Differences

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--- physics_chemistry:point_groups:oh [2018/03/21 18:47] – created Stefano Agrestini
+++ physics_chemistry:point_groups:oh [2018/03/23 00:38] – Maurits W. Haverkort
@@ Line 1: / Line 1: @@
-====== Oh ======
+====== Point Group Oh ======
+===== Character Table =====
 ###
-alligned paragraph text
+|  $  $  ^  $ \text{E} \,{\text{(1)}} $  ^  $ C_3 \,{\text{(8)}} $  ^  $ C_2 \,{\text{(6)}} $  ^  $ C_4 \,{\text{(6)}} $  ^  $ C_2 \,{\text{(3)}} $  ^  $ \text{i} \,{\text{(1)}} $  ^  $ S_4 \,{\text{(6)}} $  ^  $ S_6 \,{\text{(8)}} $  ^  $ \sigma_h \,{\text{(3)}} $  ^  $ \sigma_d \,{\text{(6)}} $  ^
+^ $ A_{1g} $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |
+^ $ A_{2g} $ |  $ 1 $ |  $ 1 $ |  $ -1 $ |  $ -1 $ |  $ 1 $ |  $ 1 $ |  $ -1 $ |  $ 1 $ |  $ 1 $ |  $ -1 $ |
+^ $ E_g $ |  $ 2 $ |  $ -1 $ |  $ 0 $ |  $ 0 $ |  $ 2 $ |  $ 2 $ |  $ 0 $ |  $ -1 $ |  $ 2 $ |  $ 0 $ |
+^ $ T_{1g} $ |  $ 3 $ |  $ 0 $ |  $ -1 $ |  $ 1 $ |  $ -1 $ |  $ 3 $ |  $ 1 $ |  $ 0 $ |  $ -1 $ |  $ -1 $ |
+^ $ T_{2g} $ |  $ 3 $ |  $ 0 $ |  $ 1 $ |  $ -1 $ |  $ -1 $ |  $ 3 $ |  $ -1 $ |  $ 0 $ |  $ -1 $ |  $ 1 $ |
+^ $ A_{1u} $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ 1 $ |  $ -1 $ |  $ -1 $ |  $ -1 $ |  $ -1 $ |  $ -1 $ |
+^ $ A_{2u} $ |  $ 1 $ |  $ 1 $ |  $ -1 $ |  $ -1 $ |  $ 1 $ |  $ -1 $ |  $ 1 $ |  $ -1 $ |  $ -1 $ |  $ 1 $ |
+^ $ E_u $ |  $ 2 $ |  $ -1 $ |  $ 0 $ |  $ 0 $ |  $ 2 $ |  $ -2 $ |  $ 0 $ |  $ 1 $ |  $ -2 $ |  $ 0 $ |
+^ $ T_{1u} $ |  $ 3 $ |  $ 0 $ |  $ -1 $ |  $ 1 $ |  $ -1 $ |  $ -3 $ |  $ -1 $ |  $ 0 $ |  $ 1 $ |  $ 1 $ |
+^ $ T_{2u} $ |  $ 3 $ |  $ 0 $ |  $ 1 $ |  $ -1 $ |  $ -1 $ |  $ -3 $ |  $ 1 $ |  $ 0 $ |  $ 1 $ |  $ -1 $ |
 ###
-===== Example =====
+===== Product Table =====
 ###
-description text
+|  $  $  ^  $ A_{1g} $  ^  $ A_{2g} $  ^  $ E_g $  ^  $ T_{1g} $  ^  $ T_{2g} $  ^  $ A_{1u} $  ^  $ A_{2u} $  ^  $ E_u $  ^  $ T_{1u} $  ^  $ T_{2u} $  ^
+^ $ A_{1g} $  | $ A_{1g} $  | $ A_{2g} $  | $ E_g $  | $ T_{1g} $  | $ T_{2g} $  | $ A_{1u} $  | $ A_{2u} $  | $ E_u $  | $ T_{1u} $  | $ T_{2u} $  |
+^ $ A_{2g} $  | $ A_{2g} $  | $ A_{1g} $  | $ E_g $  | $ T_{2g} $  | $ T_{1g} $  | $ A_{2u} $  | $ A_{1u} $  | $ E_u $  | $ T_{2u} $  | $ T_{1u} $  |
+^ $ E_g $  | $ E_g $  | $ E_g $  | $ A_{1g}+A_{2g}+E_g $  | $ T_{1g}+T_{2g} $  | $ T_{1g}+T_{2g} $  | $ E_u $  | $ E_u $  | $ A_{1u}+A_{2u}+E_u $  | $ T_{1u}+T_{2u} $  | $ T_{1u}+T_{2u} $  |
+^ $ T_{1g} $  | $ T_{1g} $  | $ T_{2g} $  | $ T_{1g}+T_{2g} $  | $ A_{1g}+E_g+T_{1g}+T_{2g} $  | $ A_{2g}+E_g+T_{1g}+T_{2g} $  | $ T_{1u} $  | $ T_{2u} $  | $ T_{1u}+T_{2u} $  | $ A_{1u}+E_u+T_{1u}+T_{2u} $  | $ A_{2u}+E_u+T_{1u}+T_{2u} $  |
+^ $ T_{2g} $  | $ T_{2g} $  | $ T_{1g} $  | $ T_{1g}+T_{2g} $  | $ A_{2g}+E_g+T_{1g}+T_{2g} $  | $ A_{1g}+E_g+T_{1g}+T_{2g} $  | $ T_{2u} $  | $ T_{1u} $  | $ T_{1u}+T_{2u} $  | $ A_{2u}+E_u+T_{1u}+T_{2u} $  | $ A_{1u}+E_u+T_{1u}+T_{2u} $  |
+^ $ A_{1u} $  | $ A_{1u} $  | $ A_{2u} $  | $ E_u $  | $ T_{1u} $  | $ T_{2u} $  | $ A_{1g} $  | $ A_{2g} $  | $ E_g $  | $ T_{1g} $  | $ T_{2g} $  |
+^ $ A_{2u} $  | $ A_{2u} $  | $ A_{1u} $  | $ E_u $  | $ T_{2u} $  | $ T_{1u} $  | $ A_{2g} $  | $ A_{1g} $  | $ E_g $  | $ T_{2g} $  | $ T_{1g} $  |
+^ $ E_u $  | $ E_u $  | $ E_u $  | $ A_{1u}+A_{2u}+E_u $  | $ T_{1u}+T_{2u} $  | $ T_{1u}+T_{2u} $  | $ E_g $  | $ E_g $  | $ A_{1g}+A_{2g}+E_g $  | $ T_{1g}+T_{2g} $  | $ T_{1g}+T_{2g} $  |
+^ $ T_{1u} $  | $ T_{1u} $  | $ T_{2u} $  | $ T_{1u}+T_{2u} $  | $ A_{1u}+E_u+T_{1u}+T_{2u} $  | $ A_{2u}+E_u+T_{1u}+T_{2u} $  | $ T_{1g} $  | $ T_{2g} $  | $ T_{1g}+T_{2g} $  | $ A_{1g}+E_g+T_{1g}+T_{2g} $  | $ A_{2g}+E_g+T_{1g}+T_{2g} $  |
+^ $ T_{2u} $  | $ T_{2u} $  | $ T_{1u} $  | $ T_{1u}+T_{2u} $  | $ A_{2u}+E_u+T_{1u}+T_{2u} $  | $ A_{1u}+E_u+T_{1u}+T_{2u} $  | $ T_{2g} $  | $ T_{1g} $  | $ T_{1g}+T_{2g} $  | $ A_{2g}+E_g+T_{1g}+T_{2g} $  | $ A_{1g}+E_g+T_{1g}+T_{2g} $  |
 ###
-==== Input ====
+===== Implemented Settings =====
-<code Quanty Example.Quanty>
--- some example code
+==== Setting 0sqrt2-1z ====
-</code>
+###
+^ Operator ^ Orientation ^
+^ $\text{E}$ | $\{0,0,0\}$ , |
+^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{-\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{0,-\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{-\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{0,\frac{2 \sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , |
+^ $C_2$ | $\left\{-\sqrt{2},0,0\right\}$ , $\left\{-\sqrt{2},-\sqrt{6},0\right\}$ , $\left\{-\sqrt{2},\sqrt{6},0\right\}$ , $\left\{0,-\sqrt{2},-2\right\}$ , $\left\{-\sqrt{6},-\sqrt{2},4\right\}$ , $\left\{-\sqrt{6},\sqrt{2},-4\right\}$ , |
+^ $C_4$ | $\left\{0,-\sqrt{2},1\right\}$ , $\left\{0,\sqrt{2},-1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},-1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $C_2$ | $\left\{0,-\sqrt{2},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $\text{i}$ | $\{0,0,0\}$ , |
+^ $S_4$ | $\left\{0,-\sqrt{2},1\right\}$ , $\left\{0,\sqrt{2},-1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},-1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $S_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{-\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{0,-\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{-\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{0,\frac{2 \sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , |
+^ $\sigma _h$ | $\left\{0,-\sqrt{2},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $\sigma _d$ | $\left\{-\sqrt{2},0,0\right\}$ , $\left\{-\sqrt{2},-\sqrt{6},0\right\}$ , $\left\{-\sqrt{2},\sqrt{6},0\right\}$ , $\left\{0,-\sqrt{2},-2\right\}$ , $\left\{-\sqrt{6},-\sqrt{2},4\right\}$ , $\left\{-\sqrt{6},\sqrt{2},-4\right\}$ , |
+###
+==== Setting 0sqrt21z ====
+###
+^ Operator ^ Orientation ^
+^ $\text{E}$ | $\{0,0,0\}$ , |
+^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{0,\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{-\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{0,-\frac{2 \sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{-\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , |
+^ $C_2$ | $\left\{\sqrt{2},0,0\right\}$ , $\left\{\sqrt{2},\sqrt{6},0\right\}$ , $\left\{\sqrt{2},-\sqrt{6},0\right\}$ , $\left\{0,\sqrt{2},-2\right\}$ , $\left\{\sqrt{6},\sqrt{2},4\right\}$ , $\left\{\sqrt{6},-\sqrt{2},-4\right\}$ , |
+^ $C_4$ | $\left\{0,\sqrt{2},1\right\}$ , $\left\{0,-\sqrt{2},-1\right\}$ , $\left\{\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},-1\right\}$ , $\left\{\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $C_2$ | $\left\{0,\sqrt{2},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $\text{i}$ | $\{0,0,0\}$ , |
+^ $S_4$ | $\left\{0,\sqrt{2},1\right\}$ , $\left\{0,-\sqrt{2},-1\right\}$ , $\left\{\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},1\right\}$ , $\left\{-\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},-1\right\}$ , $\left\{\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $S_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{0,\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{-\sqrt{\frac{2}{3}},-\frac{\sqrt{2}}{3},-\frac{1}{3}\right\}$ , $\left\{0,-\frac{2 \sqrt{2}}{3},\frac{1}{3}\right\}$ , $\left\{-\sqrt{\frac{2}{3}},\frac{\sqrt{2}}{3},\frac{1}{3}\right\}$ , |
+^ $\sigma _h$ | $\left\{0,\sqrt{2},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},-\frac{1}{\sqrt{2}},1\right\}$ , $\left\{\sqrt{\frac{3}{2}},\frac{1}{\sqrt{2}},-1\right\}$ , |
+^ $\sigma _d$ | $\left\{\sqrt{2},0,0\right\}$ , $\left\{\sqrt{2},\sqrt{6},0\right\}$ , $\left\{\sqrt{2},-\sqrt{6},0\right\}$ , $\left\{0,\sqrt{2},-2\right\}$ , $\left\{\sqrt{6},\sqrt{2},4\right\}$ , $\left\{\sqrt{6},-\sqrt{2},-4\right\}$ , |
+###
+==== Setting 111z ====
+###
+^ Operator ^ Orientation ^
+^ $\text{E}$ | $\{0,0,0\}$ , |
+^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3}\right\}$ , $\left\{\frac{2}{3},\frac{2}{3},-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(\sqrt{3}-1\right),\frac{1}{3} \left(-1-\sqrt{3}\right),-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(-1-\sqrt{3}\right),\frac{1}{3} \left(\sqrt{3}-1\right),-\frac{1}{3}\right\}$ , $\left\{-\frac{2}{3},-\frac{2}{3},\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3}\right\}$ , |
+^ $C_2$ | $\{1,-1,0\}$ , $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$ , $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$ , $\{1,1,-2\}$ , $\left\{1+\sqrt{3},1-\sqrt{3},4\right\}$ , $\left\{\sqrt{3}-1,-1-\sqrt{3},-4\right\}$ , |
+^ $C_4$ | $\{1,1,1\}$ , $\{-1,-1,-1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{-\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2}-\frac{1}{2},1\right\}$ , $\left\{\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{1}{2}+\frac{\sqrt{3}}{2},-1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , |
+^ $C_2$ | $\{1,1,1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , |
+^ $\text{i}$ | $\{0,0,0\}$ , |
+^ $S_4$ | $\{1,1,1\}$ , $\{-1,-1,-1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{-\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2}-\frac{1}{2},1\right\}$ , $\left\{\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{1}{2}+\frac{\sqrt{3}}{2},-1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , |
+^ $S_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3}\right\}$ , $\left\{\frac{2}{3},\frac{2}{3},-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(\sqrt{3}-1\right),\frac{1}{3} \left(-1-\sqrt{3}\right),-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(-1-\sqrt{3}\right),\frac{1}{3} \left(\sqrt{3}-1\right),-\frac{1}{3}\right\}$ , $\left\{-\frac{2}{3},-\frac{2}{3},\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3}\right\}$ , |
+^ $\sigma _h$ | $\{1,1,1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , |
+^ $\sigma _d$ | $\{1,-1,0\}$ , $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$ , $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$ , $\{1,1,-2\}$ , $\left\{1+\sqrt{3},1-\sqrt{3},4\right\}$ , $\left\{\sqrt{3}-1,-1-\sqrt{3},-4\right\}$ , |
+###
+==== Setting sqrt20-1z ====
+###
+^ Operator ^ Orientation ^
+^ $\text{E}$ | $\{0,0,0\}$ , |
+^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{-\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , $\left\{-\frac{2 \sqrt{2}}{3},0,-\frac{1}{3}\right\}$ , $\left\{\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{\frac{2 \sqrt{2}}{3},0,\frac{1}{3}\right\}$ , $\left\{-\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , |
+^ $C_2$ | $\left\{0,\sqrt{2},0\right\}$ , $\left\{-\sqrt{6},\sqrt{2},0\right\}$ , $\left\{\sqrt{6},\sqrt{2},0\right\}$ , $\left\{-\sqrt{2},0,-2\right\}$ , $\left\{-\sqrt{2},\sqrt{6},4\right\}$ , $\left\{\sqrt{2},\sqrt{6},-4\right\}$ , |
+^ $C_4$ | $\left\{-\sqrt{2},0,1\right\}$ , $\left\{\sqrt{2},0,-1\right\}$ , $\left\{\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},1\right\}$ , $\left\{\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},-1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $C_2$ | $\left\{-\sqrt{2},0,1\right\}$ , $\left\{\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $\text{i}$ | $\{0,0,0\}$ , |
+^ $S_4$ | $\left\{-\sqrt{2},0,1\right\}$ , $\left\{\sqrt{2},0,-1\right\}$ , $\left\{\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},1\right\}$ , $\left\{\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},-1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $S_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{-\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , $\left\{-\frac{2 \sqrt{2}}{3},0,-\frac{1}{3}\right\}$ , $\left\{\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{\frac{2 \sqrt{2}}{3},0,\frac{1}{3}\right\}$ , $\left\{-\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , |
+^ $\sigma _h$ | $\left\{-\sqrt{2},0,1\right\}$ , $\left\{\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $\sigma _d$ | $\left\{0,\sqrt{2},0\right\}$ , $\left\{-\sqrt{6},\sqrt{2},0\right\}$ , $\left\{\sqrt{6},\sqrt{2},0\right\}$ , $\left\{-\sqrt{2},0,-2\right\}$ , $\left\{-\sqrt{2},\sqrt{6},4\right\}$ , $\left\{\sqrt{2},\sqrt{6},-4\right\}$ , |
+###
+==== Setting sqrt201z ====
+###
+^ Operator ^ Orientation ^
+^ $\text{E}$ | $\{0,0,0\}$ , |
+^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , $\left\{\frac{2 \sqrt{2}}{3},0,-\frac{1}{3}\right\}$ , $\left\{-\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{-\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{-\frac{2 \sqrt{2}}{3},0,\frac{1}{3}\right\}$ , $\left\{\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , |
+^ $C_2$ | $\left\{0,-\sqrt{2},0\right\}$ , $\left\{\sqrt{6},-\sqrt{2},0\right\}$ , $\left\{-\sqrt{6},-\sqrt{2},0\right\}$ , $\left\{\sqrt{2},0,-2\right\}$ , $\left\{\sqrt{2},-\sqrt{6},4\right\}$ , $\left\{-\sqrt{2},-\sqrt{6},-4\right\}$ , |
+^ $C_4$ | $\left\{\sqrt{2},0,1\right\}$ , $\left\{-\sqrt{2},0,-1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},1\right\}$ , $\left\{\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},-1\right\}$ , $\left\{\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $C_2$ | $\left\{\sqrt{2},0,1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},1\right\}$ , $\left\{\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $\text{i}$ | $\{0,0,0\}$ , |
+^ $S_4$ | $\left\{\sqrt{2},0,1\right\}$ , $\left\{-\sqrt{2},0,-1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},1\right\}$ , $\left\{\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}},-1\right\}$ , $\left\{\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $S_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , $\left\{\frac{2 \sqrt{2}}{3},0,-\frac{1}{3}\right\}$ , $\left\{-\frac{\sqrt{2}}{3},-\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{-\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},-\frac{1}{3}\right\}$ , $\left\{-\frac{2 \sqrt{2}}{3},0,\frac{1}{3}\right\}$ , $\left\{\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},\frac{1}{3}\right\}$ , |
+^ $\sigma _h$ | $\left\{\sqrt{2},0,1\right\}$ , $\left\{-\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},1\right\}$ , $\left\{\frac{1}{\sqrt{2}},-\sqrt{\frac{3}{2}},-1\right\}$ , |
+^ $\sigma _d$ | $\left\{0,-\sqrt{2},0\right\}$ , $\left\{\sqrt{6},-\sqrt{2},0\right\}$ , $\left\{-\sqrt{6},-\sqrt{2},0\right\}$ , $\left\{\sqrt{2},0,-2\right\}$ , $\left\{\sqrt{2},-\sqrt{6},4\right\}$ , $\left\{-\sqrt{2},-\sqrt{6},-4\right\}$ , |
+###
+==== Setting XYZ ====
+###
+^ Operator ^ Orientation ^
+^ $\text{E}$ | $\{0,0,0\}$ , |
+^ $C_3$ | $\{1,1,1\}$ , $\{1,1,-1\}$ , $\{1,-1,1\}$ , $\{-1,1,1\}$ , $\{-1,-1,1\}$ , $\{-1,1,-1\}$ , $\{1,-1,-1\}$ , $\{-1,-1,-1\}$ , |
+^ $C_2$ | $\{1,1,0\}$ , $\{1,-1,0\}$ , $\{1,0,-1\}$ , $\{1,0,1\}$ , $\{0,1,1\}$ , $\{0,1,-1\}$ , |
+^ $C_4$ | $\{0,0,1\}$ , $\{0,1,0\}$ , $\{1,0,0\}$ , $\{0,0,-1\}$ , $\{0,-1,0\}$ , $\{-1,0,0\}$ , |
+^ $C_2$ | $\{0,0,1\}$ , $\{0,1,0\}$ , $\{1,0,0\}$ , |
+^ $\text{i}$ | $\{0,0,0\}$ , |
+^ $S_4$ | $\{0,0,1\}$ , $\{0,1,0\}$ , $\{1,0,0\}$ , $\{0,0,-1\}$ , $\{0,-1,0\}$ , $\{-1,0,0\}$ , |
+^ $S_6$ | $\{1,1,1\}$ , $\{1,1,-1\}$ , $\{1,-1,1\}$ , $\{-1,1,1\}$ , $\{-1,-1,1\}$ , $\{-1,1,-1\}$ , $\{1,-1,-1\}$ , $\{-1,-1,-1\}$ , |
+^ $\sigma _h$ | $\{1,0,0\}$ , $\{0,1,0\}$ , $\{0,0,1\}$ , |
+^ $\sigma _d$ | $\{1,1,0\}$ , $\{1,-1,0\}$ , $\{1,0,-1\}$ , $\{1,0,1\}$ , $\{0,1,1\}$ , $\{0,1,-1\}$ , |
+###
-==== Result ====
-<WRAP center box 100%>
-text produced as output
-</WRAP>
 ===== Table of contents =====
 {{indexmenu>.#2}}

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