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。

  • a {\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 b {\displaystyle b} c {\displaystyle c}
  • n {\displaystyle n} : この面の対角線の半分に沿って移動する
  • d {\displaystyle d} : 面の対角線の4分の1に沿って移動する滑空面
  • e {\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。 360 ∘ n {\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。 n m {\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] Γ x y {\displaystyle \Gamma _{x}^{y}} x ∈ { t , m , o , q , r h , h , c } {\displaystyle x\in \{t,m,o,q,rh,h,c\}} y ∈ { ∅ , b , v , f } {\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。 4 m 2 m 2 m {\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} P 4 m 2 m 2 m {\displaystyle P{\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} I 4 m 2 m 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。 4 m 2 m 2 m {\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} P 4 m 2 c 2 c {\displaystyle P{\tfrac {4}{m}}{\tfrac {2}{c}}{\tfrac {2}{c}}} P 4 n 2 b 2 m {\displaystyle P{\tfrac {4}{n}}{\tfrac {2}{b}}{\tfrac {2}{m}}} P 4 n 2 n 2 c {\displaystyle P{\tfrac {4}{n}}{\tfrac {2}{n}}{\tfrac {2}{c}}} I 4 m 2 c 2 m {\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。 4 m 2 m 2 m {\displaystyle {\tfrac {4}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}} P 4 m 2 1 b 2 m {\displaystyle P{\tfrac {4}{m}}{\tfrac {2_{1}}{b}}{\tfrac {2}{m}}} P 4 2 m 2 m 2 c {\displaystyle P{\tfrac {4_{2}}{m}}{\tfrac {2}{m}}{\tfrac {2}{c}}} I 4 1 a 2 c 2 d {\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 1 {\displaystyle 1} P1 P1 Γ t C 1 1 {\displaystyle \Gamma _{t}C_{1}^{1}} 1秒 ( a / b / c ) ⋅ 1 {\displaystyle (a/b/c)\cdot 1} ( ∘ ) {\displaystyle (\circ )}
2 1 × {\displaystyle \times } P1​ P1​ Γ t C i 1 {\displaystyle \Gamma _{t}C_{i}^{1}} 2秒 ( a / b / c ) ⋅ 2 ~ {\displaystyle (a/b/c)\cdot {\tilde {2}}} ( 2222 ) {\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 22 {\displaystyle 22} P2 P 1 2 1 P 1 1 2 Γ m C 2 1 {\displaystyle \Gamma _{m}C_{2}^{1}} 3秒 ( b : ( c / a ) ) : 2 {\displaystyle (b:(c/a)):2} ( 2 0 2 0 2 0 2 0 ) {\displaystyle (2_{0}2_{0}2_{0}2_{0})} ( ∗ 0 ∗ 0 ) {\displaystyle ({*}_{0}{*}_{0})}
4 P2 1 P 1 2 1 1 P 1 1 2 1 Γ m C 2 2 {\displaystyle \Gamma _{m}C_{2}^{2}} 1a ( b : ( c / a ) ) : 2 1 {\displaystyle (b:(c/a)):2_{1}} ( 2 1 2 1 2 1 2 1 ) {\displaystyle (2_{1}2_{1}2_{1}2_{1})} ( × ¯ × ¯ ) {\displaystyle ({\bar {\times }}{\bar {\times }})}
5 C2 C 1 2 1 B 1 1 2 Γ m b C 2 3 {\displaystyle \Gamma _{m}^{b}C_{2}^{3}} 4秒 ( a + b 2 / b : ( c / a ) ) : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right):2} ( 2 0 2 0 2 1 2 1 ) {\displaystyle (2_{0}2_{0}2_{1}2_{1})} ( ∗ 1 ∗ 1 ) {\displaystyle ({*}_{1}{*}_{1})} 、 ( ∗ × ¯ ) {\displaystyle ({*}{\bar {\times }})}
6 メートル ∗ {\displaystyle *} 午後 P 1 m 1 P 1 1メートル Γ m C s 1 {\displaystyle \Gamma _{m}C_{s}^{1}} 5秒 ( b : ( c / a ) ) ⋅ m {\displaystyle (b:(c/a))\cdot m} [ ∘ 0 ] {\displaystyle [\circ _{0}]} ( ∗ ⋅ ∗ ⋅ ) {\displaystyle ({*}{\cdot }{*}{\cdot })}
7 パソコン P 1 c 1 P 1 1 b Γ m C s 2 {\displaystyle \Gamma _{m}C_{s}^{2}} 1時間 ( b : ( c / a ) ) ⋅ c ~ {\displaystyle (b:(c/a))\cdot {\tilde {c}}} ( ∘ ¯ 0 ) {\displaystyle ({\bar {\circ }}_{0})} ( ∗ : ∗ : ) {\displaystyle ({*}{:}{*}{:})} 、 ( × × 0 ) {\displaystyle ({\times }{\times }_{0})}
8 Cm C 1 m 1 B 1 1メートル Γ m b C s 3 {\displaystyle \Gamma _{m}^{b}C_{s}^{3}} 6秒 ( a + b 2 / b : ( c / a ) ) ⋅ m {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m} [ ∘ 1 ] {\displaystyle [\circ _{1}]} ( ∗ ⋅ ∗ : ) {\displaystyle ({*}{\cdot }{*}{:})} 、 ( ∗ ⋅ × ) {\displaystyle ({*}{\cdot }{\times })}
9 CC C 1 c 1 B 1 1 b Γ m b C s 4 {\displaystyle \Gamma _{m}^{b}C_{s}^{4}} 2時間 ( a + b 2 / b : ( c / a ) ) ⋅ c ~ {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}} ( ∘ ¯ 1 ) {\displaystyle ({\bar {\circ }}_{1})} ( ∗ : × ) {\displaystyle ({*}{:}{\times })} 、 ( × × 1 ) {\displaystyle ({\times }{\times }_{1})}
10 2/m 2 ∗ {\displaystyle 2*} P2/m P 1 2/m 1 P 1 1 2/m Γ m C 2 h 1 {\displaystyle \Gamma _{m}C_{2h}^{1}} 7秒 ( b : ( c / a ) ) ⋅ m : 2 {\displaystyle (b:(c/a))\cdot m:2} [ 2 0 2 0 2 0 2 0 ] {\displaystyle [2_{0}2_{0}2_{0}2_{0}]} ( ∗ 2 ⋅ 22 ⋅ 2 ) {\displaystyle (*2{\cdot }22{\cdot }2)}
11 P2 1 /m P 1 2 1 /m 1 P 1 1 2 1 /m Γ m C 2 h 2 {\displaystyle \Gamma _{m}C_{2h}^{2}} 2a ( b : ( c / a ) ) ⋅ m : 2 1 {\displaystyle (b:(c/a))\cdot m:2_{1}} [ 2 1 2 1 2 1 2 1 ] {\displaystyle [2_{1}2_{1}2_{1}2_{1}]} ( 22 ∗ ⋅ ) {\displaystyle (22{*}{\cdot })}
12 C2/m C 1 2/m 1 B 1 1 2/m Γ m b C 2 h 3 {\displaystyle \Gamma _{m}^{b}C_{2h}^{3}} 8秒 ( a + b 2 / b : ( c / a ) ) ⋅ m : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m:2} [ 2 0 2 0 2 1 2 1 ] {\displaystyle [2_{0}2_{0}2_{1}2_{1}]} ( ∗ 2 ⋅ 22 : 2 ) {\displaystyle (*2{\cdot }22{:}2)} 、 ( 2 ∗ ¯ 2 ⋅ 2 ) {\displaystyle (2{\bar {*}}2{\cdot }2)}
13 P2/c P 1 2/c 1 P 1 1 2/b Γ m C 2 h 4 {\displaystyle \Gamma _{m}C_{2h}^{4}} 3時間 ( b : ( c / a ) ) ⋅ c ~ : 2 {\displaystyle (b:(c/a))\cdot {\tilde {c}}:2} ( 2 0 2 0 22 ) {\displaystyle (2_{0}2_{0}22)} ( ∗ 2 : 22 : 2 ) {\displaystyle (*2{:}22{:}2)} 、 ( 22 ∗ 0 ) {\displaystyle (22{*}_{0})}
14 P2 1 /c P 1 2 1 /c 1 P 1 1 2 1 /b Γ m C 2 h 5 {\displaystyle \Gamma _{m}C_{2h}^{5}} 3a ( b : ( c / a ) ) ⋅ c ~ : 2 1 {\displaystyle (b:(c/a))\cdot {\tilde {c}}:2_{1}} ( 2 1 2 1 22 ) {\displaystyle (2_{1}2_{1}22)} ( 22 ∗ : ) {\displaystyle (22{*}{:})} 、 ( 22 × ) {\displaystyle (22{\times })}
15 C2/c C 1 2/c 1 B 1 1 2/b Γ m b C 2 h 6 {\displaystyle \Gamma _{m}^{b}C_{2h}^{6}} 4時間 ( a + b 2 / b : ( c / a ) ) ⋅ c ~ : 2 {\displaystyle \left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}:2} ( 2 0 2 1 22 ) {\displaystyle (2_{0}2_{1}22)} ( 2 ∗ ¯ 2 : 2 ) {\displaystyle (2{\bar {*}}2{:}2)} 、 ( 22 ∗ 1 ) {\displaystyle (22{*}_{1})}

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

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

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 33 {\displaystyle 33} P3 P3 Γ h C 3 1 {\displaystyle \Gamma _{h}C_{3}^{1}} 38秒 ( c : ( a / a ) ) : 3 {\displaystyle (c:(a/a)):3} ( 3 0 3 0 3 0 ) {\displaystyle (3_{0}3_{0}3_{0})}
144 P3 1 P 3 1 Γ h C 3 2 {\displaystyle \Gamma _{h}C_{3}^{2}} 68a ( c : ( a / a ) ) : 3 1 {\displaystyle (c:(a/a)):3_{1}} ( 3 1 3 1 3 1 ) {\displaystyle (3_{1}3_{1}3_{1})}
145 P3 2 P 3 2 Γ h C 3 3 {\displaystyle \Gamma _{h}C_{3}^{3}} 69a ( c : ( a / a ) ) : 3 2 {\displaystyle (c:(a/a)):3_{2}} ( 3 1 3 1 3 1 ) {\displaystyle (3_{1}3_{1}3_{1})}
146 R3 R3 Γ r h C 3 4 {\displaystyle \Gamma _{rh}C_{3}^{4}} 39秒 ( a / a / a ) / 3 {\displaystyle (a/a/a)/3} ( 3 0 3 1 3 2 ) {\displaystyle (3_{0}3_{1}3_{2})}
147 3 3 × {\displaystyle 3\times } P3​ P3​ Γ h C 3 i 1 {\displaystyle \Gamma _{h}C_{3i}^{1}} 51秒 ( c : ( a / a ) ) : 6 ~ {\displaystyle (c:(a/a)):{\tilde {6}}} ( 63 0 2 ) {\displaystyle (63_{0}2)}
148 R3​ R3​ Γ r h C 3 i 2 {\displaystyle \Gamma _{rh}C_{3i}^{2}} 52秒 ( a / a / a ) / 6 ~ {\displaystyle (a/a/a)/{\tilde {6}}} ( 63 1 2 ) {\displaystyle (63_{1}2)}
149 32 223 {\displaystyle 223} P312 P 3 1 2 Γ h D 3 1 {\displaystyle \Gamma _{h}D_{3}^{1}} 45秒 ( c : ( a / a ) ) : 2 : 3 {\displaystyle (c:(a/a)):2:3} ( ∗ 3 0 3 0 3 0 ) {\displaystyle (*3_{0}3_{0}3_{0})}
150 P321 P 3 2 1 Γ h D 3 2 {\displaystyle \Gamma _{h}D_{3}^{2}} 44秒 ( c : ( a / a ) ) ⋅ 2 : 3 {\displaystyle (c:(a/a))\cdot 2:3} ( 3 0 ∗ 3 0 ) {\displaystyle (3_{0}{*}3_{0})}
151 P3 1 12 P 3 1 1 2 Γ h D 3 3 {\displaystyle \Gamma _{h}D_{3}^{3}} 72a ( c : ( a / a ) ) : 2 : 3 1 {\displaystyle (c:(a/a)):2:3_{1}} ( ∗ 3 1 3 1 3 1 ) {\displaystyle (*3_{1}3_{1}3_{1})}
152 P3 1 21 P 3 1 2 1 Γ h D 3 4 {\displaystyle \Gamma _{h}D_{3}^{4}} 70a ( c : ( a / a ) ) ⋅ 2 : 3 1 {\displaystyle (c:(a/a))\cdot 2:3_{1}} ( 3 1 ∗ 3 1 ) {\displaystyle (3_{1}{*}3_{1})}
153 P3 2 12 P 3 2 1 2 Γ h D 3 5 {\displaystyle \Gamma _{h}D_{3}^{5}} 73a ( c : ( a / a ) ) : 2 : 3 2 {\displaystyle (c:(a/a)):2:3_{2}} ( ∗ 3 1 3 1 3 1 ) {\displaystyle (*3_{1}3_{1}3_{1})}
154 P3 2 21 P 3 2 2 1 Γ h D 3 6 {\displaystyle \Gamma _{h}D_{3}^{6}} 71a ( c : ( a / a ) ) ⋅ 2 : 3 2 {\displaystyle (c:(a/a))\cdot 2:3_{2}} ( 3 1 ∗ 3 1 ) {\displaystyle (3_{1}{*}3_{1})}
155 R32 R 3 2 Γ r h D 3 7 {\displaystyle \Gamma _{rh}D_{3}^{7}} 46秒 ( a / a / a ) / 3 : 2 {\displaystyle (a/a/a)/3:2} ( ∗ 3 0 3 1 3 2 ) {\displaystyle (*3_{0}3_{1}3_{2})}
156 3メートル ∗ 33 {\displaystyle *33} P3m1 P 3 m 1 Γ h C 3 v 1 {\displaystyle \Gamma _{h}C_{3v}^{1}} 40代 ( c : ( a / a ) ) : m ⋅ 3 {\displaystyle (c:(a/a)):m\cdot 3} ( ∗ ⋅ 3 ⋅ 3 ⋅ 3 ) {\displaystyle (*{\cdot }3{\cdot }3{\cdot }3)}
157 3100万ペソ P 3 1メートル Γ h C 3 v 2 {\displaystyle \Gamma _{h}C_{3v}^{2}} 41秒 ( c : ( a / a ) ) ⋅ m ⋅ 3 {\displaystyle (c:(a/a))\cdot m\cdot 3} ( 3 0 ∗ ⋅ 3 ) {\displaystyle (3_{0}{*}{\cdot }3)}
158 P3c1 P 3 c 1 Γ h C 3 v 3 {\displaystyle \Gamma _{h}C_{3v}^{3}} 39時間 ( c : ( a / a ) ) : c ~ : 3 {\displaystyle (c:(a/a)):{\tilde {c}}:3} ( ∗ : 3 : 3 : 3 ) {\displaystyle (*{:}3{:}3{:}3)}
159 P31c P 3 1 秒 Γ h C 3 v 4 {\displaystyle \Gamma _{h}C_{3v}^{4}} 40時間 ( c : ( a / a ) ) ⋅ c ~ : 3 {\displaystyle (c:(a/a))\cdot {\tilde {c}}:3} ( 3 0 ∗ : 3 ) {\displaystyle (3_{0}{*}{:}3)}
160 300万ランド R 3メートル Γ r h C 3 v 5 {\displaystyle \Gamma _{rh}C_{3v}^{5}} 42秒 ( a / a / a ) / 3 ⋅ m {\displaystyle (a/a/a)/3\cdot m} ( 3 1 ∗ ⋅ 3 ) {\displaystyle (3_{1}{*}{\cdot }3)}
161 R3c R 3 c Γ r h C 3 v 6 {\displaystyle \Gamma _{rh}C_{3v}^{6}} 41時間 ( a / a / a ) / 3 ⋅ c ~ {\displaystyle (a/a/a)/3\cdot {\tilde {c}}} ( 3 1 ∗ : 3 ) {\displaystyle (3_{1}{*}{:}3)}
162 3 2/m 2 ∗ 3 {\displaystyle 2{*}3} P 3 1m P 3 1 2/m Γ h D 3 d 1 {\displaystyle \Gamma _{h}D_{3d}^{1}} 56秒 ( c : ( a / a ) ) ⋅ m ⋅ 6 ~ {\displaystyle (c:(a/a))\cdot m\cdot {\tilde {6}}} ( ∗ ⋅ 63 0 2 ) {\displaystyle (*{\cdot }63_{0}2)}
163 P 3 1c P 3 1 2/c Γ h D 3 d 2 {\displaystyle \Gamma _{h}D_{3d}^{2}} 46時間 ( c : ( a / a ) ) ⋅ c ~ ⋅ 6 ~ {\displaystyle (c:(a/a))\cdot {\tilde {c}}\cdot {\tilde {6}}} ( ∗ : 63 0 2 ) {\displaystyle (*{:}63_{0}2)}
164 P 3 m1 P 3 2/m 1 Γ h D 3 d 3 {\displaystyle \Gamma _{h}D_{3d}^{3}} 55秒 ( c : ( a / a ) ) : m ⋅ 6 ~ {\displaystyle (c:(a/a)):m\cdot {\tilde {6}}} ( ∗ 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*6{\cdot }3{\cdot }2)}
165 P 3 c1 P 3 2/c 1 Γ h D 3 d 4 {\displaystyle \Gamma _{h}D_{3d}^{4}} 45時間 ( c : ( a / a ) ) : c ~ ⋅ 6 ~ {\displaystyle (c:(a/a)):{\tilde {c}}\cdot {\tilde {6}}} ( ∗ 6 : 3 : 2 ) {\displaystyle (*6{:}3{:}2)}
166 R 3メートル R 3 2/m Γ r h D 3 d 5 {\displaystyle \Gamma _{rh}D_{3d}^{5}} 57秒 ( a / a / a ) / 6 ~ ⋅ m {\displaystyle (a/a/a)/{\tilde {6}}\cdot m} ( ∗ ⋅ 63 1 2 ) {\displaystyle (*{\cdot }63_{1}2)}
167 R 3 c R 3 2/c Γ r h D 3 d 6 {\displaystyle \Gamma _{rh}D_{3d}^{6}} 47時間 ( a / a / a ) / 6 ~ ⋅ c ~ {\displaystyle (a/a/a)/{\tilde {6}}\cdot {\tilde {c}}} ( ∗ : 63 1 2 ) {\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 66 {\displaystyle 66} P6 P6 Γ h C 6 1 {\displaystyle \Gamma _{h}C_{6}^{1}} 49秒 ( c : ( a / a ) ) : 6 {\displaystyle (c:(a/a)):6} ( 6 0 3 0 2 0 ) {\displaystyle (6_{0}3_{0}2_{0})}
169 P6 1 P 6 1 Γ h C 6 2 {\displaystyle \Gamma _{h}C_{6}^{2}} 74a ( c : ( a / a ) ) : 6 1 {\displaystyle (c:(a/a)):6_{1}} ( 6 1 3 1 2 1 ) {\displaystyle (6_{1}3_{1}2_{1})}
170 P6 5 P 6 5 Γ h C 6 3 {\displaystyle \Gamma _{h}C_{6}^{3}} 75a ( c : ( a / a ) ) : 6 5 {\displaystyle (c:(a/a)):6_{5}} ( 6 1 3 1 2 1 ) {\displaystyle (6_{1}3_{1}2_{1})}
171 P6 2 P 6 2 Γ h C 6 4 {\displaystyle \Gamma _{h}C_{6}^{4}} 76a ( c : ( a / a ) ) : 6 2 {\displaystyle (c:(a/a)):6_{2}} ( 6 2 3 2 2 0 ) {\displaystyle (6_{2}3_{2}2_{0})}
172 P6 4 P 6 4 Γ h C 6 5 {\displaystyle \Gamma _{h}C_{6}^{5}} 77a ( c : ( a / a ) ) : 6 4 {\displaystyle (c:(a/a)):6_{4}} ( 6 2 3 2 2 0 ) {\displaystyle (6_{2}3_{2}2_{0})}
173 P6 3 P 6 3 Γ h C 6 6 {\displaystyle \Gamma _{h}C_{6}^{6}} 78a ( c : ( a / a ) ) : 6 3 {\displaystyle (c:(a/a)):6_{3}} ( 6 3 3 0 2 1 ) {\displaystyle (6_{3}3_{0}2_{1})}
174 6 3 ∗ {\displaystyle 3*} P6​ P6​ Γ h C 3 h 1 {\displaystyle \Gamma _{h}C_{3h}^{1}} 43秒 ( c : ( a / a ) ) : 3 : m {\displaystyle (c:(a/a)):3:m} [ 3 0 3 0 3 0 ] {\displaystyle [3_{0}3_{0}3_{0}]}
175 6/月 6 ∗ {\displaystyle 6*} P6/m P 6/m Γ h C 6 h 1 {\displaystyle \Gamma _{h}C_{6h}^{1}} 53秒 ( c : ( a / a ) ) ⋅ m : 6 {\displaystyle (c:(a/a))\cdot m:6} [ 6 0 3 0 2 0 ] {\displaystyle [6_{0}3_{0}2_{0}]}
176 P6 3 /m P 6 3 /m Γ h C 6 h 2 {\displaystyle \Gamma _{h}C_{6h}^{2}} 81a ( c : ( a / a ) ) ⋅ m : 6 3 {\displaystyle (c:(a/a))\cdot m:6_{3}} [ 6 3 3 0 2 1 ] {\displaystyle [6_{3}3_{0}2_{1}]}
177 622 226 {\displaystyle 226} P622 P 6 2 2 Γ h D 6 1 {\displaystyle \Gamma _{h}D_{6}^{1}} 54秒 ( c : ( a / a ) ) ⋅ 2 : 6 {\displaystyle (c:(a/a))\cdot 2:6} ( ∗ 6 0 3 0 2 0 ) {\displaystyle (*6_{0}3_{0}2_{0})}
178 P6 1 22 P 6 1 2 2 Γ h D 6 2 {\displaystyle \Gamma _{h}D_{6}^{2}} 82a ( c : ( a / a ) ) ⋅ 2 : 6 1 {\displaystyle (c:(a/a))\cdot 2:6_{1}} ( ∗ 6 1 3 1 2 1 ) {\displaystyle (*6_{1}3_{1}2_{1})}
179 P6 5 22 P 6 5 2 2 Γ h D 6 3 {\displaystyle \Gamma _{h}D_{6}^{3}} 83a ( c : ( a / a ) ) ⋅ 2 : 6 5 {\displaystyle (c:(a/a))\cdot 2:6_{5}} ( ∗ 6 1 3 1 2 1 ) {\displaystyle (*6_{1}3_{1}2_{1})}
180 P6 2 22 P 6 2 2 2 Γ h D 6 4 {\displaystyle \Gamma _{h}D_{6}^{4}} 84a ( c : ( a / a ) ) ⋅ 2 : 6 2 {\displaystyle (c:(a/a))\cdot 2:6_{2}} ( ∗ 6 2 3 2 2 0 ) {\displaystyle (*6_{2}3_{2}2_{0})}
181 P6 4 22 P 6 4 2 2 Γ h D 6 5 {\displaystyle \Gamma _{h}D_{6}^{5}} 85a ( c : ( a / a ) ) ⋅ 2 : 6 4 {\displaystyle (c:(a/a))\cdot 2:6_{4}} ( ∗ 6 2 3 2 2 0 ) {\displaystyle (*6_{2}3_{2}2_{0})}
182 P6 3 22 P 6 3 2 2 Γ h D 6 6 {\displaystyle \Gamma _{h}D_{6}^{6}} 86a ( c : ( a / a ) ) ⋅ 2 : 6 3 {\displaystyle (c:(a/a))\cdot 2:6_{3}} ( ∗ 6 3 3 0 2 1 ) {\displaystyle (*6_{3}3_{0}2_{1})}
183 6mm ∗ 66 {\displaystyle *66} P6mm P 6mm Γ h C 6 v 1 {\displaystyle \Gamma _{h}C_{6v}^{1}} 50代 ( c : ( a / a ) ) : m ⋅ 6 {\displaystyle (c:(a/a)):m\cdot 6} ( ∗ ⋅ 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*{\cdot }6{\cdot }3{\cdot }2)}
184 P6cc P 6 cc Γ h C 6 v 2 {\displaystyle \Gamma _{h}C_{6v}^{2}} 44時間 ( c : ( a / a ) ) : c ~ ⋅ 6 {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6} ( ∗ : 6 : 3 : 2 ) {\displaystyle (*{:}6{:}3{:}2)}
185 P6 3cm​ P 6 3 cm Γ h C 6 v 3 {\displaystyle \Gamma _{h}C_{6v}^{3}} 80a ( c : ( a / a ) ) : c ~ ⋅ 6 3 {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 6_{3}} ( ∗ ⋅ 6 : 3 : 2 ) {\displaystyle (*{\cdot }6{:}3{:}2)}
186 P6 3 mc P 6 3 mc Γ h C 6 v 4 {\displaystyle \Gamma _{h}C_{6v}^{4}} 79a ( c : ( a / a ) ) : m ⋅ 6 3 {\displaystyle (c:(a/a)):m\cdot 6_{3}} ( ∗ : 6 ⋅ 3 ⋅ 2 ) {\displaystyle (*{:}6{\cdot }3{\cdot }2)}
187 6平方メートル ∗ 223 {\displaystyle *223} P 6平方メートル P 6 m 2 Γ h D 3 h 1 {\displaystyle \Gamma _{h}D_{3h}^{1}} 48秒 ( c : ( a / a ) ) : m ⋅ 3 : m {\displaystyle (c:(a/a)):m\cdot 3:m} [ ∗ ⋅ 3 ⋅ 3 ⋅ 3 ] {\displaystyle [*{\cdot }3{\cdot }3{\cdot }3]}
188 P 6 c2 P 6 c 2 Γ h D 3 h 2 {\displaystyle \Gamma _{h}D_{3h}^{2}} 43時間 ( c : ( a / a ) ) : c ~ ⋅ 3 : m {\displaystyle (c:(a/a)):{\tilde {c}}\cdot 3:m} [ ∗ : 3 : 3 : 3 ] {\displaystyle [*{:}3{:}3{:}3]}
189 P 6 2m P 6 2メートル Γ h D 3 h 3 {\displaystyle \Gamma _{h}D_{3h}^{3}} 47秒 ( c : ( a / a ) ) ⋅ m : 3 ⋅ m {\displaystyle (c:(a/a))\cdot m:3\cdot m} [ 3 0 ∗ ⋅ 3 ] {\displaystyle [3_{0}{*}{\cdot }3]}
190 P 6 2c P 6 2c Γ h D 3 h 4 {\displaystyle \Gamma _{h}D_{3h}^{4}} 42時間 ( c : ( a / a ) ) ⋅ m : 3 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:3\cdot {\tilde {c}}} [ 3 0 ∗ : 3 ] {\displaystyle [3_{0}{*}{:}3]}
191 6/m 2/m 2/m ∗ 226 {\displaystyle *226} P6/mmm P 6/m 2/m 2/m Γ h D 6 h 1 {\displaystyle \Gamma _{h}D_{6h}^{1}} 58秒 ( c : ( a / a ) ) ⋅ m : 6 ⋅ m {\displaystyle (c:(a/a))\cdot m:6\cdot m} [ ∗ ⋅ 6 ⋅ 3 ⋅ 2 ] {\displaystyle [*{\cdot }6{\cdot }3{\cdot }2]}
192 P6/mcc P 6/m 2/c 2/c Γ h D 6 h 2 {\displaystyle \Gamma _{h}D_{6h}^{2}} 48時間 ( c : ( a / a ) ) ⋅ m : 6 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:6\cdot {\tilde {c}}} [ ∗ : 6 : 3 : 2 ] {\displaystyle [*{:}6{:}3{:}2]}
193 P6 3 /mcm P 6 3 /m 2/c 2/m Γ h D 6 h 3 {\displaystyle \Gamma _{h}D_{6h}^{3}} 87a ( c : ( a / a ) ) ⋅ m : 6 3 ⋅ c ~ {\displaystyle (c:(a/a))\cdot m:6_{3}\cdot {\tilde {c}}} [ ∗ ⋅ 6 : 3 : 2 ] {\displaystyle [*{\cdot }6{:}3{:}2]}
194 P6 3 /mmc P 6 3 /m 2/m 2/c Γ h D 6 h 4 {\displaystyle \Gamma _{h}D_{6h}^{4}} 88a ( c : ( a / a ) ) ⋅ m : 6 3 ⋅ m {\displaystyle (c:(a/a))\cdot m:6_{3}\cdot m} [ ∗ : 6 ⋅ 3 ⋅ 2 ] {\displaystyle [*{:}6{\cdot }3{\cdot }2]}

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

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] e {\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。
ウィキメディア コモンズには、宇宙群に関連するメディアがあります。
  • 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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