空間群の一覧

3次元には230の空間群があり、番号の添え字、ヘルマン・モーガン記法による正式名称、そして短縮名（国際短縮記号）で表されます。正式名称は読みやすさを考慮してスペースが挿入されています。各空間群は単位胞の点群を持ちます。

シンボル

ヘルマン・モーガン記法では、空間群は点群識別子と格子の種類を表す大文字を組み合わせた記号で命名される。格子内の螺旋軸やすべり面といった並進運動も記され、完全な結晶学的空間群が与えられる。

これらは3次元のブラヴェ格子です。

• Pプリミティブ
• 私は身体中心です（ドイツのInnenzentriertより）
• F面中心 (ドイツ語Flächenzentriert より)
• S塩基中心 (ドイツ語のSeitenflächenzentriertより)、具体的には:
  • A面のみを中心としたA
  • BはB面のみを中心とする
  • CはC面のみを中心とする
• R菱面体

点群内の反射面m は、すべり面 に置き換えることができます。すべり面は、すべりがどの軸に沿っているかによってa、b、またはcと表記されます。また、面の対角線の半分に沿ったすべりであるnすべりや、単位胞の面対角線または空間対角線の4分の1に沿ったdすべりも存在します。d すべりはダイヤモンド構造 を特徴とするため、ダイヤモンドすべり面と呼ばれることがよくあります。

• ${\displaystyle a}$、、または：この面の格子ベクトルの半分に沿って移動する ${\displaystyle b}$ ${\displaystyle c}$
• ${\displaystyle n}$: この面の対角線の半分に沿って移動する
• ${\displaystyle d}$: 面の対角線の4分の1に沿って移動する滑空面
• ${\displaystyle e}$: 同じ滑空面を持つ2つの滑空と、2つの異なる半格子ベクトルに沿った並進。^{[注 1]}

回転点は、回転角が である数値nで表されるねじ軸に置き換えることができます。並進角は、平行格子ベクトルの一部として、軸に沿ってどれだけの距離を並進したかを示す添え字として追加されます。例えば、2 _{1は 180°（2倍）回転し、その後に}⁠並進します。 ${\displaystyle \color {Black}{\tfrac {360^{\circ }}{n}}}$1/2⁠格子ベクトルの 3 ₁は 120°（3 倍）回転し、その後に⁠の平行移動が続く。1/3⁠格子ベクトルの。可能な螺旋軸は、2 ₁、3 ₁、3 ₂、4 ₁、4 ₂、4 ₃、6 ₁、6 ₂、6 ₃、6 ₄、および6 ₅です。

回転軸（らせん軸）nと、同じ結晶方向に沿った鏡面（すべり面）mの両方が存在する場合、それらは分数またはn/mで表されます。例えば、4 ₁ /aは、問題の結晶軸に4 _{1 の}らせん軸とaに沿ったすべり面の両方が含まれていることを意味します。 ${\textstyle {\frac {n}{m}}}$

シェーンフリー記法では、空間群の記号は対応する点群の記号に上付き文字を付加したもので表されます。上付き文字は空間群の対称要素に関する追加情報を与えるものではなく、シェーンフリーが空間群を導出した順序と関連しています。これは、ブラヴェ格子を指定する形式の記号で補足されることがあります。ここでは格子系、は中心型です。^[2] ${\displaystyle \Gamma _{x}^{y}}$ ${\displaystyle x\in \{t,m,o,q,rh,h,c\}}$ ${\displaystyle y\in \{\emptyset ,b,v,f\}}$

フェドロフ記号では、空間群の種類はs（共型）、h（半共型）、a（非共型）で表されます。数字は、フェドロフが導出した空間群の順序に関係しています。共型空間群は73個、半共型空間群は54個、非共型空間群は103個あります。

共形

73個の共型空間群は、ブラヴェ格子と対応する点群の組み合わせとして得られます。これらの群は、対応する点群と同じ対称要素を含みます。点群4/mmm ( ) の例：共型空間群はP4/mmm ( , 36s ) とI4/mmm ( , 37s ) です。 ${\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}}$ ${\displaystyle P{\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}}$ ${\displaystyle I{\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}}$

半対称性

54個の半対称空間群は、対応する点群の対称要素の軸結合のみを含みます。点群4/mmm ( )の例：半対称空間群は軸結合422を含みますが、少なくとも1つの鏡面mは滑面によって置き換えられます。例えば、P4/mcc ( , 35h )、P4/nbm ( , 36h )、P4/nnc ( , 37h )、I4/mcm ( , 38h )などが挙げられます。 ${\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}}$ ${\displaystyle P{\tfrac {4}{m}}{\tfrac {2}{c}}{\tfrac {2}{c}}}$ ${\displaystyle P{\tfrac {4}{n}}{\tfrac {2}{b}}{\tfrac {2}{m}}}$ ${\displaystyle P{\tfrac {4}{n}}{\tfrac {2}{n}}{\tfrac {2}{c}}}$ ${\displaystyle I{\tfrac {4}{m}}{\tfrac {2}{c}}{\tfrac {2}{m}}}$

非対称性

残りの103の空間群は非対称です。点群4/mmm ( )の例：P4/mbm ( , 54a )、P4 ₂ /mmc ( , 60a )、I4 ₁ /acd ( , 58a )。これらの群には軸結合422は含まれません。 ${\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}}$ ${\displaystyle P{\tfrac {4}{m}}{\tfrac {2_{1}}{b}}{\tfrac {2}{m}}}$ ${\displaystyle P{\tfrac {4_{2}}{m}}{\tfrac {2}{m}}{\tfrac {2}{c}}}$ ${\displaystyle I{\tfrac {4_{1}}{a}}{\tfrac {2}{c}}{\tfrac {2}{d}}}$

三斜晶系の一覧

三斜晶系ブラヴェ格子

三斜晶系

番号	点群	オービフォールド	短縮名	フルネーム	シェーンフライ	フェドロフ	シュブニコフ	フィブリフォールド
1	1	${\displaystyle 1}$	P1	P1	${\displaystyle \Gamma _{t}C_{1}^{1}}$	1秒	${\displaystyle (a/b/c)\cdot 1}$	${\displaystyle (\circ )}$
2	1	${\displaystyle \times }$	P1​	P1​	${\displaystyle \Gamma _{t}C_{i}^{1}}$	2秒	${\displaystyle (a/b/c)\cdot {\tilde {2}}}$	${\displaystyle (2222)}$

単斜晶系の一覧

単斜晶系ブラヴェ格子

シンプル（P）	ベース（S）

単斜晶系

番号	点群	オービフォールド	短縮名	氏名		シェーンフライ	フェドロフ	シュブニコフ	フィブリフォールド（一次）	フィブリフォールド（二次）
3	2	${\displaystyle 22}$	P2	P 1 2 1	P 1 1 2	${\displaystyle \Gamma _{m}C_{2}^{1}}$	3秒	${\displaystyle (b:(c/a)):2}$	${\displaystyle (2_{0}2_{0}2_{0}2_{0})}$	${\displaystyle ({*}_{0}{*}_{0})}$
4			P2 1	P 1 2 1 1	P 1 1 2 1	${\displaystyle \Gamma _{m}C_{2}^{2}}$	1a	${\displaystyle (b:(c/a)):2_{1}}$	${\displaystyle (2_{1}2_{1}2_{1}2_{1})}$	${\displaystyle ({\bar {\times }}{\bar {\times }})}$
5			C2	C 1 2 1	B 1 1 2	${\displaystyle \Gamma _{m}^{b}C_{2}^{3}}$	4秒	${\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right):2}$	${\displaystyle (2_{0}2_{0}2_{1}2_{1})}$	${\displaystyle ({*}_{1}{*}_{1})}$、 ${\displaystyle ({*}{\bar {\times }})}$
6	メートル	${\displaystyle *}$	午後	P 1 m 1	P 1 1メートル	${\displaystyle \Gamma _{m}C_{s}^{1}}$	5秒	${\displaystyle (b:(c/a))\cdot m}$	${\displaystyle [\circ _{0}]}$	${\displaystyle ({*}{\cdot }{*}{\cdot })}$
7			パソコン	P 1 c 1	P 1 1 b	${\displaystyle \Gamma _{m}C_{s}^{2}}$	1時間	${\displaystyle (b:(c/a))\cdot {\tilde {c}}}$	${\displaystyle ({\bar {\circ }}_{0})}$	${\displaystyle ({*}{:}{*}{:})}$、 ${\displaystyle ({\times }{\times }_{0})}$
8			Cm	C 1 m 1	B 1 1メートル	${\displaystyle \Gamma _{m}^{b}C_{s}^{3}}$	6秒	${\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m}$	${\displaystyle [\circ _{1}]}$	${\displaystyle ({*}{\cdot }{*}{:})}$、 ${\displaystyle ({*}{\cdot }{\times })}$
9			CC	C 1 c 1	B 1 1 b	${\displaystyle \Gamma _{m}^{b}C_{s}^{4}}$	2時間	${\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}}$	${\displaystyle ({\bar {\circ }}_{1})}$	${\displaystyle ({*}{:}{\times })}$、 ${\displaystyle ({\times }{\times }_{1})}$
10	2/m	${\displaystyle 2*}$	P2/m	P 1 2/m 1	P 1 1 2/m	${\displaystyle \Gamma _{m}C_{2h}^{1}}$	7秒	${\displaystyle (b:(c/a))\cdot m:2}$	${\displaystyle [2_{0}2_{0}2_{0}2_{0}]}$	${\displaystyle (*2{\cdot }22{\cdot }2)}$
11			P2 1 /m	P 1 2 1 /m 1	P 1 1 2 1 /m	${\displaystyle \Gamma _{m}C_{2h}^{2}}$	2a	${\displaystyle (b:(c/a))\cdot m:2_{1}}$	${\displaystyle [2_{1}2_{1}2_{1}2_{1}]}$	${\displaystyle (22{*}{\cdot })}$
12			C2/m	C 1 2/m 1	B 1 1 2/m	${\displaystyle \Gamma _{m}^{b}C_{2h}^{3}}$	8秒	${\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m:2}$	${\displaystyle [2_{0}2_{0}2_{1}2_{1}]}$	${\displaystyle (*2{\cdot }22{:}2)}$、 ${\displaystyle (2{\bar {*}}2{\cdot }2)}$
13			P2/c	P 1 2/c 1	P 1 1 2/b	${\displaystyle \Gamma _{m}C_{2h}^{4}}$	3時間	${\displaystyle (b:(c/a))\cdot {\tilde {c}}:2}$	${\displaystyle (2_{0}2_{0}22)}$	${\displaystyle (*2{:}22{:}2)}$、 ${\displaystyle (22{*}_{0})}$
14			P2 1 /c	P 1 2 1 /c 1	P 1 1 2 1 /b	${\displaystyle \Gamma _{m}C_{2h}^{5}}$	3a	${\displaystyle (b:(c/a))\cdot {\tilde {c}}:2_{1}}$	${\displaystyle (2_{1}2_{1}22)}$	${\displaystyle (22{*}{:})}$、 ${\displaystyle (22{\times })}$
15			C2/c	C 1 2/c 1	B 1 1 2/b	${\displaystyle \Gamma _{m}^{b}C_{2h}^{6}}$	4時間	${\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}:2}$	${\displaystyle (2_{0}2_{1}22)}$	${\displaystyle (2{\bar {*}}2{:}2)}$、 ${\displaystyle (22{*}_{1})}$

斜方晶系の一覧

斜方晶ブラヴェ格子

シンプル（P）	本体（I）	顔（F）	ベース（S）

斜方晶系

番号	点群	オービフォールド	短縮名	フルネーム	シェーンフライ	フェドロフ	シュブニコフ	フィブリフォールド（一次）	フィブリフォールド（二次）
16	222	${\displaystyle 222}$	P222	P 2 2 2	${\displaystyle \Gamma _{o}D_{2}^{1}}$	9秒	${\displaystyle (c:a:b):2:2}$	${\displaystyle (*2_{0}2_{0}2_{0}2_{0})}$
17			P222 1	P 2 2 2 1	${\displaystyle \Gamma _{o}D_{2}^{2}}$	4a	${\displaystyle (c:a:b):2_{1}:2}$	${\displaystyle (*2_{1}2_{1}2_{1}2_{1})}$	${\displaystyle (2_{0}2_{0}{*})}$
18			P2 1 2 1 2	P 2 1 2 1 2	${\displaystyle \Gamma _{o}D_{2}^{3}}$	7a	${\displaystyle (c:a:b):2}$ ${\displaystyle 2_{1}}$	${\displaystyle (2_{0}2_{0}{\bar {\times }})}$	${\displaystyle (2_{1}2_{1}{*})}$
19			P2 1 2 1 2 1	P 2 1 2 1 2 1	${\displaystyle \Gamma _{o}D_{2}^{4}}$	8a	${\displaystyle (c:a:b):2_{1}}$ ${\displaystyle 2_{1}}$	${\displaystyle (2_{1}2_{1}{\bar {\times }})}$
20			C222 1	C 2 2 2 1	${\displaystyle \Gamma _{o}^{b}D_{2}^{5}}$	5a	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):2_{1}:2}$	${\displaystyle (2_{1}{*}2_{1}2_{1})}$	${\displaystyle (2_{0}2_{1}{*})}$
21			C222	C 2 2 2	${\displaystyle \Gamma _{o}^{b}D_{2}^{6}}$	10秒	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):2:2}$	${\displaystyle (2_{0}{*}2_{0}2_{0})}$	${\displaystyle (*2_{0}2_{0}2_{1}2_{1})}$
22			F222	F 2 2 2	${\displaystyle \Gamma _{o}^{f}D_{2}^{7}}$	12秒	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):2:2}$	${\displaystyle (*2_{0}2_{1}2_{0}2_{1})}$
23			I222	私 2 2 2	${\displaystyle \Gamma _{o}^{v}D_{2}^{8}}$	11秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2}$	${\displaystyle (2_{1}{*}2_{0}2_{0})}$
24			私2 1 2 1 2 1	私 2 1 2 1 2 1	${\displaystyle \Gamma _{o}^{v}D_{2}^{9}}$	6a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2_{1}}$	${\displaystyle (2_{0}{*}2_{1}2_{1})}$
25	mm2	${\displaystyle *22}$	ピムム2	P mm 2	${\displaystyle \Gamma _{o}C_{2v}^{1}}$	13秒	${\displaystyle (c:a:b):m\cdot 2}$	${\displaystyle (*{\cdot }2{\cdot }2{\cdot }2{\cdot }2)}$	${\displaystyle [{*}_{0}{\cdot }{*}_{0}{\cdot }]}$
26			Pmc2 1	P mc 2 1	${\displaystyle \Gamma _{o}C_{2v}^{2}}$	9a	${\displaystyle (c:a:b):{\tilde {c}}\cdot 2_{1}}$	${\displaystyle (*{\cdot }2{:}2{\cdot }2{:}2)}$	${\displaystyle ({\bar {*}}{\cdot }{\bar {*}}{\cdot })}$、 ${\displaystyle [{\times _{0}}{\times _{0}}]}$
27			PCC2	P cc 2	${\displaystyle \Gamma _{o}C_{2v}^{3}}$	5時間	${\displaystyle (c:a:b):{\tilde {c}}\cdot 2}$	${\displaystyle (*{:}2{:}2{:}2{:}2)}$	${\displaystyle ({\bar {*}}_{0}{\bar {*}}_{0})}$
28			Pma2	P ma 2	${\displaystyle \Gamma _{o}C_{2v}^{4}}$	6時間	${\displaystyle (c:a:b):{\tilde {a}}\cdot 2}$	${\displaystyle (2_{0}2_{0}{*}{\cdot })}$	${\displaystyle [{*}_{0}{:}{*}_{0}{:}]}$、 ${\displaystyle (*{\cdot }{*}_{0})}$
29			PCA2 1	P 約 2 1	${\displaystyle \Gamma _{o}C_{2v}^{5}}$	11a	${\displaystyle (c:a:b):{\tilde {a}}\cdot 2_{1}}$	${\displaystyle (2_{1}2_{1}{*}{:})}$	${\displaystyle ({\bar {*}}{:}{\bar {*}}{:})}$
30			Pnc2	P nc 2	${\displaystyle \Gamma _{o}C_{2v}^{6}}$	7時間	${\displaystyle (c:a:b):{\tilde {c}}\odot 2}$	${\displaystyle (2_{0}2_{0}{*}{:})}$	${\displaystyle ({\bar {*}}_{1}{\bar {*}}_{1})}$、 ${\displaystyle ({*}_{0}{\times }_{0})}$
31			PMN2 1	P mn 2 1	${\displaystyle \Gamma _{o}C_{2v}^{7}}$	10a	${\displaystyle (c:a:b):{\widetilde {ac}}\cdot 2_{1}}$	${\displaystyle (2_{1}2_{1}{*}{\cdot })}$	${\displaystyle (*{\cdot }{\bar {\times }})}$、 ${\displaystyle [{\times }_{0}{\times }_{1}]}$
32			Pba2	P ba 2	${\displaystyle \Gamma _{o}C_{2v}^{8}}$	9時間	${\displaystyle (c:a:b):{\tilde {a}}\odot 2}$	${\displaystyle (2_{0}2_{0}{\times }_{0})}$	${\displaystyle (*{:}{*}_{0})}$
33			Pna2 1	P na 2 1	${\displaystyle \Gamma _{o}C_{2v}^{9}}$	12a	${\displaystyle (c:a:b):{\tilde {a}}\odot 2_{1}}$	${\displaystyle (2_{1}2_{1}{\times })}$	${\displaystyle (*{:}{\times })}$、 ${\displaystyle ({\times }{\times }_{1})}$
34			Pnn2	P nn 2	${\displaystyle \Gamma _{o}C_{2v}^{10}}$	8時間	${\displaystyle (c:a:b):{\widetilde {ac}}\odot 2}$	${\displaystyle (2_{0}2_{0}{\times }_{1})}$	${\displaystyle (*_{0}{\times }_{1})}$
35			cm2	C mm 2	${\displaystyle \Gamma _{o}^{b}C_{2v}^{11}}$	14秒	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2}$	${\displaystyle (2_{0}{*}{\cdot }2{\cdot }2)}$	${\displaystyle [*_{0}{\cdot }{*}_{0}{:}]}$
36			Cmc2 1	C mc 2 1	${\displaystyle \Gamma _{o}^{b}C_{2v}^{12}}$	13a	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2_{1}}$	${\displaystyle (2_{1}{*}{\cdot }2{:}2)}$	${\displaystyle ({\bar {*}}{\cdot }{\bar {*}}{:})}$、 ${\displaystyle [{\times }_{1}{\times }_{1}]}$
37			Ccc2	C cc 2	${\displaystyle \Gamma _{o}^{b}C_{2v}^{13}}$	10時間	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2}$	${\displaystyle (2_{0}{*}{:}2{:}2)}$	${\displaystyle ({\bar {*}}_{0}{\bar {*}}_{1})}$
38			アム2	A mm 2	${\displaystyle \Gamma _{o}^{b}C_{2v}^{14}}$	15秒	${\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2}$	${\displaystyle (*{\cdot }2{\cdot }2{\cdot }2{:}2)}$	${\displaystyle [{*}_{1}{\cdot }{*}_{1}{\cdot }]}$、 ${\displaystyle [*{\cdot }{\times }_{0}]}$
39			Aem2	A bm 2	${\displaystyle \Gamma _{o}^{b}C_{2v}^{15}}$	11時間	${\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2_{1}}$	${\displaystyle (*{\cdot }2{:}2{:}2{:}2)}$	${\displaystyle [{*}_{1}{:}{*}_{1}{:}]}$、 ${\displaystyle ({\bar {*}}{\cdot }{\bar {*}}_{0})}$
40			アマ2	ア・マ2	${\displaystyle \Gamma _{o}^{b}C_{2v}^{16}}$	12時間	${\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2}$	${\displaystyle (2_{0}2_{1}{*}{\cdot })}$	${\displaystyle (*{\cdot }{*}_{1})}$、 ${\displaystyle [*{:}{\times }_{1}]}$
41			Aea2	アバ2	${\displaystyle \Gamma _{o}^{b}C_{2v}^{17}}$	13時間	${\displaystyle \left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2_{1}}$	${\displaystyle (2_{0}2_{1}{*}{:})}$	${\displaystyle (*{:}{*}_{1})}$、 ${\displaystyle ({\bar {*}}{:}{\bar {*}}_{1})}$
42			Fmm2	F mm 2	${\displaystyle \Gamma _{o}^{f}C_{2v}^{18}}$	17秒	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2}$	${\displaystyle (*{\cdot }2{\cdot }2{:}2{:}2)}$	${\displaystyle [{*}_{1}{\cdot }{*}_{1}{:}]}$
43			Fdd2	F dd 2	${\displaystyle \Gamma _{o}^{f}C_{2v}^{19}}$	16時間	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):{\tfrac {1}{2}}{\widetilde {ac}}\odot 2}$	${\displaystyle (2_{0}2_{1}{\times })}$	${\displaystyle ({*}_{1}{\times })}$
44			イム2	1 mm 2	${\displaystyle \Gamma _{o}^{v}C_{2v}^{20}}$	16秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):m\cdot 2}$	${\displaystyle (2_{1}{*}{\cdot }2{\cdot }2)}$	${\displaystyle [*{\cdot }{\times }_{1}]}$
45			イバ2	私は2	${\displaystyle \Gamma _{o}^{v}C_{2v}^{21}}$	15時間	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {c}}\cdot 2}$	${\displaystyle (2_{1}{*}{:}2{:}2)}$	${\displaystyle ({\bar {*}}{:}{\bar {*}}_{0})}$
46			今2	私は2	${\displaystyle \Gamma _{o}^{v}C_{2v}^{22}}$	14時間	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2}$	${\displaystyle (2_{0}{*}{\cdot }2{:}2)}$	${\displaystyle ({\bar {*}}{\cdot }{\bar {*}}_{1})}$、 ${\displaystyle [*{:}{\times }_{0}]}$
47	${\displaystyle {\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}}$	${\displaystyle *222}$	んん	P 2/m 2/m 2/m	${\displaystyle \Gamma _{o}D_{2h}^{1}}$	18秒	${\displaystyle \left(c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]}$
48			ぷん	P 2/n 2/n 2/n	${\displaystyle \Gamma _{o}D_{2h}^{2}}$	19時間	${\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\widetilde {ac}}}$	${\displaystyle (2{\bar {*}}_{1}2_{0}2_{0})}$
49			PCCM	P 2/c 2/c 2/m	${\displaystyle \Gamma _{o}D_{2h}^{3}}$	17時間	${\displaystyle \left(c:a:b\right)\cdot m:2\cdot {\tilde {c}}}$	${\displaystyle [*{:}2{:}2{:}2{:}2]}$	${\displaystyle (*2_{0}2_{0}2{\cdot }2)}$
50			Pban	P 2/b 2/a 2/n	${\displaystyle \Gamma _{o}D_{2h}^{4}}$	18時間	${\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\tilde {a}}}$	${\displaystyle (2{\bar {*}}_{0}2_{0}2_{0})}$	${\displaystyle (*2_{0}2_{0}2{:}2)}$
51			プマ	P 2 1 /m 2/m 2/a	${\displaystyle \Gamma _{o}D_{2h}^{5}}$	14a	${\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\cdot m}$	${\displaystyle [2_{0}2_{0}{*}{\cdot }]}$	${\displaystyle [*{\cdot }2{:}2{\cdot }2{:}2]}$、 ${\displaystyle [*2{\cdot }2{\cdot }2{\cdot }2]}$
52			プナ	P 2/n 2 1 /n 2/a	${\displaystyle \Gamma _{o}D_{2h}^{6}}$	17a	${\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\odot {\widetilde {ac}}}$	${\displaystyle (2_{0}2{\bar {*}}_{1})}$	${\displaystyle (2_{0}{*}2{:}2)}$、 ${\displaystyle (2{\bar {*}}2_{1}2_{1})}$
53			プムナ	P 2/m 2/n 2 1 /a	${\displaystyle \Gamma _{o}D_{2h}^{7}}$	15a	${\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\widetilde {ac}}}$	${\displaystyle [2_{0}2_{0}{*}{:}]}$	${\displaystyle (*2_{1}2_{1}2{\cdot }2)}$、 ${\displaystyle (2_{0}{*}2{\cdot }2)}$
54			ペッカ	P 2 1 /c 2/c 2/a	${\displaystyle \Gamma _{o}D_{2h}^{8}}$	16a	${\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}}$	${\displaystyle (2_{0}2{\bar {*}}_{0})}$	${\displaystyle (*2{:}2{:}2{:}2)}$、 ${\displaystyle (*2_{1}2_{1}2{:}2)}$
55			Pbam	P 2 1 /b 2 1 /a 2/m	${\displaystyle \Gamma _{o}D_{2h}^{9}}$	22a	${\displaystyle \left(c:a:b\right)\cdot m:2\odot {\tilde {a}}}$	${\displaystyle [2_{0}2_{0}{\times }_{0}]}$	${\displaystyle (*2{\cdot }2{:}2{\cdot }2)}$
56			PCN	P 2 1 /c 2 1 /c 2/n	${\displaystyle \Gamma _{o}D_{2h}^{10}}$	27a	${\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot {\tilde {c}}}$	${\displaystyle (2{\bar {*}}{:}2{:}2)}$	${\displaystyle (2_{1}2{\bar {*}}_{0})}$
57			Pbcm	P 2/b 2 1 /c 2 1 /m	${\displaystyle \Gamma _{o}D_{2h}^{11}}$	23a	${\displaystyle \left(c:a:b\right)\cdot m:2_{1}\odot {\tilde {c}}}$	${\displaystyle (2_{0}2{\bar {*}}{\cdot })}$	${\displaystyle (*2{:}2{\cdot }2{:}2)}$、 ${\displaystyle [2_{1}2_{1}{*}{:}]}$
58			プンム	P 2 1 /n 2 1 /n 2/m	${\displaystyle \Gamma _{o}D_{2h}^{12}}$	25a	${\displaystyle \left(c:a:b\right)\cdot m:2\odot {\widetilde {ac}}}$	${\displaystyle [2_{0}2_{0}{\times }_{1}]}$	${\displaystyle (2_{1}{*}2{\cdot }2)}$
59			午後	P 2 1 /m 2 1 /m 2/n	${\displaystyle \Gamma _{o}D_{2h}^{13}}$	24a	${\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot m}$	${\displaystyle (2{\bar {*}}{\cdot }2{\cdot }2)}$	${\displaystyle [2_{1}2_{1}{*}{\cdot }]}$
60			Pbcn	P 2 1 /b 2/c 2 1 /n	${\displaystyle \Gamma _{o}D_{2h}^{14}}$	26a	${\displaystyle \left(c:a:b\right)\cdot {\widetilde {ab}}:2_{1}\odot {\tilde {c}}}$	${\displaystyle (2_{0}2{\bar {*}}{:})}$	${\displaystyle (2_{1}{*}2{:}2)}$、 ${\displaystyle (2_{1}2{\bar {*}}_{1})}$
61			Pbca	P 2 1 /b 2 1 /c 2 1 /a	${\displaystyle \Gamma _{o}D_{2h}^{15}}$	29a	${\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot {\tilde {c}}}$	${\displaystyle (2_{1}2{\bar {*}}{:})}$
62			プンマ	P 2 1 /n 2 1 /m 2 1 /a	${\displaystyle \Gamma _{o}D_{2h}^{16}}$	28a	${\displaystyle \left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot m}$	${\displaystyle (2_{1}2{\bar {*}}{\cdot })}$	${\displaystyle (2{\bar {*}}{\cdot }2{:}2)}$、 ${\displaystyle [2_{1}2_{1}{\times }]}$
63			センチセンチ	C 2/m 2/c 2 1 /m	${\displaystyle \Gamma _{o}^{b}D_{2h}^{17}}$	18a	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2_{1}\cdot {\tilde {c}}}$	${\displaystyle [2_{0}2_{1}{*}{\cdot }]}$	${\displaystyle (*2{\cdot }2{\cdot }2{:}2)}$、 ${\displaystyle [2_{1}{*}{\cdot }2{:}2]}$
64			Cmce	C 2/m 2/c 2 1 /a	${\displaystyle \Gamma _{o}^{b}D_{2h}^{18}}$	19a	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\tilde {c}}}$	${\displaystyle [2_{0}2_{1}{*}{:}]}$	${\displaystyle (*2{\cdot }2{:}2{:}2)}$、 ${\displaystyle (*2_{1}2{\cdot }2{:}2)}$
65			んん	C 2/m 2/m 2/m	${\displaystyle \Gamma _{o}^{b}D_{2h}^{19}}$	19秒	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [2_{0}{*}{\cdot }2{\cdot }2]}$	${\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{:}2]}$
66			Cccm	C 2/c 2/c 2/m	${\displaystyle \Gamma _{o}^{b}D_{2h}^{20}}$	20時間	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot {\tilde {c}}}$	${\displaystyle [2_{0}{*}{:}2{:}2]}$	${\displaystyle (*2_{0}2_{1}2{\cdot }2)}$
67			センチ	C 2/m 2/m 2/e	${\displaystyle \Gamma _{o}^{b}D_{2h}^{21}}$	21時間	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot m}$	${\displaystyle (*2_{0}2{\cdot }2{\cdot }2)}$	${\displaystyle [*{\cdot }2{:}2{:}2{:}2]}$
68			CCCE	C 2/c 2/c 2/e	${\displaystyle \Gamma _{o}^{b}D_{2h}^{22}}$	22時間	${\displaystyle \left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}}$	${\displaystyle (*2_{0}2{:}2{:}2)}$	${\displaystyle (*2_{0}2_{1}2{:}2)}$
69			ふーん	F 2/m 2/m 2/m	${\displaystyle \Gamma _{o}^{f}D_{2h}^{23}}$	21秒	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]}$
70			ファッド	F 2/d 2/d 2/d	${\displaystyle \Gamma _{o}^{f}D_{2h}^{24}}$	24時間	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tfrac {1}{2}}{\widetilde {ab}}:2\odot {\tfrac {1}{2}}{\widetilde {ac}}}$	${\displaystyle (2{\bar {*}}2_{0}2_{1})}$
71			ええと	1 2/m 2/m 2/m	${\displaystyle \Gamma _{o}^{v}D_{2h}^{25}}$	20代	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot m}$	${\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]}$
72			イバム	私 2/b 2/a 2/m	${\displaystyle \Gamma _{o}^{v}D_{2h}^{26}}$	23時間	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot {\tilde {c}}}$	${\displaystyle [2_{1}{*}{:}2{:}2]}$	${\displaystyle (*2_{0}2{\cdot }2{:}2)}$
73			イブカ	私 2/b 2/c 2/a	${\displaystyle \Gamma _{o}^{v}D_{2h}^{27}}$	21a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}}$	${\displaystyle (*2_{1}2{:}2{:}2)}$
74			イマ	1 2/m 2/m 2/a	${\displaystyle \Gamma _{o}^{v}D_{2h}^{28}}$	20a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot m}$	${\displaystyle (*2_{1}2{\cdot }2{\cdot }2)}$	${\displaystyle [2_{0}{*}{\cdot }2{:}2]}$

正方晶系の一覧

正方ブラヴェ格子

シンプル（P）	本体（I）

正方晶系

番号	点群	オービフォールド	短縮名	フルネーム	シェーンフライ	フェドロフ	シュブニコフ	フィブリフォールド
75	4	${\displaystyle 44}$	P4	P4	${\displaystyle \Gamma _{q}C_{4}^{1}}$	22秒	${\displaystyle (c:a:a):4}$	${\displaystyle (4_{0}4_{0}2_{0})}$
76			P4 1	P 4 1	${\displaystyle \Gamma _{q}C_{4}^{2}}$	30a	${\displaystyle (c:a:a):4_{1}}$	${\displaystyle (4_{1}4_{1}2_{1})}$
77			P4 2	P 4 2	${\displaystyle \Gamma _{q}C_{4}^{3}}$	33a	${\displaystyle (c:a:a):4_{2}}$	${\displaystyle (4_{2}4_{2}2_{0})}$
78			P4 3	P 4 3	${\displaystyle \Gamma _{q}C_{4}^{4}}$	31a	${\displaystyle (c:a:a):4_{3}}$	${\displaystyle (4_{1}4_{1}2_{1})}$
79			I4	私 4	${\displaystyle \Gamma _{q}^{v}C_{4}^{5}}$	23秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4}$	${\displaystyle (4_{2}4_{0}2_{1})}$
80			I4 1	私 4 1	${\displaystyle \Gamma _{q}^{v}C_{4}^{6}}$	32a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}}$	${\displaystyle (4_{3}4_{1}2_{0})}$
81	4	${\displaystyle 2\times }$	P4​	P4​	${\displaystyle \Gamma _{q}S_{4}^{1}}$	26秒	${\displaystyle (c:a:a):{\tilde {4}}}$	${\displaystyle (442_{0})}$
82			私4	私4	${\displaystyle \Gamma _{q}^{v}S_{4}^{2}}$	27秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}}$	${\displaystyle (442_{1})}$
83	4/m	${\displaystyle 4*}$	P4/m	P 4/m	${\displaystyle \Gamma _{q}C_{4h}^{1}}$	28秒	${\displaystyle (c:a:a)\cdot m:4}$	${\displaystyle [4_{0}4_{0}2_{0}]}$
84			P4 2 /m	P 4 2 /m	${\displaystyle \Gamma _{q}C_{4h}^{2}}$	41a	${\displaystyle (c:a:a)\cdot m:4_{2}}$	${\displaystyle [4_{2}4_{2}2_{0}]}$
85			P4/n	P 4/n	${\displaystyle \Gamma _{q}C_{4h}^{3}}$	29時間	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4}$	${\displaystyle (44_{0}2)}$
86			P4 2 /n	P 4 2 /n	${\displaystyle \Gamma _{q}C_{4h}^{4}}$	42a	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}}$	${\displaystyle (44_{2}2)}$
87			I4/m	私 4/m	${\displaystyle \Gamma _{q}^{v}C_{4h}^{5}}$	29秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4}$	${\displaystyle [4_{2}4_{0}2_{1}]}$
88			I4 1 /a	私 4 1 /a	${\displaystyle \Gamma _{q}^{v}C_{4h}^{6}}$	40a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}}$	${\displaystyle (44_{1}2)}$
89	422	${\displaystyle 224}$	P422	P 4 2 2	${\displaystyle \Gamma _{q}D_{4}^{1}}$	30代	${\displaystyle (c:a:a):4:2}$	${\displaystyle (*4_{0}4_{0}2_{0})}$
90			P42 1 2	P42 1 2	${\displaystyle \Gamma _{q}D_{4}^{2}}$	43a	${\displaystyle (c:a:a):4}$ ${\displaystyle 2_{1}}$	${\displaystyle (4_{0}{*}2_{0})}$
91			P4 1 22	P 4 1 2 2	${\displaystyle \Gamma _{q}D_{4}^{3}}$	44a	${\displaystyle (c:a:a):4_{1}:2}$	${\displaystyle (*4_{1}4_{1}2_{1})}$
92			P4 1 2 1 2	P 4 1 2 1 2	${\displaystyle \Gamma _{q}D_{4}^{4}}$	48a	${\displaystyle (c:a:a):4_{1}}$ ${\displaystyle 2_{1}}$	${\displaystyle (4_{1}{*}2_{1})}$
93			P4 2 22	P 4 2 2 2	${\displaystyle \Gamma _{q}D_{4}^{5}}$	47a	${\displaystyle (c:a:a):4_{2}:2}$	${\displaystyle (*4_{2}4_{2}2_{0})}$
94			P4 2 2 1 2	P 4 2 2 1 2	${\displaystyle \Gamma _{q}D_{4}^{6}}$	50a	${\displaystyle (c:a:a):4_{2}}$ ${\displaystyle 2_{1}}$	${\displaystyle (4_{2}{*}2_{0})}$
95			P4 3 22	P 4 3 2 2	${\displaystyle \Gamma _{q}D_{4}^{7}}$	45a	${\displaystyle (c:a:a):4_{3}:2}$	${\displaystyle (*4_{1}4_{1}2_{1})}$
96			P4 3 2 1 2	P 4 3 2 1 2	${\displaystyle \Gamma _{q}D_{4}^{8}}$	49a	${\displaystyle (c:a:a):4_{3}}$ ${\displaystyle 2_{1}}$	${\displaystyle (4_{1}{*}2_{1})}$
97			I422	私 4 2 2	${\displaystyle \Gamma _{q}^{v}D_{4}^{9}}$	31秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2}$	${\displaystyle (*4_{2}4_{0}2_{1})}$
98			I4 1 22	私 4 1 2 2	${\displaystyle \Gamma _{q}^{v}D_{4}^{10}}$	46a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2_{1}}$	${\displaystyle (*4_{3}4_{1}2_{0})}$
99	4mm	${\displaystyle *44}$	P4mm	P 4mm	${\displaystyle \Gamma _{q}C_{4v}^{1}}$	24秒	${\displaystyle (c:a:a):4\cdot m}$	${\displaystyle (*{\cdot }4{\cdot }4{\cdot }2)}$
100			P4bm	P 4 bm	${\displaystyle \Gamma _{q}C_{4v}^{2}}$	26時間	${\displaystyle (c:a:a):4\odot {\tilde {a}}}$	${\displaystyle (4_{0}{*}{\cdot }2)}$
101			P4 2cm​	P 4 2 cm	${\displaystyle \Gamma _{q}C_{4v}^{3}}$	37a	${\displaystyle (c:a:a):4_{2}\cdot {\tilde {c}}}$	${\displaystyle (*{:}4{\cdot }4{:}2)}$
102			P4 2 nm	P 4 2 nm	${\displaystyle \Gamma _{q}C_{4v}^{4}}$	38a	${\displaystyle (c:a:a):4_{2}\odot {\widetilde {ac}}}$	${\displaystyle (4_{2}{*}{\cdot }2)}$
103			P4cc	P 4 cc	${\displaystyle \Gamma _{q}C_{4v}^{5}}$	25時間	${\displaystyle (c:a:a):4\cdot {\tilde {c}}}$	${\displaystyle (*{:}4{:}4{:}2)}$
104			P4nc	P 4 nc	${\displaystyle \Gamma _{q}C_{4v}^{6}}$	27時間	${\displaystyle (c:a:a):4\odot {\widetilde {ac}}}$	${\displaystyle (4_{0}{*}{:}2)}$
105			P4 2 mc	P 4 2 mc	${\displaystyle \Gamma _{q}C_{4v}^{7}}$	36a	${\displaystyle (c:a:a):4_{2}\cdot m}$	${\displaystyle (*{\cdot }4{:}4{\cdot }2)}$
106			P4 2 bc	P 4 2 bc	${\displaystyle \Gamma _{q}C_{4v}^{8}}$	39a	${\displaystyle (c:a:a):4\odot {\tilde {a}}}$	${\displaystyle (4_{2}{*}{:}2)}$
107			I4mm	I 4mm	${\displaystyle \Gamma _{q}^{v}C_{4v}^{9}}$	25秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot m}$	${\displaystyle (*{\cdot }4{\cdot }4{:}2)}$
108			I4cm	1 4 cm	${\displaystyle \Gamma _{q}^{v}C_{4v}^{10}}$	28時間	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot {\tilde {c}}}$	${\displaystyle (*{\cdot }4{:}4{:}2)}$
109			I4 1 md	私 4 1 md	${\displaystyle \Gamma _{q}^{v}C_{4v}^{11}}$	34a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot m}$	${\displaystyle (4_{1}{*}{\cdot }2)}$
110			I4 1 CD	I 4 1 CD	${\displaystyle \Gamma _{q}^{v}C_{4v}^{12}}$	35a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot {\tilde {c}}}$	${\displaystyle (4_{1}{*}{:}2)}$
111	4 2m	${\displaystyle 2{*}2}$	P 4 2m	P 4 2メートル	${\displaystyle \Gamma _{q}D_{2d}^{1}}$	32秒	${\displaystyle (c:a:a):{\tilde {4}}:2}$	${\displaystyle (*4{\cdot }42_{0})}$
112			P 4 2c	P 4 2 c	${\displaystyle \Gamma _{q}D_{2d}^{2}}$	30時間	${\displaystyle (c:a:a):{\tilde {4}}}$ ${\displaystyle 2}$	${\displaystyle (*4{:}42_{0})}$
113			P 4 2 1メートル	P 4 2 1メートル	${\displaystyle \Gamma _{q}D_{2d}^{3}}$	52a	${\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {ab}}}$	${\displaystyle (4{\bar {*}}{\cdot }2)}$
114			P 4 2 1 c	P 4 2 1 c	${\displaystyle \Gamma _{q}D_{2d}^{4}}$	53a	${\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {abc}}}$	${\displaystyle (4{\bar {*}}{:}2)}$
115			P 4㎡​	P 4 m 2	${\displaystyle \Gamma _{q}D_{2d}^{5}}$	33秒	${\displaystyle (c:a:a):{\tilde {4}}\cdot m}$	${\displaystyle (*{\cdot }44{\cdot }2)}$
116			P 4 c2	P 4 c 2	${\displaystyle \Gamma _{q}D_{2d}^{6}}$	31時間	${\displaystyle (c:a:a):{\tilde {4}}\cdot {\tilde {c}}}$	${\displaystyle (*{:}44{:}2)}$
117			P 4 b2	P 4 b 2	${\displaystyle \Gamma _{q}D_{2d}^{7}}$	32時間	${\displaystyle (c:a:a):{\tilde {4}}\odot {\tilde {a}}}$	${\displaystyle (4{\bar {*}}_{0}2_{0})}$
118			P 4 n2	P 4 n 2	${\displaystyle \Gamma _{q}D_{2d}^{8}}$	33時間	${\displaystyle (c:a:a):{\tilde {4}}\cdot {\widetilde {ac}}}$	${\displaystyle (4{\bar {*}}_{1}2_{0})}$
119			1 4平方メートル	1 4 m 2	${\displaystyle \Gamma _{q}^{v}D_{2d}^{9}}$	35秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot m}$	${\displaystyle (*4{\cdot }42_{1})}$
120			私4 c2	私4 c 2	${\displaystyle \Gamma _{q}^{v}D_{2d}^{10}}$	34時間	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot {\tilde {c}}}$	${\displaystyle (*4{:}42_{1})}$
121			私4 2m	I 4 2メートル	${\displaystyle \Gamma _{q}^{v}D_{2d}^{11}}$	34秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}:2}$	${\displaystyle (*{\cdot }44{:}2)}$
122			I 4 2d	私4 2日	${\displaystyle \Gamma _{q}^{v}D_{2d}^{12}}$	51a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\odot {\tfrac {1}{2}}{\widetilde {abc}}}$	${\displaystyle (4{\bar {*}}2_{1})}$
123	4/m 2/m 2/m	${\displaystyle *224}$	P4/mmm	P 4/m 2/m 2/m	${\displaystyle \Gamma _{q}D_{4h}^{1}}$	36秒	${\displaystyle (c:a:a)\cdot m:4\cdot m}$	${\displaystyle [*{\cdot }4{\cdot }4{\cdot }2]}$
124			P4/mcc	P 4/m 2/c 2/c	${\displaystyle \Gamma _{q}D_{4h}^{2}}$	35時間	${\displaystyle (c:a:a)\cdot m:4\cdot {\tilde {c}}}$	${\displaystyle [*{:}4{:}4{:}2]}$
125			P4/nbm	P 4/n 2/b 2/m	${\displaystyle \Gamma _{q}D_{4h}^{3}}$	36時間	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\odot {\tilde {a}}}$	${\displaystyle (*4_{0}4{\cdot }2)}$
126			P4/nnc	P 4/n 2/n 2/c	${\displaystyle \Gamma _{q}D_{4h}^{4}}$	37時間	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\odot {\widetilde {ac}}}$	${\displaystyle (*4_{0}4{:}2)}$
127			P4/mbm	P 4/m 2 1 /b 2/m	${\displaystyle \Gamma _{q}D_{4h}^{5}}$	54a	${\displaystyle (c:a:a)\cdot m:4\odot {\tilde {a}}}$	${\displaystyle [4_{0}{*}{\cdot }2]}$
128			P4/mnc	P 4/m 2 1 /n 2/c	${\displaystyle \Gamma _{q}D_{4h}^{6}}$	56a	${\displaystyle (c:a:a)\cdot m:4\odot {\widetilde {ac}}}$	${\displaystyle [4_{0}{*}{:}2]}$
129			P4/nmm	P 4/n 2 1 /m 2/m	${\displaystyle \Gamma _{q}D_{4h}^{7}}$	55a	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\cdot m}$	${\displaystyle (*4{\cdot }4{\cdot }2)}$
130			P4/ncc	P 4/n 2 1 /c 2/c	${\displaystyle \Gamma _{q}D_{4h}^{8}}$	57a	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4\cdot {\tilde {c}}}$	${\displaystyle (*4{:}4{:}2)}$
131			P4 2 /mmc	P 4 2 /m 2/m 2/c	${\displaystyle \Gamma _{q}D_{4h}^{9}}$	60a	${\displaystyle (c:a:a)\cdot m:4_{2}\cdot m}$	${\displaystyle [*{\cdot }4{:}4{\cdot }2]}$
132			P4 2 /mcm	P 4 2 /m 2/c 2/m	${\displaystyle \Gamma _{q}D_{4h}^{10}}$	61a	${\displaystyle (c:a:a)\cdot m:4_{2}\cdot {\tilde {c}}}$	${\displaystyle [*{:}4{\cdot }4{:}2]}$
133			P4 2 /NBC	P 4 2 /n 2/b 2/c	${\displaystyle \Gamma _{q}D_{4h}^{11}}$	63a	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\tilde {a}}}$	${\displaystyle (*4_{2}4{:}2)}$
134			P4 2 /nnm	P 4 2 /n 2/n 2/m	${\displaystyle \Gamma _{q}D_{4h}^{12}}$	62a	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\widetilde {ac}}}$	${\displaystyle (*4_{2}4{\cdot }2)}$
135			P4 2 /mbc	P 4 2 /m 2 1 /b 2/c	${\displaystyle \Gamma _{q}D_{4h}^{13}}$	66a	${\displaystyle (c:a:a)\cdot m:4_{2}\odot {\tilde {a}}}$	${\displaystyle [4_{2}{*}{:}2]}$
136			P4 2 /分	P 4 2 /m 2 1 /n 2/m	${\displaystyle \Gamma _{q}D_{4h}^{14}}$	65a	${\displaystyle (c:a:a)\cdot m:4_{2}\odot {\widetilde {ac}}}$	${\displaystyle [4_{2}{*}{\cdot }2]}$
137			P4 2 /nmc	P 4 2 /n 2 1 /m 2/c	${\displaystyle \Gamma _{q}D_{4h}^{15}}$	67a	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot m}$	${\displaystyle (*4{\cdot }4{:}2)}$
138			P4 2 /ncm	P 4 2 /n 2 1 /c 2/m	${\displaystyle \Gamma _{q}D_{4h}^{16}}$	65a	${\displaystyle (c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot {\tilde {c}}}$	${\displaystyle (*4{:}4{\cdot }2)}$
139			I4/mmm	1 4/m 2/m 2/m	${\displaystyle \Gamma _{q}^{v}D_{4h}^{17}}$	37秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot m}$	${\displaystyle [*{\cdot }4{\cdot }4{:}2]}$
140			I4/mcm	1 4/m 2/c 2/m	${\displaystyle \Gamma _{q}^{v}D_{4h}^{18}}$	38時間	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot {\tilde {c}}}$	${\displaystyle [*{\cdot }4{:}4{:}2]}$
141			I4 1 /amd	1 4 1 /a 2/m 2/d	${\displaystyle \Gamma _{q}^{v}D_{4h}^{19}}$	59a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot m}$	${\displaystyle (*4_{1}4{\cdot }2)}$
142			I4 1 /acd	私 4 1 /a 2/c 2/d	${\displaystyle \Gamma _{q}^{v}D_{4h}^{20}}$	58a	${\displaystyle \left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot {\tilde {c}}}$	${\displaystyle (*4_{1}4{:}2)}$

三角のリスト

三方ブラヴェ格子

菱面体（R）	六角形（P）

三方晶系

番号	点群	オービフォールド	短縮名	フルネーム	シェーンフライ	フェドロフ	シュブニコフ	フィブリフォールド
143	3	${\displaystyle 33}$	P3	P3	${\displaystyle \Gamma _{h}C_{3}^{1}}$	38秒	${\displaystyle (c:(a/a)):3}$	${\displaystyle (3_{0}3_{0}3_{0})}$
144			P3 1	P 3 1	${\displaystyle \Gamma _{h}C_{3}^{2}}$	68a	${\displaystyle (c:(a/a)):3_{1}}$	${\displaystyle (3_{1}3_{1}3_{1})}$
145			P3 2	P 3 2	${\displaystyle \Gamma _{h}C_{3}^{3}}$	69a	${\displaystyle (c:(a/a)):3_{2}}$	${\displaystyle (3_{1}3_{1}3_{1})}$
146			R3	R3	${\displaystyle \Gamma _{rh}C_{3}^{4}}$	39秒	${\displaystyle (a/a/a)/3}$	${\displaystyle (3_{0}3_{1}3_{2})}$
147	3	${\displaystyle 3\times }$	P3​	P3​	${\displaystyle \Gamma _{h}C_{3i}^{1}}$	51秒	${\displaystyle (c:(a/a)):{\tilde {6}}}$	${\displaystyle (63_{0}2)}$
148			R3​	R3​	${\displaystyle \Gamma _{rh}C_{3i}^{2}}$	52秒	${\displaystyle (a/a/a)/{\tilde {6}}}$	${\displaystyle (63_{1}2)}$
149	32	${\displaystyle 223}$	P312	P 3 1 2	${\displaystyle \Gamma _{h}D_{3}^{1}}$	45秒	${\displaystyle (c:(a/a)):2:3}$	${\displaystyle (*3_{0}3_{0}3_{0})}$
150			P321	P 3 2 1	${\displaystyle \Gamma _{h}D_{3}^{2}}$	44秒	${\displaystyle (c:(a/a))\cdot 2:3}$	${\displaystyle (3_{0}{*}3_{0})}$
151			P3 1 12	P 3 1 1 2	${\displaystyle \Gamma _{h}D_{3}^{3}}$	72a	${\displaystyle (c:(a/a)):2:3_{1}}$	${\displaystyle (*3_{1}3_{1}3_{1})}$
152			P3 1 21	P 3 1 2 1	${\displaystyle \Gamma _{h}D_{3}^{4}}$	70a	${\displaystyle (c:(a/a))\cdot 2:3_{1}}$	${\displaystyle (3_{1}{*}3_{1})}$
153			P3 2 12	P 3 2 1 2	${\displaystyle \Gamma _{h}D_{3}^{5}}$	73a	${\displaystyle (c:(a/a)):2:3_{2}}$	${\displaystyle (*3_{1}3_{1}3_{1})}$
154			P3 2 21	P 3 2 2 1	${\displaystyle \Gamma _{h}D_{3}^{6}}$	71a	${\displaystyle (c:(a/a))\cdot 2:3_{2}}$	${\displaystyle (3_{1}{*}3_{1})}$
155			R32	R 3 2	${\displaystyle \Gamma _{rh}D_{3}^{7}}$	46秒	${\displaystyle (a/a/a)/3:2}$	${\displaystyle (*3_{0}3_{1}3_{2})}$
156	3メートル	${\displaystyle *33}$	P3m1	P 3 m 1	${\displaystyle \Gamma _{h}C_{3v}^{1}}$	40代	${\displaystyle (c:(a/a)):m\cdot 3}$	${\displaystyle (*{\cdot }3{\cdot }3{\cdot }3)}$
157			3100万ペソ	P 3 1メートル	${\displaystyle \Gamma _{h}C_{3v}^{2}}$	41秒	${\displaystyle (c:(a/a))\cdot m\cdot 3}$	${\displaystyle (3_{0}{*}{\cdot }3)}$
158			P3c1	P 3 c 1	${\displaystyle \Gamma _{h}C_{3v}^{3}}$	39時間	${\displaystyle (c:(a/a)):{\tilde {c}}:3}$	${\displaystyle (*{:}3{:}3{:}3)}$
159			P31c	P 3 1 秒	${\displaystyle \Gamma _{h}C_{3v}^{4}}$	40時間	${\displaystyle (c:(a/a))\cdot {\tilde {c}}:3}$	${\displaystyle (3_{0}{*}{:}3)}$
160			300万ランド	R 3メートル	${\displaystyle \Gamma _{rh}C_{3v}^{5}}$	42秒	${\displaystyle (a/a/a)/3\cdot m}$	${\displaystyle (3_{1}{*}{\cdot }3)}$
161			R3c	R 3 c	${\displaystyle \Gamma _{rh}C_{3v}^{6}}$	41時間	${\displaystyle (a/a/a)/3\cdot {\tilde {c}}}$	${\displaystyle (3_{1}{*}{:}3)}$
162	3 2/m	${\displaystyle 2{*}3}$	P 3 1m	P 3 1 2/m	${\displaystyle \Gamma _{h}D_{3d}^{1}}$	56秒	${\displaystyle (c:(a/a))\cdot m\cdot {\tilde {6}}}$	${\displaystyle (*{\cdot }63_{0}2)}$
163			P 3 1c	P 3 1 2/c	${\displaystyle \Gamma _{h}D_{3d}^{2}}$	46時間	${\displaystyle (c:(a/a))\cdot {\tilde {c}}\cdot {\tilde {6}}}$	${\displaystyle (*{:}63_{0}2)}$
164			P 3 m1	P 3 2/m 1	${\displaystyle \Gamma _{h}D_{3d}^{3}}$	55秒	${\displaystyle (c:(a/a)):m\cdot {\tilde {6}}}$	${\displaystyle (*6{\cdot }3{\cdot }2)}$
165			P 3 c1	P 3 2/c 1	${\displaystyle \Gamma _{h}D_{3d}^{4}}$	45時間	${\displaystyle (c:(a/a)):{\tilde {c}}\cdot {\tilde {6}}}$	${\displaystyle (*6{:}3{:}2)}$
166			R 3メートル	R 3 2/m	${\displaystyle \Gamma _{rh}D_{3d}^{5}}$	57秒	${\displaystyle (a/a/a)/{\tilde {6}}\cdot m}$	${\displaystyle (*{\cdot }63_{1}2)}$
167			R 3 c	R 3 2/c	${\displaystyle \Gamma _{rh}D_{3d}^{6}}$	47時間	${\displaystyle (a/a/a)/{\tilde {6}}\cdot {\tilde {c}}}$	${\displaystyle (*{:}63_{1}2)}$

六角形のリスト

六方ブラヴェ格子

六方晶系

番号	点群	オービフォールド	短縮名	フルネーム	シェーンフライ	フェドロフ	シュブニコフ	フィブリフォールド
168	6	${\displaystyle 66}$	P6	P6	${\displaystyle \Gamma _{h}C_{6}^{1}}$	49秒	${\displaystyle (c:(a/a)):6}$	${\displaystyle (6_{0}3_{0}2_{0})}$
169			P6 1	P 6 1	${\displaystyle \Gamma _{h}C_{6}^{2}}$	74a	${\displaystyle (c:(a/a)):6_{1}}$	${\displaystyle (6_{1}3_{1}2_{1})}$
170			P6 5	P 6 5	${\displaystyle \Gamma _{h}C_{6}^{3}}$	75a	${\displaystyle (c:(a/a)):6_{5}}$	${\displaystyle (6_{1}3_{1}2_{1})}$
171			P6 2	P 6 2	${\displaystyle \Gamma _{h}C_{6}^{4}}$	76a	${\displaystyle (c:(a/a)):6_{2}}$	${\displaystyle (6_{2}3_{2}2_{0})}$
172			P6 4	P 6 4	${\displaystyle \Gamma _{h}C_{6}^{5}}$	77a	${\displaystyle (c:(a/a)):6_{4}}$	${\displaystyle (6_{2}3_{2}2_{0})}$
173			P6 3	P 6 3	${\displaystyle \Gamma _{h}C_{6}^{6}}$	78a	${\displaystyle (c:(a/a)):6_{3}}$	${\displaystyle (6_{3}3_{0}2_{1})}$
174	6	${\displaystyle 3*}$	P6​	P6​	${\displaystyle \Gamma _{h}C_{3h}^{1}}$	43秒	${\displaystyle (c:(a/a)):3:m}$	${\displaystyle [3_{0}3_{0}3_{0}]}$
175	6/月	${\displaystyle 6*}$	P6/m	P 6/m	${\displaystyle \Gamma _{h}C_{6h}^{1}}$	53秒	${\displaystyle (c:(a/a))\cdot m:6}$	${\displaystyle [6_{0}3_{0}2_{0}]}$
176			P6 3 /m	P 6 3 /m	${\displaystyle \Gamma _{h}C_{6h}^{2}}$	81a	${\displaystyle (c:(a/a))\cdot m:6_{3}}$	${\displaystyle [6_{3}3_{0}2_{1}]}$
177	622	${\displaystyle 226}$	P622	P 6 2 2	${\displaystyle \Gamma _{h}D_{6}^{1}}$	54秒	${\displaystyle (c:(a/a))\cdot 2:6}$	${\displaystyle (*6_{0}3_{0}2_{0})}$
178			P6 1 22	P 6 1 2 2	${\displaystyle \Gamma _{h}D_{6}^{2}}$	82a	${\displaystyle (c:(a/a))\cdot 2:6_{1}}$	${\displaystyle (*6_{1}3_{1}2_{1})}$
179			P6 5 22	P 6 5 2 2	${\displaystyle \Gamma _{h}D_{6}^{3}}$	83a	${\displaystyle (c:(a/a))\cdot 2:6_{5}}$	${\displaystyle (*6_{1}3_{1}2_{1})}$
180			P6 2 22	P 6 2 2 2	${\displaystyle \Gamma _{h}D_{6}^{4}}$	84a	${\displaystyle (c:(a/a))\cdot 2:6_{2}}$	${\displaystyle (*6_{2}3_{2}2_{0})}$
181			P6 4 22	P 6 4 2 2	${\displaystyle \Gamma _{h}D_{6}^{5}}$	85a	${\displaystyle (c:(a/a))\cdot 2:6_{4}}$	${\displaystyle (*6_{2}3_{2}2_{0})}$
182			P6 3 22	P 6 3 2 2	${\displaystyle \Gamma _{h}D_{6}^{6}}$	86a	${\displaystyle (c:(a/a))\cdot 2:6_{3}}$	${\displaystyle (*6_{3}3_{0}2_{1})}$
183	6mm	${\displaystyle *66}$	P6mm	P 6mm	${\displaystyle \Gamma _{h}C_{6v}^{1}}$	50代	${\displaystyle (c:(a/a)):m\cdot 6}$	${\displaystyle (*{\cdot }6{\cdot }3{\cdot }2)}$
184			P6cc	P 6 cc	${\displaystyle \Gamma _{h}C_{6v}^{2}}$	44時間	${\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6}$	${\displaystyle (*{:}6{:}3{:}2)}$
185			P6 3cm​	P 6 3 cm	${\displaystyle \Gamma _{h}C_{6v}^{3}}$	80a	${\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6_{3}}$	${\displaystyle (*{\cdot }6{:}3{:}2)}$
186			P6 3 mc	P 6 3 mc	${\displaystyle \Gamma _{h}C_{6v}^{4}}$	79a	${\displaystyle (c:(a/a)):m\cdot 6_{3}}$	${\displaystyle (*{:}6{\cdot }3{\cdot }2)}$
187	6平方メートル	${\displaystyle *223}$	P 6平方メートル	P 6 m 2	${\displaystyle \Gamma _{h}D_{3h}^{1}}$	48秒	${\displaystyle (c:(a/a)):m\cdot 3:m}$	${\displaystyle [*{\cdot }3{\cdot }3{\cdot }3]}$
188			P 6 c2	P 6 c 2	${\displaystyle \Gamma _{h}D_{3h}^{2}}$	43時間	${\displaystyle (c:(a/a)):{\tilde {c}}\cdot 3:m}$	${\displaystyle [*{:}3{:}3{:}3]}$
189			P 6 2m	P 6 2メートル	${\displaystyle \Gamma _{h}D_{3h}^{3}}$	47秒	${\displaystyle (c:(a/a))\cdot m:3\cdot m}$	${\displaystyle [3_{0}{*}{\cdot }3]}$
190			P 6 2c	P 6 2c	${\displaystyle \Gamma _{h}D_{3h}^{4}}$	42時間	${\displaystyle (c:(a/a))\cdot m:3\cdot {\tilde {c}}}$	${\displaystyle [3_{0}{*}{:}3]}$
191	6/m 2/m 2/m	${\displaystyle *226}$	P6/mmm	P 6/m 2/m 2/m	${\displaystyle \Gamma _{h}D_{6h}^{1}}$	58秒	${\displaystyle (c:(a/a))\cdot m:6\cdot m}$	${\displaystyle [*{\cdot }6{\cdot }3{\cdot }2]}$
192			P6/mcc	P 6/m 2/c 2/c	${\displaystyle \Gamma _{h}D_{6h}^{2}}$	48時間	${\displaystyle (c:(a/a))\cdot m:6\cdot {\tilde {c}}}$	${\displaystyle [*{:}6{:}3{:}2]}$
193			P6 3 /mcm	P 6 3 /m 2/c 2/m	${\displaystyle \Gamma _{h}D_{6h}^{3}}$	87a	${\displaystyle (c:(a/a))\cdot m:6_{3}\cdot {\tilde {c}}}$	${\displaystyle [*{\cdot }6{:}3{:}2]}$
194			P6 3 /mmc	P 6 3 /m 2/m 2/c	${\displaystyle \Gamma _{h}D_{6h}^{4}}$	88a	${\displaystyle (c:(a/a))\cdot m:6_{3}\cdot m}$	${\displaystyle [*{:}6{\cdot }3{\cdot }2]}$

立方体のリスト

立方ブラヴェ格子

シンプル（P）	体中心（I）	面中心（F）

立方構造の例

• 
  （221）塩化セシウム。2種類の原子ごとに異なる色で表示されています。
• 
  （216）閃亜鉛鉱
• 
  （223）ウィア・フェラン構造

立方晶系

番号	点群	オービフォールド	短縮名	フルネーム	シェーンフライ	フェドロフ	シュブニコフ	コンウェイ	フィブリフォールド（保存） ${\displaystyle z}$	フィブリフォールド（ 、、を保存） ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle z}$
195	23	${\displaystyle 332}$	P23	P 2 3	${\displaystyle \Gamma _{c}T^{1}}$	59秒	${\displaystyle \left(a:a:a\right):2/3}$	${\displaystyle 2^{\circ }}$	${\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}3}$	${\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}3}$
196			F23	F 2 3	${\displaystyle \Gamma _{c}^{f}T^{2}}$	61秒	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):2/3}$	${\displaystyle 1^{\circ }}$	${\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}3}$	${\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}3}$
197			I23	私 2 3	${\displaystyle \Gamma _{c}^{v}T^{3}}$	60年代	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):2/3}$	${\displaystyle 4^{\circ \circ }}$	${\displaystyle (2_{1}{*}2_{0}2_{0}){:}3}$	${\displaystyle (2_{1}{*}2_{0}2_{0}){:}3}$
198			P2 1 3	P 2 1 3	${\displaystyle \Gamma _{c}T^{4}}$	89a	${\displaystyle \left(a:a:a\right):2_{1}/3}$	${\displaystyle 1^{\circ }/4}$	${\displaystyle (2_{1}2_{1}{\bar {\times }}){:}3}$	${\displaystyle (2_{1}2_{1}{\bar {\times }}){:}3}$
199			私2 1 3	私 2 1 3	${\displaystyle \Gamma _{c}^{v}T^{5}}$	90a	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):2_{1}/3}$	${\displaystyle 2^{\circ }/4}$	${\displaystyle (2_{0}{*}2_{1}2_{1}){:}3}$	${\displaystyle (2_{0}{*}2_{1}2_{1}){:}3}$
200	2/m 3	${\displaystyle 3{*}2}$	午後3時	P 2/m 3	${\displaystyle \Gamma _{c}T_{h}^{1}}$	62秒	${\displaystyle \left(a:a:a\right)\cdot m/{\tilde {6}}}$	${\displaystyle 4^{-}}$	${\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3}$	${\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3}$
201			Pn 3	P 2/n 3	${\displaystyle \Gamma _{c}T_{h}^{2}}$	49時間	${\displaystyle \left(a:a:a\right)\cdot {\widetilde {ab}}/{\tilde {6}}}$	${\displaystyle 4^{\circ +}}$	${\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}3}$	${\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}3}$
202			Fm 3	F 2/m 3	${\displaystyle \Gamma _{c}^{f}T_{h}^{3}}$	64秒	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right)\cdot m/{\tilde {6}}}$	${\displaystyle 2^{-}}$	${\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}3}$	${\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}3}$
203			Fd 3	F 2/d 3	${\displaystyle \Gamma _{c}^{f}T_{h}^{4}}$	50時間	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right)\cdot {\tfrac {1}{2}}{\widetilde {ab}}/{\tilde {6}}}$	${\displaystyle 2^{\circ +}}$	${\displaystyle (2{\bar {*}}2_{0}2_{1}){:}3}$	${\displaystyle (2{\bar {*}}2_{0}2_{1}){:}3}$
204			私は3歳です	1 2/m 3	${\displaystyle \Gamma _{c}^{v}T_{h}^{5}}$	63秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot m/{\tilde {6}}}$	${\displaystyle 8^{-\circ }}$	${\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}3}$	${\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}3}$
205			パ3	P 2 1 /a 3	${\displaystyle \Gamma _{c}T_{h}^{6}}$	91a	${\displaystyle \left(a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}}$	${\displaystyle 2^{-}/4}$	${\displaystyle (2_{1}2{\bar {*}}{:}){:}3}$	${\displaystyle (2_{1}2{\bar {*}}{:}){:}3}$
206			Ia 3	私 2 1 /a 3	${\displaystyle \Gamma _{c}^{v}T_{h}^{7}}$	92a	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}}$	${\displaystyle 4^{-}/4}$	${\displaystyle (*2_{1}2{:}2{:}2){:}3}$	${\displaystyle (*2_{1}2{:}2{:}2){:}3}$
207	432	${\displaystyle 432}$	P432	P 4 3 2	${\displaystyle \Gamma _{c}O^{1}}$	68秒	${\displaystyle \left(a:a:a\right):4/3}$	${\displaystyle 4^{\circ -}}$	${\displaystyle (*4_{0}4_{0}2_{0}){:}3}$	${\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6}$
208			P4 2 32	P 4 2 3 2	${\displaystyle \Gamma _{c}O^{2}}$	98a	${\displaystyle \left(a:a:a\right):4_{2}//3}$	${\displaystyle 4^{+}}$	${\displaystyle (*4_{2}4_{2}2_{0}){:}3}$	${\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6}$
209			F432	F 4 3 2	${\displaystyle \Gamma _{c}^{f}O^{3}}$	70年代	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/3}$	${\displaystyle 2^{\circ -}}$	${\displaystyle (*4_{2}4_{0}2_{1}){:}3}$	${\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6}$
210			F4 1 32	F 4 1 3 2	${\displaystyle \Gamma _{c}^{f}O^{4}}$	97a	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//3}$	${\displaystyle 2^{+}}$	${\displaystyle (*4_{3}4_{1}2_{0}){:}3}$	${\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6}$
211			I432	私 4 3 2	${\displaystyle \Gamma _{c}^{v}O^{5}}$	69秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):4/3}$	${\displaystyle 8^{+\circ }}$	${\displaystyle (4_{2}4_{0}2_{1}){:}3}$	${\displaystyle (2_{1}{*}2_{0}2_{0}){:}6}$
212			P4 3 32	P 4 3 3 2	${\displaystyle \Gamma _{c}O^{6}}$	94a	${\displaystyle \left(a:a:a\right):4_{3}//3}$	${\displaystyle 2^{+}/4}$	${\displaystyle (4_{1}{*}2_{1}){:}3}$	${\displaystyle (2_{1}2_{1}{\bar {\times }}){:}6}$
213			P4 1 32	P 4 1 3 2	${\displaystyle \Gamma _{c}O^{7}}$	95a	${\displaystyle \left(a:a:a\right):4_{1}//3}$	${\displaystyle 2^{+}/4}$	${\displaystyle (4_{1}{*}2_{1}){:}3}$	${\displaystyle (2_{1}2_{1}{\bar {\times }}){:}6}$
214			I4 1 32	私 4 1 3 2	${\displaystyle \Gamma _{c}^{v}O^{8}}$	96a	${\displaystyle \left({\tfrac {a+b+c}{2}}/:a:a:a\right):4_{1}//3}$	${\displaystyle 4^{+}/4}$	${\displaystyle (*4_{3}4_{1}2_{0}){:}3}$	${\displaystyle (2_{0}{*}2_{1}2_{1}){:}6}$
215	4 3m	${\displaystyle *332}$	P 4 3m	P 4 3メートル	${\displaystyle \Gamma _{c}T_{d}^{1}}$	65秒	${\displaystyle \left(a:a:a\right):{\tilde {4}}/3}$	${\displaystyle 2^{\circ }{:}2}$	${\displaystyle (*4{\cdot }42_{0}){:}3}$	${\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6}$
216			F 4 3m	F 4 3メートル	${\displaystyle \Gamma _{c}^{f}T_{d}^{2}}$	67秒	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}/3}$	${\displaystyle 1^{\circ }{:}2}$	${\displaystyle (*4{\cdot }42_{1}){:}3}$	${\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6}$
217			私4 3m	I 4 3メートル	${\displaystyle \Gamma _{c}^{v}T_{d}^{3}}$	66秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}/3}$	${\displaystyle 4^{\circ }{:}2}$	${\displaystyle (*{\cdot }44{:}2){:}3}$	${\displaystyle (2_{1}{*}2_{0}2_{0}){:}6}$
218			P 4 3n	P 4 3 n	${\displaystyle \Gamma _{c}T_{d}^{4}}$	51時間	${\displaystyle \left(a:a:a\right):{\tilde {4}}//3}$	${\displaystyle 4^{\circ }}$	${\displaystyle (*4{:}42_{0}){:}3}$	${\displaystyle (*2_{0}2_{0}2_{0}2_{0}){:}6}$
219			F 4 3c	F 4 3 c	${\displaystyle \Gamma _{c}^{f}T_{d}^{5}}$	52時間	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}//3}$	${\displaystyle 2^{\circ \circ }}$	${\displaystyle (*4{:}42_{1}){:}3}$	${\displaystyle (*2_{0}2_{1}2_{0}2_{1}){:}6}$
220			I 4 3d	私4 3日	${\displaystyle \Gamma _{c}^{v}T_{d}^{6}}$	93a	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}//3}$	${\displaystyle 4^{\circ }/4}$	${\displaystyle (4{\bar {*}}2_{1}){:}3}$	${\displaystyle (2_{0}{*}2_{1}2_{1}){:}6}$
221	4/m 3 2/m	${\displaystyle *432}$	午後3時	P 4/m 3 2/m	${\displaystyle \Gamma _{c}O_{h}^{1}}$	71秒	${\displaystyle \left(a:a:a\right):4/{\tilde {6}}\cdot m}$	${\displaystyle 4^{-}{:}2}$	${\displaystyle [*{\cdot }4{\cdot }4{\cdot }2]{:}3}$	${\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6}$
222			Pn 3 n	P 4/n 3 2/n	${\displaystyle \Gamma _{c}O_{h}^{2}}$	53時間	${\displaystyle \left(a:a:a\right):4/{\tilde {6}}\cdot {\widetilde {abc}}}$	${\displaystyle 8^{\circ \circ }}$	${\displaystyle (*4_{0}4{:}2){:}3}$	${\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}6}$
223			午後3時	P 4 2 /m 3 2/n	${\displaystyle \Gamma _{c}O_{h}^{3}}$	102a	${\displaystyle \left(a:a:a\right):4_{2}//{\tilde {6}}\cdot {\widetilde {abc}}}$	${\displaystyle 8^{\circ }}$	${\displaystyle [*{\cdot }4{:}4{\cdot }2]{:}3}$	${\displaystyle [*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6}$
224			Pn 3 m	P 4 2 /n 3 2/m	${\displaystyle \Gamma _{c}O_{h}^{4}}$	103a	${\displaystyle \left(a:a:a\right):4_{2}//{\tilde {6}}\cdot m}$	${\displaystyle 4^{+}{:}2}$	${\displaystyle (*4_{2}4{\cdot }2){:}3}$	${\displaystyle (2{\bar {*}}_{1}2_{0}2_{0}){:}6}$
225			Fm 3 m	F 4/m 3 2/m	${\displaystyle \Gamma _{c}^{f}O_{h}^{5}}$	73秒	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot m}$	${\displaystyle 2^{-}{:}2}$	${\displaystyle [*{\cdot }4{\cdot }4{:}2]{:}3}$	${\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}6}$
226			Fm 3 c	F 4/m 3 2/c	${\displaystyle \Gamma _{c}^{f}O_{h}^{6}}$	54時間	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot {\tilde {c}}}$	${\displaystyle 4^{--}}$	${\displaystyle [*{\cdot }4{:}4{:}2]{:}3}$	${\displaystyle [*{\cdot }2{\cdot }2{:}2{:}2]{:}6}$
227			Fd 3 m	F 4 1 /d 3 2/m	${\displaystyle \Gamma _{c}^{f}O_{h}^{7}}$	100a	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//{\tilde {6}}\cdot m}$	${\displaystyle 2^{+}{:}2}$	${\displaystyle (*4_{1}4{\cdot }2){:}3}$	${\displaystyle (2{\bar {*}}2_{0}2_{1}){:}6}$
228			Fd 3 c	F 4 1 /d 3 2/c	${\displaystyle \Gamma _{c}^{f}O_{h}^{8}}$	101a	${\displaystyle \left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//{\tilde {6}}\cdot {\tilde {c}}}$	${\displaystyle 4^{++}}$	${\displaystyle (*4_{1}4{:}2){:}3}$	${\displaystyle (2{\bar {*}}2_{0}2_{1}){:}6}$
229			私は3ヶ月です	1 4/m 3 2/m	${\displaystyle \Gamma _{c}^{v}O_{h}^{9}}$	72秒	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):4/{\tilde {6}}\cdot m}$	${\displaystyle 8^{\circ }{:}2}$	${\displaystyle [*{\cdot }4{\cdot }4{:}2]{:}3}$	${\displaystyle [2_{1}{*}{\cdot }2{\cdot }2]{:}6}$
230			Ia 3日	私 4 1 /a 3 2/d	${\displaystyle \Gamma _{c}^{v}O_{h}^{10}}$	99a	${\displaystyle \left({\tfrac {a+b+c}{2}}/a:a:a\right):4_{1}//{\tilde {6}}\cdot {\tfrac {1}{2}}{\widetilde {abc}}}$	${\displaystyle 8^{\circ }/4}$	${\displaystyle (*4_{1}4{:}2){:}3}$	${\displaystyle (*2_{1}2{:}2{:}2){:}6}$

注記

1. この記号は1992年にIUCRによって導入されました。それ以前は、空間群Aem2（39番）、Aea2（41番）、Cmce（64番）、Cmme（67番）、Ccce（68番）はそれぞれAbm2（39番）、Aba2（41番）、Cmca（64番）、Cmma（67番）、Ccca（68番）として知られていました。歴史的文献では古い名称が参照されている場合もありますが、その意味は変わりません。^[1] ${\displaystyle e}$

参考文献

1. de Wolff, PM; Billiet, Y.; Donnay, JDH; Fischer, W.; Galiulin, RB; Glazer, AM; Hahn, T.; Senechal, M.; Shoemaker, DP; Wondratschek, H.; Wilson, AJC; Abrahams, SC (1992-09-01). 「対称要素と対称操作の記号．対称性の命名法に関するIUCr特別委員会最終報告書」. Acta Crystallographica Section A. 48 ( 5): 727– 732. Bibcode :1992AcCrA..48..727D. doi : 10.1107/s0108767392003428 . ISSN  0108-7673.
2. Bradley, CJ; Cracknell, AP (2010).固体における対称性の数学的理論：点群と空間群の表現論. Oxford New York: Clarendon Press. pp.  127– 134. ISBN 978-0-19-958258-7. OCLC  859155300。

外部リンク

• 国際結晶学連合
• 点群とブラヴェ格子
• 230個の結晶学的空間群の完全なリスト
• Conwayらによるフィブリフォールド表記法

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