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physics_chemistry:point_groups:d5h [2018/04/04 23:31] – created Maurits W. Haverkortphysics_chemistry:point_groups:d5h [2018/04/04 23:43] (current) – Maurits W. Haverkort
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-|    ^  E(1)  ^  C5(2)  ^  C25(2)  ^  $ C_2^'{} \,{\text{(5)}} ^ \sigma_h \,{\text{(1)}} ^ S_5 \,{\text{(2)}} ^ S_5^3{} \,{\text{(2)}} ^ \sigma_v \,{\text{(5)}} $  ^ +|    ^  E(1)  ^  C5(2)  ^  C25(2)  ^  C2(5)  ^  σh(1)  ^  S5(2)  ^  S35(2)  ^  σv(5)  ^ 
-^ $ A_1^' | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 $ | +^ $ A'_1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 $ | 
-^ $ A_1^{''} | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 $ | +^ $ A''_1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 $ | 
-^ $ A_2^' | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 $ | +^ $ A'_2 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 $ | 
-^ $ A_2^{''} | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 $ | +^ $ A''_2 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 $ | 
-^ $ E_1^' | 2 | \frac{1}{2} \left(-1+\sqrt{5}\right) | \frac{1}{2} \left(-1-\sqrt{5}\right) | 0 | 2 | \frac{1}{2} \left(-1+\sqrt{5}\right) | \frac{1}{2} \left(-1-\sqrt{5}\right) | 0 $ | +^ $ E'_1 | 2 | \frac{1}{2} \left(-1+\sqrt{5}\right) | \frac{1}{2} \left(-1-\sqrt{5}\right) | 0 | 2 | \frac{1}{2} \left(-1+\sqrt{5}\right) | \frac{1}{2} \left(-1-\sqrt{5}\right) | 0 $ | 
-^ $ E_1^{''} | 2 | \frac{1}{2} \left(-1+\sqrt{5}\right) | \frac{1}{2} \left(-1-\sqrt{5}\right) | 0 | -2 | \frac{1}{2} \left(1-\sqrt{5}\right) | \frac{1}{2} \left(1+\sqrt{5}\right) | 0 $ | +^ $ E''_1 | 2 | \frac{1}{2} \left(-1+\sqrt{5}\right) | \frac{1}{2} \left(-1-\sqrt{5}\right) | 0 | -2 | \frac{1}{2} \left(1-\sqrt{5}\right) | \frac{1}{2} \left(1+\sqrt{5}\right) | 0 $ | 
-^ $ E_2^' | 2 | \frac{1}{2} \left(-1-\sqrt{5}\right) | \frac{1}{2} \left(-1+\sqrt{5}\right) | 0 | 2 | \frac{1}{2} \left(-1-\sqrt{5}\right) | \frac{1}{2} \left(-1+\sqrt{5}\right) | 0 $ | +^ $ E'_2 | 2 | \frac{1}{2} \left(-1-\sqrt{5}\right) | \frac{1}{2} \left(-1+\sqrt{5}\right) | 0 | 2 | \frac{1}{2} \left(-1-\sqrt{5}\right) | \frac{1}{2} \left(-1+\sqrt{5}\right) | 0 $ | 
-^ $ E_2^{''} | 2 | \frac{1}{2} \left(-1-\sqrt{5}\right) | \frac{1}{2} \left(-1+\sqrt{5}\right) | 0 | -2 | \frac{1}{2} \left(1+\sqrt{5}\right) | \frac{1}{2} \left(1-\sqrt{5}\right) | 0 $ |+^ $ E''_2 | 2 | \frac{1}{2} \left(-1-\sqrt{5}\right) | \frac{1}{2} \left(-1+\sqrt{5}\right) | 0 | -2 | \frac{1}{2} \left(1+\sqrt{5}\right) | \frac{1}{2} \left(1-\sqrt{5}\right) | 0 $ |
  
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-|    ^  $ A_1^' ^ A_1^{''} ^ A_2^' ^ A_2^{''} ^ E_1^' ^ E_1^{''} ^ E_2^' ^ E_2^{''} $  ^ +|    ^  $ A'_1 ^ A''_1 ^ A'_2 ^ A''_2 ^ E'_1 ^ E''_1 ^ E'_2 ^ E''_2 $  ^ 
-^ $ A_1^' | A_1^' | A_1^{''} | A_2^' | A_2^{''} | E_1^' | E_1^{''} | E_2^' | E_2^{''} $  | +^ $ A'_1 | A'_1 | A''_1 | A'_2 | A''_2 | E'_1 | E''_1 | E'_2 | E''_2 $  | 
-^ $ A_1^{''} | A_1^{''} | A_1^' | A_2^{''} | A_2^' | E_1^{''} | E_1^' | E_2^{''} | E_2^' $  | +^ $ A''_1 | A''_1 | A'_1 | A''_2 | A'_2 | E''_1 | E'_1 | E''_2 | E'_2 $  | 
-^ $ A_2^' | A_2^' | A_2^{''} | A_1^' | A_1^{''} | E_1^' | E_1^{''} | E_2^' | E_2^{''} $  | +^ $ A'_2 | A'_2 | A''_2 | A'_1 | A''_1 | E'_1 | E''_1 | E'_2 | E''_2 $  | 
-^ $ A_2^{''} | A_2^{''} | A_2^' | A_1^{''} | A_1^' | E_1^{''} | E_1^' | E_2^{''} | E_2^' $  | +^ $ A''_2 | A''_2 | A'_2 | A''_1 | A'_1 | E''_1 | E'_1 | E''_2 | E'_2 $  | 
-^ $ E_1^' | E_1^' | E_1^{''} | E_1^' | E_1^{''} | A_1^'+A_2^'+E_2^' | A_1^{''}+A_2^{''}+E_2^{''} | E_1^'+E_2^' | E_1^{''}+E_2^{''} $  | +^ $ E'_1 | E'_1 | E''_1 | E'_1 | E''_1 | A'_1+A'_2+E'_2 | A''_1+A''_2+E''_2 | E'_1+E'_2 | E''_1+E''_2 $  | 
-^ $ E_1^{''} | E_1^{''} | E_1^' | E_1^{''} | E_1^' | A_1^{''}+A_2^{''}+E_2^{''} | A_1^'+A_2^'+E_2^' | E_1^{''}+E_2^{''} | E_1^'+E_2^' $  | +^ $ E''_1 | E''_1 | E'_1 | E''_1 | E'_1 | A''_1+A''_2+E''_2 | A'_1+A'_2+E'_2 | E''_1+E''_2 | E'_1+E'_2 $  | 
-^ $ E_2^' | E_2^' | E_2^{''} | E_2^' | E_2^{''} | E_1^'+E_2^' | E_1^{''}+E_2^{''} | A_1^'+A_2^'+E_1^' | A_1^{''}+A_2^{''}+E_1^{''} $  | +^ $ E'_2 | E'_2 | E''_2 | E'_2 | E''_2 | E'_1+E'_2 | E''_1+E''_2 | A'_1+A'_2+E'_1 | A''_1+A''_2+E''_1 $  | 
-^ $ E_2^{''} | E_2^{''} | E_2^' | E_2^{''} | E_2^' | E_1^{''}+E_2^{''} | E_1^'+E_2^' | A_1^{''}+A_2^{''}+E_1^{''} | A_1^'+A_2^'+E_1^' $  |+^ $ E''_2 | E''_2 | E'_2 | E''_2 | E'_2 | E''_1+E''_2 | E'_1+E'_2 | A''_1+A''_2+E''_1 | A'_1+A'_2+E'_1 $  |
  
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 ^ C5 | {0,0,1} , {0,0,−1} , | ^ C5 | {0,0,1} , {0,0,−1} , |
 ^ C25 | {0,0,1} , {0,0,−1} , | ^ C25 | {0,0,1} , {0,0,−1} , |
-^ $C_2^'|\{1,0,0\},\left\{1,\sqrt{5+2 \sqrt{5}},0\right\},\left\{-\sqrt{1+\frac{2}{\sqrt{5}}},1,0\right\},\left\{\sqrt{1+\frac{2}{\sqrt{5}}},1,0\right\},\left\{1,-\sqrt{5+2 \sqrt{5}},0\right\}$ , |+^ C2 | {1,0,0} , {1,√5+2√5,0} , {−√1+2√5,1,0} , {√1+2√5,1,0} , {1,−√5+2√5,0} , |
 ^ σh | {0,0,1} , | ^ σh | {0,0,1} , |
 ^ S5 | {0,0,1} , {0,0,−1} , | ^ S5 | {0,0,1} , {0,0,−1} , |
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 ^ C5 | {0,0,1} , {0,0,−1} , | ^ C5 | {0,0,1} , {0,0,−1} , |
 ^ C25 | {0,0,1} , {0,0,−1} , | ^ C25 | {0,0,1} , {0,0,−1} , |
-^ $C_2^'|\{0,1,0\},\left\{-\sqrt{5+2 \sqrt{5}},1,0\right\},\left\{1,\sqrt{1+\frac{2}{\sqrt{5}}},0\right\},\left\{1,-\sqrt{1+\frac{2}{\sqrt{5}}},0\right\},\left\{\sqrt{5+2 \sqrt{5}},1,0\right\}$ , |+^ C2 | {0,1,0} , {−√5+2√5,1,0} , {1,√1+2√5,0} , {1,−√1+2√5,0} , {√5+2√5,1,0} , |
 ^ σh | {0,0,1} , | ^ σh | {0,0,1} , |
 ^ S5 | {0,0,1} , {0,0,−1} , | ^ S5 | {0,0,1} , {0,0,−1} , |

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