [ ∗ : 4 ⋅ 4 : 2 ] {\displaystyle [*{:}4{\cdot }4{:}2]} </td></tr><tr><td>133</td><td>P42/nbc</td><td>P 42/n 2/b 2/c</td><td> Γ q D 4 h 11 {\displaystyle \Gamma _{q}D_{4h}^{11}} </td><td>63a</td><td> ( c : a : a ) ⋅ a b ~ : 4 2 ⊙ a ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\tilde {a}}} </td><td> ( ∗ 4 2 4 : 2 ) {\displaystyle (*4_{2}4{:}2)} </td></tr><tr><td>134</td><td>P42/nnm</td><td>P 42/n 2/n 2/m</td><td> Γ q D 4 h 12 {\displaystyle \Gamma _{q}D_{4h}^{12}} </td><td>62a</td><td> ( c : a : a ) ⋅ a b ~ : 4 2 ⊙ a c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\widetilde {ac}}} </td><td> ( ∗ 4 2 4 ⋅ 2 ) {\displaystyle (*4_{2}4{\cdot }2)} </td></tr><tr><td>135</td><td>P42/mbc</td><td>P 42/m 21/b 2/c</td><td> Γ q D 4 h 13 {\displaystyle \Gamma _{q}D_{4h}^{13}} </td><td>66a</td><td> ( c : a : a ) ⋅ m : 4 2 ⊙ a ~ {\displaystyle (c:a:a)\cdot m:4_{2}\odot {\tilde {a}}} </td><td> [ 4 2 ∗ : 2 ] {\displaystyle [4_{2}{*}{:}2]} </td></tr><tr><td>136</td><td>P42/mnm</td><td>P 42/m 21/n 2/m</td><td> Γ q D 4 h 14 {\displaystyle \Gamma _{q}D_{4h}^{14}} </td><td>65a</td><td> ( c : a : a ) ⋅ m : 4 2 ⊙ a c ~ {\displaystyle (c:a:a)\cdot m:4_{2}\odot {\widetilde {ac}}} </td><td> [ 4 2 ∗ ⋅ 2 ] {\displaystyle [4_{2}{*}{\cdot }2]} </td></tr><tr><td>137</td><td>P42/nmc</td><td>P 42/n 21/m 2/c</td><td> Γ q D 4 h 15 {\displaystyle \Gamma _{q}D_{4h}^{15}} </td><td>67a</td><td> ( c : a : a ) ⋅ a b ~ : 4 2 ⋅ m {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot m} </td><td> ( ∗ 4 ⋅ 4 : 2 ) {\displaystyle (*4{\cdot }4{:}2)} </td></tr><tr><td>138</td><td>P42/ncm</td><td>P 42/n 21/c 2/m</td><td> Γ q D 4 h 16 {\displaystyle \Gamma _{q}D_{4h}^{16}} </td><td>65a</td><td> ( c : a : a ) ⋅ a b ~ : 4 2 ⋅ c ~ {\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot {\tilde {c}}} </td><td> ( ∗ 4 : 4 ⋅ 2 ) {\displaystyle (*4{:}4{\cdot }2)} </td></tr><tr><td>139</td><td>I4/mmm</td><td>I 4/m 2/m 2/m</td><td> Γ q v D 4 h 17 {\displaystyle \Gamma _{q}^{v}D_{4h}^{17}} </td><td>37s</td><td> ( 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} </td><td> [ ∗ ⋅ 4 ⋅ 4 : 2 ] {\displaystyle [*{\cdot }4{\cdot }4{:}2]} </td></tr><tr><td>140</td><td>I4/mcm</td><td>I 4/m 2/c 2/m</td><td> Γ q v D 4 h 18 {\displaystyle \Gamma _{q}^{v}D_{4h}^{18}} </td><td>38h</td><td> ( 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}}} </td><td> [ ∗ ⋅ 4 : 4 : 2 ] {\displaystyle [*{\cdot }4{:}4{:}2]} </td></tr><tr><td>141</td><td>I41/amd</td><td>I 41/a 2/m 2/d</td><td> Γ q v D 4 h 19 {\displaystyle \Gamma _{q}^{v}D_{4h}^{19}} </td><td>59a</td><td> ( 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} </td><td> ( ∗ 4 1 4 ⋅ 2 ) {\displaystyle (*4_{1}4{\cdot }2)} </td></tr><tr><td>142</td><td>I41/acd</td><td>I 41/a 2/c 2/d</td><td> Γ q v D 4 h 20 {\displaystyle \Gamma _{q}^{v}D_{4h}^{20}} </td><td>58a</td><td> ( 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}}} </td><td> ( ∗ 4 1 4 : 2 ) {\displaystyle (*4_{1}4{:}2)} </td></tr></tbody></table>
<h2 id="list-of-trigonal">List of trigonal</h2>
Trigonal Bravais lattice<table><tbody><tr><th>Rhombohedral (R)</th><th>Hexagonal (P)</th></tr><tr><td></td><td></td></tr></tbody></table>
<a href="/facts/Trigonal_crystal_system/sSSok8wo">Trigonal crystal system</a><table><tbody><tr><th>Number</th><th><a href="/facts/Point_group/41NSqUN6">Point group</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></th><th>Short name</th><th>Full name</th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies</a></th><th><a href="/facts/Evgraf_Fedorov/fPqQhHMn">Fedorov</a></th><th><a href="/facts/Shubnikov_group/bCtqSDhI">Shubnikov</a></th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a></th></tr><tr><td>143</td><td rowspan="4">3</td><td rowspan="4"> 33 {\displaystyle 33} </td><td>P3</td><td>P 3</td><td> Γ h C 3 1 {\displaystyle \Gamma _{h}C_{3}^{1}} </td><td>38s</td><td> ( c : ( a / a ) ) : 3 {\displaystyle (c:(a/a)):3} </td><td> ( 3 0 3 0 3 0 ) {\displaystyle (3_{0}3_{0}3_{0})} </td></tr><tr><td>144</td><td>P31</td><td>P 31</td><td> Γ h C 3 2 {\displaystyle \Gamma _{h}C_{3}^{2}} </td><td>68a</td><td> ( c : ( a / a ) ) : 3 1 {\displaystyle (c:(a/a)):3_{1}} </td><td> ( 3 1 3 1 3 1 ) {\displaystyle (3_{1}3_{1}3_{1})} </td></tr><tr><td>145</td><td>P32</td><td>P 32</td><td> Γ h C 3 3 {\displaystyle \Gamma _{h}C_{3}^{3}} </td><td>69a</td><td> ( c : ( a / a ) ) : 3 2 {\displaystyle (c:(a/a)):3_{2}} </td><td> ( 3 1 3 1 3 1 ) {\displaystyle (3_{1}3_{1}3_{1})} </td></tr><tr><td>146</td><td>R3</td><td>R 3</td><td> Γ r h C 3 4 {\displaystyle \Gamma _{rh}C_{3}^{4}} </td><td>39s</td><td> ( a / a / a ) / 3 {\displaystyle (a/a/a)/3} </td><td> ( 3 0 3 1 3 2 ) {\displaystyle (3_{0}3_{1}3_{2})} </td></tr><tr><td>147</td><td rowspan="2">3</td><td rowspan="2"> 3 × {\displaystyle 3\times } </td><td>P3</td><td>P 3</td><td> Γ h C 3 i 1 {\displaystyle \Gamma _{h}C_{3i}^{1}} </td><td>51s</td><td> ( c : ( a / a ) ) : 6 ~ {\displaystyle (c:(a/a)):{\tilde {6}}} </td><td> ( 63 0 2 ) {\displaystyle (63_{0}2)} </td></tr><tr><td>148</td><td>R3</td><td>R 3</td><td> Γ r h C 3 i 2 {\displaystyle \Gamma _{rh}C_{3i}^{2}} </td><td>52s</td><td> ( a / a / a ) / 6 ~ {\displaystyle (a/a/a)/{\tilde {6}}} </td><td> ( 63 1 2 ) {\displaystyle (63_{1}2)} </td></tr><tr><td>149</td><td rowspan="7">32</td><td rowspan="7"> 223 {\displaystyle 223} </td><td>P312</td><td>P 3 1 2</td><td> Γ h D 3 1 {\displaystyle \Gamma _{h}D_{3}^{1}} </td><td>45s</td><td> ( c : ( a / a ) ) : 2 : 3 {\displaystyle (c:(a/a)):2:3} </td><td> ( ∗ 3 0 3 0 3 0 ) {\displaystyle (*3_{0}3_{0}3_{0})} </td></tr><tr><td>150</td><td>P321</td><td>P 3 2 1</td><td> Γ h D 3 2 {\displaystyle \Gamma _{h}D_{3}^{2}} </td><td>44s</td><td> ( c : ( a / a ) ) ⋅ 2 : 3 {\displaystyle (c:(a/a))\cdot 2:3} </td><td> ( 3 0 ∗ 3 0 ) {\displaystyle (3_{0}{*}3_{0})} </td></tr><tr><td>151</td><td>P3112</td><td>P 31 1 2</td><td> Γ h D 3 3 {\displaystyle \Gamma _{h}D_{3}^{3}} </td><td>72a</td><td> ( c : ( a / a ) ) : 2 : 3 1 {\displaystyle (c:(a/a)):2:3_{1}} </td><td> ( ∗ 3 1 3 1 3 1 ) {\displaystyle (*3_{1}3_{1}3_{1})} </td></tr><tr><td>152</td><td>P3121</td><td>P 31 2 1</td><td> Γ h D 3 4 {\displaystyle \Gamma _{h}D_{3}^{4}} </td><td>70a</td><td> ( c : ( a / a ) ) ⋅ 2 : 3 1 {\displaystyle (c:(a/a))\cdot 2:3_{1}} </td><td> ( 3 1 ∗ 3 1 ) {\displaystyle (3_{1}{*}3_{1})} </td></tr><tr><td>153</td><td>P3212</td><td>P 32 1 2</td><td> Γ h D 3 5 {\displaystyle \Gamma _{h}D_{3}^{5}} </td><td>73a</td><td> ( c : ( a / a ) ) : 2 : 3 2 {\displaystyle (c:(a/a)):2:3_{2}} </td><td> ( ∗ 3 1 3 1 3 1 ) {\displaystyle (*3_{1}3_{1}3_{1})} </td></tr><tr><td>154</td><td>P3221</td><td>P 32 2 1</td><td> Γ h D 3 6 {\displaystyle \Gamma _{h}D_{3}^{6}} </td><td>71a</td><td> ( c : ( a / a ) ) ⋅ 2 : 3 2 {\displaystyle (c:(a/a))\cdot 2:3_{2}} </td><td> ( 3 1 ∗ 3 1 ) {\displaystyle (3_{1}{*}3_{1})} </td></tr><tr><td>155</td><td>R32</td><td>R 3 2</td><td> Γ r h D 3 7 {\displaystyle \Gamma _{rh}D_{3}^{7}} </td><td>46s</td><td> ( a / a / a ) / 3 : 2 {\displaystyle (a/a/a)/3:2} </td><td> ( ∗ 3 0 3 1 3 2 ) {\displaystyle (*3_{0}3_{1}3_{2})} </td></tr><tr><td>156</td><td rowspan="6">3m</td><td rowspan="6"> ∗ 33 {\displaystyle *33} </td><td>P3m1</td><td>P 3 m 1</td><td> Γ h C 3 v 1 {\displaystyle \Gamma _{h}C_{3v}^{1}} </td><td>40s</td><td> ( c : ( a / a ) ) : m ⋅ 3 {\displaystyle (c:(a/a)):m\cdot 3} </td><td> ( ∗ ⋅ 3 ⋅ 3 ⋅ 3 ) {\displaystyle (*{\cdot }3{\cdot }3{\cdot }3)} </td></tr><tr><td>157</td><td>P31m</td><td>P 3 1 m</td><td> Γ h C 3 v 2 {\displaystyle \Gamma _{h}C_{3v}^{2}} </td><td>41s</td><td> ( c : ( a / a ) ) ⋅ m ⋅ 3 {\displaystyle (c:(a/a))\cdot m\cdot 3} </td><td> ( 3 0 ∗ ⋅ 3 ) {\displaystyle (3_{0}{*}{\cdot }3)} </td></tr><tr><td>158</td><td>P3c1</td><td>P 3 c 1</td><td> Γ h C 3 v 3 {\displaystyle \Gamma _{h}C_{3v}^{3}} </td><td>39h</td><td> ( c : ( a / a ) ) : c ~ : 3 {\displaystyle (c:(a/a)):{\tilde {c}}:3} </td><td> ( ∗ : 3 : 3 : 3 ) {\displaystyle (*{:}3{:}3{:}3)} </td></tr><tr><td>159</td><td>P31c</td><td>P 3 1 c</td><td> Γ h C 3 v 4 {\displaystyle \Gamma _{h}C_{3v}^{4}} </td><td>40h</td><td> ( c : ( a / a ) ) ⋅ c ~ : 3 {\displaystyle (c:(a/a))\cdot {\tilde {c}}:3} </td><td> ( 3 0 ∗ : 3 ) {\displaystyle (3_{0}{*}{:}3)} </td></tr><tr><td>160</td><td>R3m</td><td>R 3 m</td><td> Γ r h C 3 v 5 {\displaystyle \Gamma _{rh}C_{3v}^{5}} </td><td>42s</td><td> ( a / a / a ) / 3 ⋅ m {\displaystyle (a/a/a)/3\cdot m} </td><td> ( 3 1 ∗ ⋅ 3 ) {\displaystyle (3_{1}{*}{\cdot }3)} </td></tr><tr><td>161</td><td>R3c</td><td>R 3 c</td><td> Γ r h C 3 v 6 {\displaystyle \Gamma _{rh}C_{3v}^{6}} </td><td>41h</td><td> ( a / a / a ) / 3 ⋅ c ~ {\displaystyle (a/a/a)/3\cdot {\tilde {c}}} </td><td> ( 3 1 ∗ : 3 ) {\displaystyle (3_{1}{*}{:}3)} </td></tr><tr><td>162</td><td rowspan="6">3 2/m</td><td rowspan="6"> 2 ∗ 3 {\displaystyle 2{*}3} </td><td>P31m</td><td>P 3 1 2/m</td><td> Γ h D 3 d 1 {\displaystyle \Gamma _{h}D_{3d}^{1}} </td><td>56s</td><td> ( c : ( a / a ) ) ⋅ m ⋅ 6 ~ {\displaystyle (c:(a/a))\cdot m\cdot {\tilde {6}}} </td><td> ( ∗ ⋅ 63 0 2 ) {\displaystyle (*{\cdot }63_{0}2)} </td></tr><tr><td>163</td><td>P31c</td><td>P 3 1 2/c</td><td> Γ h D 3 d 2 {\displaystyle \Gamma _{h}D_{3d}^{2}} </td><td>46h</td><td> ( c : ( a / a ) ) ⋅ c ~ ⋅ 6 ~ {\displaystyle (c:(a/a))\cdot {\tilde {c}}\cdot {\tilde {6}}} </td><td> ( ∗ : 63 0 2 ) {\displaystyle (*{:}63_{0}2)} </td></tr><tr><td>164</td><td>P3m1</td><td>P 3 2/m 1</td><td> Γ h D 3 d 3 {\displaystyle \Gamma _{h}D_{3d}^{3}} </td><td>55s</td><td> ( c : ( a / a ) ) : m ⋅ 6 ~ {\displaystyle (c:(a/a)):m\cdot {\tilde {6}}} </td><td> ( ∗ 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*6{\cdot }3{\cdot }2)} </td></tr><tr><td>165</td><td>P3c1</td><td>P 3 2/c 1</td><td> Γ h D 3 d 4 {\displaystyle \Gamma _{h}D_{3d}^{4}} </td><td>45h</td><td> ( c : ( a / a ) ) : c ~ ⋅ 6 ~ {\displaystyle (c:(a/a)):{\tilde {c}}\cdot {\tilde {6}}} </td><td> ( ∗ 6 : 3 : 2 ) {\displaystyle (*6{:}3{:}2)} </td></tr><tr><td>166</td><td>R3m</td><td>R 3 2/m</td><td> Γ r h D 3 d 5 {\displaystyle \Gamma _{rh}D_{3d}^{5}} </td><td>57s</td><td> ( a / a / a ) / 6 ~ ⋅ m {\displaystyle (a/a/a)/{\tilde {6}}\cdot m} </td><td> ( ∗ ⋅ 63 1 2 ) {\displaystyle (*{\cdot }63_{1}2)} </td></tr><tr><td>167</td><td>R3c</td><td>R 3 2/c</td><td> Γ r h D 3 d 6 {\displaystyle \Gamma _{rh}D_{3d}^{6}} </td><td>47h</td><td> ( a / a / a ) / 6 ~ ⋅ c ~ {\displaystyle (a/a/a)/{\tilde {6}}\cdot {\tilde {c}}} </td><td> ( ∗ : 63 1 2 ) {\displaystyle (*{:}63_{1}2)} </td></tr></tbody></table>
<h2 id="list-of-hexagonal">List of hexagonal</h2>
Hexagonal Bravais lattice<table><tbody><tr><td></td></tr></tbody></table>
<a href="/facts/Hexagonal_crystal_system/sSSok8wo">Hexagonal crystal system</a><table><tbody><tr><th>Number</th><th><a href="/facts/Point_group/41NSqUN6">Point group</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></th><th>Short name</th><th>Full name</th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies</a></th><th><a href="/facts/Evgraf_Fedorov/fPqQhHMn">Fedorov</a></th><th><a href="/facts/Shubnikov_group/bCtqSDhI">Shubnikov</a></th><th><a href="/facts/Fibrifold_notation/2Eb13dNI">Fibrifold</a></th></tr><tr><td>168</td><td rowspan="6">6</td><td rowspan="6"> 66 {\displaystyle 66} </td><td>P6</td><td>P 6</td><td> Γ h C 6 1 {\displaystyle \Gamma _{h}C_{6}^{1}} </td><td>49s</td><td> ( c : ( a / a ) ) : 6 {\displaystyle (c:(a/a)):6} </td><td> ( 6 0 3 0 2 0 ) {\displaystyle (6_{0}3_{0}2_{0})} </td></tr><tr><td>169</td><td>P61</td><td>P 61</td><td> Γ h C 6 2 {\displaystyle \Gamma _{h}C_{6}^{2}} </td><td>74a</td><td> ( c : ( a / a ) ) : 6 1 {\displaystyle (c:(a/a)):6_{1}} </td><td> ( 6 1 3 1 2 1 ) {\displaystyle (6_{1}3_{1}2_{1})} </td></tr><tr><td>170</td><td>P65</td><td>P 65</td><td> Γ h C 6 3 {\displaystyle \Gamma _{h}C_{6}^{3}} </td><td>75a</td><td> ( c : ( a / a ) ) : 6 5 {\displaystyle (c:(a/a)):6_{5}} </td><td> ( 6 1 3 1 2 1 ) {\displaystyle (6_{1}3_{1}2_{1})} </td></tr><tr><td>171</td><td>P62</td><td>P 62</td><td> Γ h C 6 4 {\displaystyle \Gamma _{h}C_{6}^{4}} </td><td>76a</td><td> ( c : ( a / a ) ) : 6 2 {\displaystyle (c:(a/a)):6_{2}} </td><td> ( 6 2 3 2 2 0 ) {\displaystyle (6_{2}3_{2}2_{0})} </td></tr><tr><td>172</td><td>P64</td><td>P 64</td><td> Γ h C 6 5 {\displaystyle \Gamma _{h}C_{6}^{5}} </td><td>77a</td><td> ( c : ( a / a ) ) : 6 4 {\displaystyle (c:(a/a)):6_{4}} </td><td> ( 6 2 3 2 2 0 ) {\displaystyle (6_{2}3_{2}2_{0})} </td></tr><tr><td>173</td><td>P63</td><td>P 63</td><td> Γ h C 6 6 {\displaystyle \Gamma _{h}C_{6}^{6}} </td><td>78a</td><td> ( c : ( a / a ) ) : 6 3 {\displaystyle (c:(a/a)):6_{3}} </td><td> ( 6 3 3 0 2 1 ) {\displaystyle (6_{3}3_{0}2_{1})} </td></tr><tr><td>174</td><td>6</td><td> 3 ∗ {\displaystyle 3*} </td><td>P6</td><td>P 6</td><td> Γ h C 3 h 1 {\displaystyle \Gamma _{h}C_{3h}^{1}} </td><td>43s</td><td> ( c : ( a / a ) ) : 3 : m {\displaystyle (c:(a/a)):3:m} </td><td> [ 3 0 3 0 3 0 ] {\displaystyle [3_{0}3_{0}3_{0}]} </td></tr><tr><td>175</td><td rowspan="2">6/m</td><td rowspan="2"> 6 ∗ {\displaystyle 6*} </td><td>P6/m</td><td>P 6/m</td><td> Γ h C 6 h 1 {\displaystyle \Gamma _{h}C_{6h}^{1}} </td><td>53s</td><td> ( c : ( a / a ) ) ⋅ m : 6 {\displaystyle (c:(a/a))\cdot m:6} </td><td> [ 6 0 3 0 2 0 ] {\displaystyle [6_{0}3_{0}2_{0}]} </td></tr><tr><td>176</td><td>P63/m</td><td>P 63/m</td><td> Γ h C 6 h 2 {\displaystyle \Gamma _{h}C_{6h}^{2}} </td><td>81a</td><td> ( c : ( a / a ) ) ⋅ m : 6 3 {\displaystyle (c:(a/a))\cdot m:6_{3}} </td><td> [ 6 3 3 0 2 1 ] {\displaystyle [6_{3}3_{0}2_{1}]} </td></tr><tr><td>177</td><td rowspan="6">622</td><td rowspan="6"> 226 {\displaystyle 226} </td><td>P622</td><td>P 6 2 2</td><td> Γ h D 6 1 {\displaystyle \Gamma _{h}D_{6}^{1}} </td><td>54s</td><td> ( c : ( a / a ) ) ⋅ 2 : 6 {\displaystyle (c:(a/a))\cdot 2:6} </td><td> ( ∗ 6 0 3 0 2 0 ) {\displaystyle (*6_{0}3_{0}2_{0})} </td></tr><tr><td>178</td><td>P6122</td><td>P 61 2 2</td><td> Γ h D 6 2 {\displaystyle \Gamma _{h}D_{6}^{2}} </td><td>82a</td><td> ( c : ( a / a ) ) ⋅ 2 : 6 1 {\displaystyle (c:(a/a))\cdot 2:6_{1}} </td><td> ( ∗ 6 1 3 1 2 1 ) {\displaystyle (*6_{1}3_{1}2_{1})} </td></tr><tr><td>179</td><td>P6522</td><td>P 65 2 2</td><td> Γ h D 6 3 {\displaystyle \Gamma _{h}D_{6}^{3}} </td><td>83a</td><td> ( c : ( a / a ) ) ⋅ 2 : 6 5 {\displaystyle (c:(a/a))\cdot 2:6_{5}} </td><td> ( ∗ 6 1 3 1 2 1 ) {\displaystyle (*6_{1}3_{1}2_{1})} </td></tr><tr><td>180</td><td>P6222</td><td>P 62 2 2</td><td> Γ h D 6 4 {\displaystyle \Gamma _{h}D_{6}^{4}} </td><td>84a</td><td> ( c : ( a / a ) ) ⋅ 2 : 6 2 {\displaystyle (c:(a/a))\cdot 2:6_{2}} </td><td> ( ∗ 6 2 3 2 2 0 ) {\displaystyle (*6_{2}3_{2}2_{0})} </td></tr><tr><td>181</td><td>P6422</td><td>P 64 2 2</td><td> Γ h D 6 5 {\displaystyle \Gamma _{h}D_{6}^{5}} </td><td>85a</td><td> ( c : ( a / a ) ) ⋅ 2 : 6 4 {\displaystyle (c:(a/a))\cdot 2:6_{4}} </td><td> ( ∗ 6 2 3 2 2 0 ) {\displaystyle (*6_{2}3_{2}2_{0})} </td></tr><tr><td>182</td><td>P6322</td><td>P 63 2 2</td><td> Γ h D 6 6 {\displaystyle \Gamma _{h}D_{6}^{6}} </td><td>86a</td><td> ( c : ( a / a ) ) ⋅ 2 : 6 3 {\displaystyle (c:(a/a))\cdot 2:6_{3}} </td><td> ( ∗ 6 3 3 0 2 1 ) {\displaystyle (*6_{3}3_{0}2_{1})} </td></tr><tr><td>183</td><td rowspan="4">6mm</td><td rowspan="4"> ∗ 66 {\displaystyle *66} </td><td>P6mm</td><td>P 6 m m</td><td> Γ h C 6 v 1 {\displaystyle \Gamma _{h}C_{6v}^{1}} </td><td>50s</td><td> ( c : ( a / a ) ) : m ⋅ 6 {\displaystyle (c:(a/a)):m\cdot 6} </td><td> ( ∗ ⋅ 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*{\cdot }6{\cdot }3{\cdot }2)} </td></tr><tr><td>184</td><td>P6cc</td><td>P 6 c c</td><td> Γ h C 6 v 2 {\displaystyle \Gamma _{h}C_{6v}^{2}} </td><td>44h</td><td> ( c : ( a / a ) ) : c ~ ⋅ 6 {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6} </td><td> ( ∗ : 6 : 3 : 2 ) {\displaystyle (*{:}6{:}3{:}2)} </td></tr><tr><td>185</td><td>P63cm</td><td>P 63 c m</td><td> Γ h C 6 v 3 {\displaystyle \Gamma _{h}C_{6v}^{3}} </td><td>80a</td><td> ( c : ( a / a ) ) : c ~ ⋅ 6 3 {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6_{3}} </td><td> ( ∗ ⋅ 6 : 3 : 2 ) {\displaystyle (*{\cdot }6{:}3{:}2)} </td></tr><tr><td>186</td><td>P63mc</td><td>P 63 m c</td><td> Γ h C 6 v 4 {\displaystyle \Gamma _{h}C_{6v}^{4}} </td><td>79a</td><td> ( c : ( a / a ) ) : m ⋅ 6 3 {\displaystyle (c:(a/a)):m\cdot 6_{3}} </td><td> ( ∗ : 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*{:}6{\cdot }3{\cdot }2)} </td></tr><tr><td>187</td><td rowspan="4">6m2</td><td rowspan="4"> ∗ 223 {\displaystyle *223} </td><td>P6m2</td><td>P 6 m 2</td><td> Γ h D 3 h 1 {\displaystyle \Gamma _{h}D_{3h}^{1}} </td><td>48s</td><td> ( c : ( a / a ) ) : m ⋅ 3 : m {\displaystyle (c:(a/a)):m\cdot 3:m} </td><td> [ ∗ ⋅ 3 ⋅ 3 ⋅ 3 ] {\displaystyle [*{\cdot }3{\cdot }3{\cdot }3]} </td></tr><tr><td>188</td><td>P6c2</td><td>P 6 c 2</td><td> Γ h D 3 h 2 {\displaystyle \Gamma _{h}D_{3h}^{2}} </td><td>43h</td><td> ( c : ( a / a ) ) : c ~ ⋅ 3 : m {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 3:m} </td><td> [ ∗ : 3 : 3 : 3 ] {\displaystyle [*{:}3{:}3{:}3]} </td></tr><tr><td>189</td><td>P62m</td><td>P 6 2 m</td><td> Γ h D 3 h 3 {\displaystyle \Gamma _{h}D_{3h}^{3}} </td><td>47s</td><td> ( c : ( a / a ) ) ⋅ m : 3 ⋅ m {\displaystyle (c:(a/a))\cdot m:3\cdot m} </td><td> [ 3 0 ∗ ⋅ 3 ] {\displaystyle [3_{0}{*}{\cdot }3]} </td></tr><tr><td>190</td><td>P62c</td><td>P 6 2 c</td><td> Γ h D 3 h 4 {\displaystyle \Gamma _{h}D_{3h}^{4}} </td><td>42h</td><td> ( c : ( a / a ) ) ⋅ m : 3 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:3\cdot {\tilde {c}}} </td><td> [ 3 0 ∗ : 3 ] {\displaystyle [3_{0}{*}{:}3]} </td></tr><tr><td>191</td><td rowspan="4">6/m 2/m 2/m</td><td rowspan="4"> ∗ 226 {\displaystyle *226} </td><td>P6/mmm</td><td>P 6/m 2/m 2/m</td><td> Γ h D 6 h 1 {\displaystyle \Gamma _{h}D_{6h}^{1}} </td><td>58s</td><td> ( c : ( a / a ) ) ⋅ m : 6 ⋅ m {\displaystyle (c:(a/a))\cdot m:6\cdot m} </td><td> [ ∗ ⋅ 6 ⋅ 3 ⋅ 2 ] {\displaystyle [*{\cdot }6{\cdot }3{\cdot }2]} </td></tr><tr><td>192</td><td>P6/mcc</td><td>P 6/m 2/c 2/c</td><td> Γ h D 6 h 2 {\displaystyle \Gamma _{h}D_{6h}^{2}} </td><td>48h</td><td> ( c : ( a / a ) ) ⋅ m : 6 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:6\cdot {\tilde {c}}} </td><td> [ ∗ : 6 : 3 : 2 ] {\displaystyle [*{:}6{:}3{:}2]} </td></tr><tr><td>193</td><td>P63/mcm</td><td>P 63/m 2/c 2/m</td><td> Γ h D 6 h 3 {\displaystyle \Gamma _{h}D_{6h}^{3}} </td><td>87a</td><td> ( c : ( a / a ) ) ⋅ m : 6 3 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:6_{3}\cdot {\tilde {c}}} </td><td> [ ∗ ⋅ 6 : 3 : 2 ] {\displaystyle [*{\cdot }6{:}3{:}2]} </td></tr><tr><td>194</td><td>P63/mmc</td><td>P 63/m 2/m 2/c</td><td> Γ h D 6 h 4 {\displaystyle \Gamma _{h}D_{6h}^{4}} </td><td>88a</td><td> ( c : ( a / a ) ) ⋅ m : 6 3 ⋅ m {\displaystyle (c:(a/a))\cdot m:6_{3}\cdot m} </td><td> [ ∗ : 6 ⋅ 3 ⋅ 2 ] {\displaystyle [*{:}6{\cdot }3{\cdot }2]} </td></tr></tbody></table>
<h2 id="list-of-cubic">List of cubic</h2>
Cubic Bravais lattice<table><tbody><tr><th>Simple (P)</th><th>Body centered (I)</th><th>Face centered (F)</th></tr><tr><td></td><td></td><td></td></tr></tbody></table>
Example cubic structures
<a href="/facts/Cubic_crystal_system/92Co7BKM">Cubic crystal system</a><table><tbody><tr><th>Number</th><th><a href="/facts/Point_group/41NSqUN6">Point group</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></th><th>Short name</th><th>Full name</th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies</a></th><th><a href="/facts/Evgraf_Fedorov/fPqQhHMn">Fedorov</a></th><th><a href="/facts/Shubnikov_group/bCtqSDhI">Shubnikov</a></th><th>Conway</th><th>Fibrifold (preserving z {\displaystyle z} )</th><th>Fibrifold (preserving x {\displaystyle x} , y {\displaystyle y} , z {\displaystyle z} )</th></tr><tr><td>195</td><td rowspan="5">23</td><td rowspan="5"> 332 {\displaystyle 332} </td><td>P23</td><td>P 2 3</td><td> Γ c T 1 {\displaystyle \Gamma _{c}T^{1}} </td><td>59s</td><td> ( a : a : a ) : 2 / 3 {\displaystyle \left(a:a:a\right):2/3} </td><td> 2 ∘ {\displaystyle 2^{\circ }} </td><td> ( ∗ 2 0 2 0 2 0 2 0 ) : 3 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}3} </td><td> ( ∗ 2 0 2 0 2 0 2 0 ) : 3 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}3} </td></tr><tr><td>196</td><td>F23</td><td>F 2 3</td><td> Γ c f T 2 {\displaystyle \Gamma _{c}^{f}T^{2}} </td><td>61s</td><td> ( 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} </td><td> 1 ∘ {\displaystyle 1^{\circ }} </td><td> ( ∗ 2 0 2 1 2 0 2 1 ) : 3 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}3} </td><td> ( ∗ 2 0 2 1 2 0 2 1 ) : 3 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}3} </td></tr><tr><td>197</td><td>I23</td><td>I 2 3</td><td> Γ c v T 3 {\displaystyle \Gamma _{c}^{v}T^{3}} </td><td>60s</td><td> ( a + b + c 2 / a : a : a ) : 2 / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):2/3} </td><td> 4 ∘ ∘ {\displaystyle 4^{\circ \circ }} </td><td> ( 2 1 ∗ 2 0 2 0 ) : 3 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}3} </td><td> ( 2 1 ∗ 2 0 2 0 ) : 3 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}3} </td></tr><tr><td>198</td><td>P213</td><td>P 21 3</td><td> Γ c T 4 {\displaystyle \Gamma _{c}T^{4}} </td><td>89a</td><td> ( a : a : a ) : 2 1 / 3 {\displaystyle \left(a:a:a\right):2_{1}/3} </td><td> 1 ∘ / 4 {\displaystyle 1^{\circ }/4} </td><td> ( 2 1 2 1 × ¯ ) : 3 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}3} </td><td> ( 2 1 2 1 × ¯ ) : 3 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}3} </td></tr><tr><td>199</td><td>I213</td><td>I 21 3</td><td> Γ c v T 5 {\displaystyle \Gamma _{c}^{v}T^{5}} </td><td>90a</td><td> ( a + b + c 2 / a : a : a ) : 2 1 / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):2_{1}/3} </td><td> 2 ∘ / 4 {\displaystyle 2^{\circ }/4} </td><td> ( 2 0 ∗ 2 1 2 1 ) : 3 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}3} </td><td> ( 2 0 ∗ 2 1 2 1 ) : 3 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}3} </td></tr><tr><td>200</td><td rowspan="7">2/m 3</td><td rowspan="7"> 3 ∗ 2 {\displaystyle 3{*}2} </td><td>Pm3</td><td>P 2/m 3</td><td> Γ c T h 1 {\displaystyle \Gamma _{c}T_{h}^{1}} </td><td>62s</td><td> ( a : a : a ) ⋅ m / 6 ~ {\displaystyle \left(a:a:a\right)\cdot m/{\tilde {6}}} </td><td> 4 − {\displaystyle 4^{-}} </td><td> [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3} </td><td> [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3} </td></tr><tr><td>201</td><td>Pn3</td><td>P 2/n 3</td><td> Γ c T h 2 {\displaystyle \Gamma _{c}T_{h}^{2}} </td><td>49h</td><td> ( a : a : a ) ⋅ a b ~ / 6 ~ {\displaystyle \left(a:a:a\right)\cdot {\widetilde {ab}}/{\tilde {6}}} </td><td> 4 ∘ + {\displaystyle 4^{\circ +}} </td><td> ( 2 ∗ ¯ 1 2 0 2 0 ) : 3 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}3} </td><td> ( 2 ∗ ¯ 1 2 0 2 0 ) : 3 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}3} </td></tr><tr><td>202</td><td>Fm3</td><td>F 2/m 3</td><td> Γ c f T h 3 {\displaystyle \Gamma _{c}^{f}T_{h}^{3}} </td><td>64s</td><td> ( 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}}} </td><td> 2 − {\displaystyle 2^{-}} </td><td> [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}3} </td><td> [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 3 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}3} </td></tr><tr><td>203</td><td>Fd3</td><td>F 2/d 3</td><td> Γ c f T h 4 {\displaystyle \Gamma _{c}^{f}T_{h}^{4}} </td><td>50h</td><td> ( 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}}} </td><td> 2 ∘ + {\displaystyle 2^{\circ +}} </td><td> ( 2 ∗ ¯ 2 0 2 1 ) : 3 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}3} </td><td> ( 2 ∗ ¯ 2 0 2 1 ) : 3 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}3} </td></tr><tr><td>204</td><td>Im3</td><td>I 2/m 3</td><td> Γ c v T h 5 {\displaystyle \Gamma _{c}^{v}T_{h}^{5}} </td><td>63s</td><td> ( a + b + c 2 / a : a : a ) ⋅ m / 6 ~ {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot m/{\tilde {6}}} </td><td> 8 − ∘ {\displaystyle 8^{-\circ }} </td><td> [ 2 1 ∗ ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}3} </td><td> [ 2 1 ∗ ⋅ 2 ⋅ 2 ] : 3 {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}3} </td></tr><tr><td>205</td><td>Pa3</td><td>P 21/a 3</td><td> Γ c T h 6 {\displaystyle \Gamma _{c}T_{h}^{6}} </td><td>91a</td><td> ( a : a : a ) ⋅ a ~ / 6 ~ {\displaystyle \left(a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}} </td><td> 2 − / 4 {\displaystyle 2^{-}/4} </td><td> ( 2 1 2 ∗ ¯ : ) : 3 {\displaystyle (2_{1}2{\bar {*}}{:}){:}3} </td><td> ( 2 1 2 ∗ ¯ : ) : 3 {\displaystyle (2_{1}2{\bar {*}}{:}){:}3} </td></tr><tr><td>206</td><td>Ia3</td><td>I 21/a 3</td><td> Γ c v T h 7 {\displaystyle \Gamma _{c}^{v}T_{h}^{7}} </td><td>92a</td><td> ( 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}}} </td><td> 4 − / 4 {\displaystyle 4^{-}/4} </td><td> ( ∗ 2 1 2 : 2 : 2 ) : 3 {\displaystyle (*2_{1}2{:}2{:}2){:}3} </td><td> ( ∗ 2 1 2 : 2 : 2 ) : 3 {\displaystyle (*2_{1}2{:}2{:}2){:}3} </td></tr><tr><td>207</td><td rowspan="8">432</td><td rowspan="8"> 432 {\displaystyle 432} </td><td>P432</td><td>P 4 3 2</td><td> Γ c O 1 {\displaystyle \Gamma _{c}O^{1}} </td><td>68s</td><td> ( a : a : a ) : 4 / 3 {\displaystyle \left(a:a:a\right):4/3} </td><td> 4 ∘ − {\displaystyle 4^{\circ -}} </td><td> ( ∗ 4 0 4 0 2 0 ) : 3 {\displaystyle (*4_{0}4_{0}2_{0}){:}3} </td><td> ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} </td></tr><tr><td>208</td><td>P4232</td><td>P 42 3 2</td><td> Γ c O 2 {\displaystyle \Gamma _{c}O^{2}} </td><td>98a</td><td> ( a : a : a ) : 4 2 / / 3 {\displaystyle \left(a:a:a\right):4_{2}//3} </td><td> 4 + {\displaystyle 4^{+}} </td><td> ( ∗ 4 2 4 2 2 0 ) : 3 {\displaystyle (*4_{2}4_{2}2_{0}){:}3} </td><td> ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} </td></tr><tr><td>209</td><td>F432</td><td>F 4 3 2</td><td> Γ c f O 3 {\displaystyle \Gamma _{c}^{f}O^{3}} </td><td>70s</td><td> ( 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} </td><td> 2 ∘ − {\displaystyle 2^{\circ -}} </td><td> ( ∗ 4 2 4 0 2 1 ) : 3 {\displaystyle (*4_{2}4_{0}2_{1}){:}3} </td><td> ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} </td></tr><tr><td>210</td><td>F4132</td><td>F 41 3 2</td><td> Γ c f O 4 {\displaystyle \Gamma _{c}^{f}O^{4}} </td><td>97a</td><td> ( 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} </td><td> 2 + {\displaystyle 2^{+}} </td><td> ( ∗ 4 3 4 1 2 0 ) : 3 {\displaystyle (*4_{3}4_{1}2_{0}){:}3} </td><td> ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} </td></tr><tr><td>211</td><td>I432</td><td>I 4 3 2</td><td> Γ c v O 5 {\displaystyle \Gamma _{c}^{v}O^{5}} </td><td>69s</td><td> ( a + b + c 2 / a : a : a ) : 4 / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):4/3} </td><td> 8 + ∘ {\displaystyle 8^{+\circ }} </td><td> ( 4 2 4 0 2 1 ) : 3 {\displaystyle (4_{2}4_{0}2_{1}){:}3} </td><td> ( 2 1 ∗ 2 0 2 0 ) : 6 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}6} </td></tr><tr><td>212</td><td>P4332</td><td>P 43 3 2</td><td> Γ c O 6 {\displaystyle \Gamma _{c}O^{6}} </td><td>94a</td><td> ( a : a : a ) : 4 3 / / 3 {\displaystyle \left(a:a:a\right):4_{3}//3} </td><td> 2 + / 4 {\displaystyle 2^{+}/4} </td><td> ( 4 1 ∗ 2 1 ) : 3 {\displaystyle (4_{1}{*}2_{1}){:}3} </td><td> ( 2 1 2 1 × ¯ ) : 6 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}6} </td></tr><tr><td>213</td><td>P4132</td><td>P 41 3 2</td><td> Γ c O 7 {\displaystyle \Gamma _{c}O^{7}} </td><td>95a</td><td> ( a : a : a ) : 4 1 / / 3 {\displaystyle \left(a:a:a\right):4_{1}//3} </td><td> 2 + / 4 {\displaystyle 2^{+}/4} </td><td> ( 4 1 ∗ 2 1 ) : 3 {\displaystyle (4_{1}{*}2_{1}){:}3} </td><td> ( 2 1 2 1 × ¯ ) : 6 {\displaystyle (2_{1}2_{1}{\bar {\times }}){:}6} </td></tr><tr><td>214</td><td>I4132</td><td>I 41 3 2</td><td> Γ c v O 8 {\displaystyle \Gamma _{c}^{v}O^{8}} </td><td>96a</td><td> ( a + b + c 2 / : a : a : a ) : 4 1 / / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/:a:a:a\right):4_{1}//3} </td><td> 4 + / 4 {\displaystyle 4^{+}/4} </td><td> ( ∗ 4 3 4 1 2 0 ) : 3 {\displaystyle (*4_{3}4_{1}2_{0}){:}3} </td><td> ( 2 0 ∗ 2 1 2 1 ) : 6 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}6} </td></tr><tr><td>215</td><td rowspan="6">43m</td><td rowspan="6"> ∗ 332 {\displaystyle *332} </td><td>P43m</td><td>P 4 3 m</td><td> Γ c T d 1 {\displaystyle \Gamma _{c}T_{d}^{1}} </td><td>65s</td><td> ( a : a : a ) : 4 ~ / 3 {\displaystyle \left(a:a:a\right):{\tilde {4}}/3} </td><td> 2 ∘ : 2 {\displaystyle 2^{\circ }{:}2} </td><td> ( ∗ 4 ⋅ 42 0 ) : 3 {\displaystyle (*4{\cdot }42_{0}){:}3} </td><td> ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} </td></tr><tr><td>216</td><td>F43m</td><td>F 4 3 m</td><td> Γ c f T d 2 {\displaystyle \Gamma _{c}^{f}T_{d}^{2}} </td><td>67s</td><td> ( 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} </td><td> 1 ∘ : 2 {\displaystyle 1^{\circ }{:}2} </td><td> ( ∗ 4 ⋅ 42 1 ) : 3 {\displaystyle (*4{\cdot }42_{1}){:}3} </td><td> ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} </td></tr><tr><td>217</td><td>I43m</td><td>I 4 3 m</td><td> Γ c v T d 3 {\displaystyle \Gamma _{c}^{v}T_{d}^{3}} </td><td>66s</td><td> ( a + b + c 2 / a : a : a ) : 4 ~ / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}/3} </td><td> 4 ∘ : 2 {\displaystyle 4^{\circ }{:}2} </td><td> ( ∗ ⋅ 44 : 2 ) : 3 {\displaystyle (*{\cdot }44{:}2){:}3} </td><td> ( 2 1 ∗ 2 0 2 0 ) : 6 {\displaystyle (2_{1}{*}2_{0}2_{0}){:}6} </td></tr><tr><td>218</td><td>P43n</td><td>P 4 3 n</td><td> Γ c T d 4 {\displaystyle \Gamma _{c}T_{d}^{4}} </td><td>51h</td><td> ( a : a : a ) : 4 ~ / / 3 {\displaystyle \left(a:a:a\right):{\tilde {4}}//3} </td><td> 4 ∘ {\displaystyle 4^{\circ }} </td><td> ( ∗ 4 : 42 0 ) : 3 {\displaystyle (*4{:}42_{0}){:}3} </td><td> ( ∗ 2 0 2 0 2 0 2 0 ) : 6 {\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6} </td></tr><tr><td>219</td><td>F43c</td><td>F 4 3 c</td><td> Γ c f T d 5 {\displaystyle \Gamma _{c}^{f}T_{d}^{5}} </td><td>52h</td><td> ( 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} </td><td> 2 ∘ ∘ {\displaystyle 2^{\circ \circ }} </td><td> ( ∗ 4 : 42 1 ) : 3 {\displaystyle (*4{:}42_{1}){:}3} </td><td> ( ∗ 2 0 2 1 2 0 2 1 ) : 6 {\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6} </td></tr><tr><td>220</td><td>I43d</td><td>I 4 3 d</td><td> Γ c v T d 6 {\displaystyle \Gamma _{c}^{v}T_{d}^{6}} </td><td>93a</td><td> ( a + b + c 2 / a : a : a ) : 4 ~ / / 3 {\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}//3} </td><td> 4 ∘ / 4 {\displaystyle 4^{\circ }/4} </td><td> ( 4 ∗ ¯ 2 1 ) : 3 {\displaystyle (4{\bar {*}}2_{1}){:}3} </td><td> ( 2 0 ∗ 2 1 2 1 ) : 6 {\displaystyle (2_{0}{*}2_{1}2_{1}){:}6} </td></tr><tr><td>221</td><td rowspan="10">4/m 3 2/m</td><td rowspan="10"> ∗ 432 {\displaystyle *432} </td><td>Pm3m</td><td>P 4/m 3 2/m</td><td> Γ c O h 1 {\displaystyle \Gamma _{c}O_{h}^{1}} </td><td>71s</td><td> ( a : a : a ) : 4 / 6 ~ ⋅ m {\displaystyle \left(a:a:a\right):4/{\tilde {6}}\cdot m} </td><td> 4 − : 2 {\displaystyle 4^{-}{:}2} </td><td> [ ∗ ⋅ 4 ⋅ 4 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }4{\cdot }4{\cdot }2]{:}3} </td><td> [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6} </td></tr><tr><td>222</td><td>Pn3n</td><td>P 4/n 3 2/n</td><td> Γ c O h 2 {\displaystyle \Gamma _{c}O_{h}^{2}} </td><td>53h</td><td> ( a : a : a ) : 4 / 6 ~ ⋅ a b c ~ {\displaystyle \left(a:a:a\right):4/{\tilde {6}}\cdot {\widetilde {abc}}} </td><td> 8 ∘ ∘ {\displaystyle 8^{\circ \circ }} </td><td> ( ∗ 4 0 4 : 2 ) : 3 {\displaystyle (*4_{0}4{:}2){:}3} </td><td> ( 2 ∗ ¯ 1 2 0 2 0 ) : 6 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}6} </td></tr><tr><td>223</td><td>Pm3n</td><td>P 42/m 3 2/n</td><td> Γ c O h 3 {\displaystyle \Gamma _{c}O_{h}^{3}} </td><td>102a</td><td> ( a : a : a ) : 4 2 / / 6 ~ ⋅ a b c ~ {\displaystyle \left(a:a:a\right):4_{2}//{\tilde {6}}\cdot {\widetilde {abc}}} </td><td> 8 ∘ {\displaystyle 8^{\circ }} </td><td> [ ∗ ⋅ 4 : 4 ⋅ 2 ] : 3 {\displaystyle [*{\cdot }4{:}4{\cdot }2]{:}3} </td><td> [ ∗ ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6} </td></tr><tr><td>224</td><td>Pn3m</td><td>P 42/n 3 2/m</td><td> Γ c O h 4 {\displaystyle \Gamma _{c}O_{h}^{4}} </td><td>103a</td><td> ( a : a : a ) : 4 2 / / 6 ~ ⋅ m {\displaystyle \left(a:a:a\right):4_{2}//{\tilde {6}}\cdot m} </td><td> 4 + : 2 {\displaystyle 4^{+}{:}2} </td><td> ( ∗ 4 2 4 ⋅ 2 ) : 3 {\displaystyle (*4_{2}4{\cdot }2){:}3} </td><td> ( 2 ∗ ¯ 1 2 0 2 0 ) : 6 {\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}6} </td></tr><tr><td>225</td><td>Fm3m</td><td>F 4/m 3 2/m</td><td> Γ c f O h 5 {\displaystyle \Gamma _{c}^{f}O_{h}^{5}} </td><td>73s</td><td> ( 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} </td><td> 2 − : 2 {\displaystyle 2^{-}{:}2} </td><td> [ ∗ ⋅ 4 ⋅ 4 : 2 ] : 3 {\displaystyle [*{\cdot }4{\cdot }4{:}2]{:}3} </td><td> [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}6} </td></tr><tr><td>226</td><td>Fm3c</td><td>F 4/m 3 2/c</td><td> Γ c f O h 6 {\displaystyle \Gamma _{c}^{f}O_{h}^{6}} </td><td>54h</td><td> ( 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}}} </td><td> 4 − − {\displaystyle 4^{--}} </td><td> [ ∗ ⋅ 4 : 4 : 2 ] : 3 {\displaystyle [*{\cdot }4{:}4{:}2]{:}3} </td><td> [ ∗ ⋅ 2 ⋅ 2 : 2 : 2 ] : 6 {\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}6} </td></tr><tr><td>227</td><td>Fd3m</td><td>F 41/d 3 2/m</td><td> Γ c f O h 7 {\displaystyle \Gamma _{c}^{f}O_{h}^{7}} </td><td>100a</td><td> ( 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} </td><td> 2 + : 2 {\displaystyle 2^{+}{:}2} </td><td> ( ∗ 4 1 4 ⋅ 2 ) : 3 {\displaystyle (*4_{1}4{\cdot }2){:}3} </td><td> ( 2 ∗ ¯ 2 0 2 1 ) : 6 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}6} </td></tr><tr><td>228</td><td>Fd3c</td><td>F 41/d 3 2/c</td><td> Γ c f O h 8 {\displaystyle \Gamma _{c}^{f}O_{h}^{8}} </td><td>101a</td><td> ( 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}}} </td><td> 4 + + {\displaystyle 4^{++}} </td><td> ( ∗ 4 1 4 : 2 ) : 3 {\displaystyle (*4_{1}4{:}2){:}3} </td><td> ( 2 ∗ ¯ 2 0 2 1 ) : 6 {\displaystyle (2{\bar {*}}2_{0}2_{1}){:}6} </td></tr><tr><td>229</td><td>Im3m</td><td>I 4/m 3 2/m</td><td> Γ c v O h 9 {\displaystyle \Gamma _{c}^{v}O_{h}^{9}} </td><td>72s</td><td> ( 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} </td><td> 8 ∘ : 2 {\displaystyle 8^{\circ }{:}2} </td><td> [ ∗ ⋅ 4 ⋅ 4 : 2 ] : 3 {\displaystyle [*{\cdot }4{\cdot }4{:}2]{:}3} </td><td> [ 2 1 ∗ ⋅ 2 ⋅ 2 ] : 6 {\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}6} </td></tr><tr><td>230</td><td>Ia3d</td><td>I 41/a 3 2/d</td><td> Γ c v O h 10 {\displaystyle \Gamma _{c}^{v}O_{h}^{10}} </td><td>99a</td><td> ( 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}}} </td><td> 8 ∘ / 4 {\displaystyle 8^{\circ }/4} </td><td> ( ∗ 4 1 4 : 2 ) : 3 {\displaystyle (*4_{1}4{:}2){:}3} </td><td> ( ∗ 2 1 2 : 2 : 2 ) : 6 {\displaystyle (*2_{1}2{:}2{:}2){:}6} </td></tr></tbody></table>
<h2 id="notes">Notes</h2>

<h2 id="external-links">External links</h2>

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<ul><li><a href="https://www.iucr.org/">International Union of Crystallography</a></li>
<li><a href="http://neon.mems.cmu.edu/degraef/pointgroups/">Point Groups and Bravais Lattices</a></li>
<li><a href="http://img.chem.ucl.ac.uk/sgp/mainmenu.htm">Full list of 230 crystallographic space groups</a></li>
<li><a href="https://www.emis.de/journals/BAG/vol.42/no.2/b42h2con.pdf">Conway et al. on fibrifold notation</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">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] <a href="/wiki/International_Union_of_Crystallography" target="_blank">/wiki/International_Union_of_Crystallography</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">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. <a href="978-0-19-958258-7" target="_blank">978-0-19-958258-7</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
</ol>

List of space groups open-in-new

List of space groups