====== Point Group C6v ======
===== Character Table =====
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| $ $ ^ $ \text{E} \,{\text{(1)}} $ ^ $ C_6 \,{\text{(2)}} $ ^ $ C_3 \,{\text{(2)}} $ ^ $ C_2 \,{\text{(1)}} $ ^ $ \sigma_v \,{\text{(3)}} $ ^ $ \sigma_d \,{\text{(3)}} $ ^
^ $ A_1 $ | $ 1 $ | $ 1 $ | $ 1 $ | $ 1 $ | $ 1 $ | $ 1 $ |
^ $ A_2 $ | $ 1 $ | $ 1 $ | $ 1 $ | $ 1 $ | $ -1 $ | $ -1 $ |
^ $ B_1 $ | $ 1 $ | $ -1 $ | $ 1 $ | $ -1 $ | $ 1 $ | $ -1 $ |
^ $ B_2 $ | $ 1 $ | $ -1 $ | $ 1 $ | $ -1 $ | $ -1 $ | $ 1 $ |
^ $ E_1 $ | $ 2 $ | $ 1 $ | $ -1 $ | $ -2 $ | $ 0 $ | $ 0 $ |
^ $ E_2 $ | $ 2 $ | $ -1 $ | $ -1 $ | $ 2 $ | $ 0 $ | $ 0 $ |
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===== Product Table =====
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| $ $ ^ $ A_1 $ ^ $ A_2 $ ^ $ B_1 $ ^ $ B_2 $ ^ $ E_1 $ ^ $ E_2 $ ^
^ $ A_1 $ | $ A_1 $ | $ A_2 $ | $ B_1 $ | $ B_2 $ | $ E_1 $ | $ E_2 $ |
^ $ A_2 $ | $ A_2 $ | $ A_1 $ | $ B_2 $ | $ B_1 $ | $ E_1 $ | $ E_2 $ |
^ $ B_1 $ | $ B_1 $ | $ B_2 $ | $ A_1 $ | $ A_2 $ | $ E_2 $ | $ E_1 $ |
^ $ B_2 $ | $ B_2 $ | $ B_1 $ | $ A_2 $ | $ A_1 $ | $ E_2 $ | $ E_1 $ |
^ $ E_1 $ | $ E_1 $ | $ E_1 $ | $ E_2 $ | $ E_2 $ | $ A_1+A_2+E_2 $ | $ B_1+B_2+E_1 $ |
^ $ E_2 $ | $ E_2 $ | $ E_2 $ | $ E_1 $ | $ E_1 $ | $ B_1+B_2+E_1 $ | $ A_1+A_2+E_2 $ |
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===== Implemented Settings =====
[[physics_chemistry:point_groups:c6v:orientation_zx| C6v_Zx ]] [[physics_chemistry:point_groups:c6v:orientation_zy| C6v_Zy ]]
==== Setting Zx ====
[[physics_chemistry:point_groups:c6v:orientation_zx|Details of the C6v group in with setting Zx]]
{{:physics_chemistry:pointgroup:c6v_zx.png }}
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^ Operator ^ Orientation ^
^ $\text{E}$ | $\{0,0,0\}$ , |
^ $C_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , |
^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , |
^ $C_2$ | $\{0,0,1\}$ , |
^ $\sigma _v$ | $\{1,0,0\}$ , $\left\{1,\sqrt{3},0\right\}$ , $\left\{1,-\sqrt{3},0\right\}$ , |
^ $\sigma _d$ | $\{0,1,0\}$ , $\left\{\sqrt{3},1,0\right\}$ , $\left\{\sqrt{3},-1,0\right\}$ , |
###
==== Setting Zy ====
[[physics_chemistry:point_groups:c6v:orientation_zy|Details of the C6v group in with setting Zy]]
{{:physics_chemistry:pointgroup:c6v_zy.png }}
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^ Operator ^ Orientation ^
^ $\text{E}$ | $\{0,0,0\}$ , |
^ $C_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , |
^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , |
^ $C_2$ | $\{0,0,1\}$ , |
^ $\sigma _v$ | $\{0,1,0\}$ , $\left\{\sqrt{3},1,0\right\}$ , $\left\{\sqrt{3},-1,0\right\}$ , |
^ $\sigma _d$ | $\{1,0,0\}$ , $\left\{1,\sqrt{3},0\right\}$ , $\left\{1,-\sqrt{3},0\right\}$ , |
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===== Table of several point groups =====
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[[physics_chemistry:point_groups|Return to Main page on Point Groups]]
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^Nonaxial groups | [[physics_chemistry:point_groups:c1|C]][[physics_chemistry:point_groups:c1|1]] | [[physics_chemistry:point_groups:cs|C]][[physics_chemistry:point_groups:cs|s]] | [[physics_chemistry:point_groups:ci|C]][[physics_chemistry:point_groups:ci|i]] | | | | |
^Cn groups | [[physics_chemistry:point_groups:c2|C]][[physics_chemistry:point_groups:c2|2]] | [[physics_chemistry:point_groups:c3|C]][[physics_chemistry:point_groups:c3|3]] | [[physics_chemistry:point_groups:c4|C]][[physics_chemistry:point_groups:c4|4]] | [[physics_chemistry:point_groups:c5|C]][[physics_chemistry:point_groups:c5|5]] | [[physics_chemistry:point_groups:c6|C]][[physics_chemistry:point_groups:c6|6]] | [[physics_chemistry:point_groups:c7|C]][[physics_chemistry:point_groups:c7|7]] | [[physics_chemistry:point_groups:c8|C]][[physics_chemistry:point_groups:c8|8]] |
^Dn groups | [[physics_chemistry:point_groups:d2|D]][[physics_chemistry:point_groups:d2|2]] | [[physics_chemistry:point_groups:d3|D]][[physics_chemistry:point_groups:d3|3]] | [[physics_chemistry:point_groups:d4|D]][[physics_chemistry:point_groups:d4|4]] | [[physics_chemistry:point_groups:d5|D]][[physics_chemistry:point_groups:d5|5]] | [[physics_chemistry:point_groups:d6|D]][[physics_chemistry:point_groups:d6|6]] | [[physics_chemistry:point_groups:d7|D]][[physics_chemistry:point_groups:d7|7]] | [[physics_chemistry:point_groups:d8|D]][[physics_chemistry:point_groups:d8|8]] |
^Cnv groups | [[physics_chemistry:point_groups:c2v|C]][[physics_chemistry:point_groups:c2v|2v]] | [[physics_chemistry:point_groups:c3v|C]][[physics_chemistry:point_groups:c3v|3v]] | [[physics_chemistry:point_groups:c4v|C]][[physics_chemistry:point_groups:c4v|4v]] | [[physics_chemistry:point_groups:c5v|C]][[physics_chemistry:point_groups:c5v|5v]] | [[physics_chemistry:point_groups:c6v|C]][[physics_chemistry:point_groups:c6v|6v]] | [[physics_chemistry:point_groups:c7v|C]][[physics_chemistry:point_groups:c7v|7v]] | [[physics_chemistry:point_groups:c8v|C]][[physics_chemistry:point_groups:c8v|8v]] |
^Cnh groups | [[physics_chemistry:point_groups:c2h|C]][[physics_chemistry:point_groups:c2h|2h]] | [[physics_chemistry:point_groups:c3h|C]][[physics_chemistry:point_groups:c3h|3h]] | [[physics_chemistry:point_groups:c4h|C]][[physics_chemistry:point_groups:c4h|4h]] | [[physics_chemistry:point_groups:c5h|C]][[physics_chemistry:point_groups:c5h|5h]] | [[physics_chemistry:point_groups:c6h|C]][[physics_chemistry:point_groups:c6h|6h]] | | |
^Dnh groups | [[physics_chemistry:point_groups:d2h|D]][[physics_chemistry:point_groups:d2h|2h]] | [[physics_chemistry:point_groups:d3h|D]][[physics_chemistry:point_groups:d3h|3h]] | [[physics_chemistry:point_groups:d4h|D]][[physics_chemistry:point_groups:d4h|4h]] | [[physics_chemistry:point_groups:d5h|D]][[physics_chemistry:point_groups:d5h|5h]] | [[physics_chemistry:point_groups:d6h|D]][[physics_chemistry:point_groups:d6h|6h]] | [[physics_chemistry:point_groups:d7h|D]][[physics_chemistry:point_groups:d7h|7h]] | [[physics_chemistry:point_groups:d8h|D]][[physics_chemistry:point_groups:d8h|8h]] |
^Dnd groups | [[physics_chemistry:point_groups:d2d|D]][[physics_chemistry:point_groups:d2d|2d]] | [[physics_chemistry:point_groups:d3d|D]][[physics_chemistry:point_groups:d3d|3d]] | [[physics_chemistry:point_groups:d4d|D]][[physics_chemistry:point_groups:d4d|4d]] | [[physics_chemistry:point_groups:d5d|D]][[physics_chemistry:point_groups:d5d|5d]] | [[physics_chemistry:point_groups:d6d|D]][[physics_chemistry:point_groups:d6d|6d]] | [[physics_chemistry:point_groups:d7d|D]][[physics_chemistry:point_groups:d7d|7d]] | [[physics_chemistry:point_groups:d8d|D]][[physics_chemistry:point_groups:d8d|8d]] |
^Sn groups | [[physics_chemistry:point_groups:S2|S]][[physics_chemistry:point_groups:S2|2]] | [[physics_chemistry:point_groups:S4|S]][[physics_chemistry:point_groups:S4|4]] | [[physics_chemistry:point_groups:S6|S]][[physics_chemistry:point_groups:S6|6]] | [[physics_chemistry:point_groups:S8|S]][[physics_chemistry:point_groups:S8|8]] | [[physics_chemistry:point_groups:S10|S]][[physics_chemistry:point_groups:S10|10]] | [[physics_chemistry:point_groups:S12|S]][[physics_chemistry:point_groups:S12|12]] | |
^Cubic groups | [[physics_chemistry:point_groups:T|T]] | [[physics_chemistry:point_groups:Th|T]][[physics_chemistry:point_groups:Th|h]] | [[physics_chemistry:point_groups:Td|T]][[physics_chemistry:point_groups:Td|d]] | [[physics_chemistry:point_groups:O|O]] | [[physics_chemistry:point_groups:Oh|O]][[physics_chemistry:point_groups:Oh|h]] | [[physics_chemistry:point_groups:I|I]] | [[physics_chemistry:point_groups:Ih|I]][[physics_chemistry:point_groups:Ih|h]] |
^Linear groups | [[physics_chemistry:point_groups:cinfv|C]][[physics_chemistry:point_groups:cinfv|$\infty$v]] | [[physics_chemistry:point_groups:cinfv|D]][[physics_chemistry:point_groups:dinfh|$\infty$h]] | | | | | |
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