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| physics_chemistry:point_groups:d6 [2018/03/21 15:24] – created Stefano Agrestini | physics_chemistry:point_groups:d6 [2018/03/23 10:36] (current) – Stefano Agrestini |
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| ====== D6 ====== | ====== Point Group D6 ====== |
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| | ===== Character Table ===== |
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| ### | ### |
| alligned paragraph text | |
| | | $ $ ^ $ \text{E} \,{\text{(1)}} $ ^ $ C_6 \,{\text{(2)}} $ ^ $ C_3 \,{\text{(2)}} $ ^ $ C_2 \,{\text{(1)}} $ ^ $ C_2' \,{\text{(3)}} $ ^ $ C_2\text{''} \,{\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 $ | |
| ### | ### |
| |
| ===== Example ===== | ===== Product Table ===== |
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| ### | ### |
| description text | |
| | | $ $ ^ $ 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 $ | |
| ### | ### |
| |
| ==== Input ==== | ===== Implemented Settings ===== |
| <code Quanty Example.Quanty> | |
| -- some example code | |
| </code> | |
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| ==== Result ==== | [[physics_chemistry:point_groups:d6:orientation_zxy| D6_Zxy ]] |
| <WRAP center box 100%> | |
| text produced as output | |
| </WRAP> | |
| |
| ===== Table of contents ===== | ==== Setting Zxy ==== |
| {{indexmenu>.#2}} | |
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| | [[physics_chemistry:point_groups:d6:orientation_zxy|Details of the D6 group in with setting Zxy]] |
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| | {{:physics_chemistry:pointgroup:d6_zxy.png }} |
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| | ### |
| | |
| | ^ Operator ^ Orientation ^ |
| | ^ $\text{E}$ | $\{0,0,0\}$ , | |
| | ^ $C_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , | |
| | ^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , | |
| | ^ $C_2$ | $\{0,0,1\}$ , | |
| | ^ $C_2'$ | $\{1,0,0\}$ , $\left\{1,\sqrt{3},0\right\}$ , $\left\{1,-\sqrt{3},0\right\}$ , | |
| | ^ $C_2\text{''}$ | $\{0,1,0\}$ , $\left\{\sqrt{3},1,0\right\}$ , $\left\{\sqrt{3},-1,0\right\}$ , | |
| | |
| | ### |
| | |
| | |
| | ===== Table of several point groups ===== |
| | |
| | ### |
| | |
| | [[physics_chemistry:point_groups|Return to Main page on Point Groups]] |
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| | ### |
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| | ### |
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| | ^Nonaxial groups | [[physics_chemistry:point_groups:c1|C]]<sub>[[physics_chemistry:point_groups:c1|1]]</sub> | [[physics_chemistry:point_groups:cs|C]]<sub>[[physics_chemistry:point_groups:cs|s]]</sub> | [[physics_chemistry:point_groups:ci|C]]<sub>[[physics_chemistry:point_groups:ci|i]]</sub> | | | | | |
| | ^C<sub>n</sub> groups | [[physics_chemistry:point_groups:c2|C]]<sub>[[physics_chemistry:point_groups:c2|2]]</sub> | [[physics_chemistry:point_groups:c3|C]]<sub>[[physics_chemistry:point_groups:c3|3]]</sub> | [[physics_chemistry:point_groups:c4|C]]<sub>[[physics_chemistry:point_groups:c4|4]]</sub> | [[physics_chemistry:point_groups:c5|C]]<sub>[[physics_chemistry:point_groups:c5|5]]</sub> | [[physics_chemistry:point_groups:c6|C]]<sub>[[physics_chemistry:point_groups:c6|6]]</sub> | [[physics_chemistry:point_groups:c7|C]]<sub>[[physics_chemistry:point_groups:c7|7]]</sub> | [[physics_chemistry:point_groups:c8|C]]<sub>[[physics_chemistry:point_groups:c8|8]]</sub> | |
| | ^D<sub>n</sub> groups | [[physics_chemistry:point_groups:d2|D]]<sub>[[physics_chemistry:point_groups:d2|2]]</sub> | [[physics_chemistry:point_groups:d3|D]]<sub>[[physics_chemistry:point_groups:d3|3]]</sub> | [[physics_chemistry:point_groups:d4|D]]<sub>[[physics_chemistry:point_groups:d4|4]]</sub> | [[physics_chemistry:point_groups:d5|D]]<sub>[[physics_chemistry:point_groups:d5|5]]</sub> | [[physics_chemistry:point_groups:d6|D]]<sub>[[physics_chemistry:point_groups:d6|6]]</sub> | [[physics_chemistry:point_groups:d7|D]]<sub>[[physics_chemistry:point_groups:d7|7]]</sub> | [[physics_chemistry:point_groups:d8|D]]<sub>[[physics_chemistry:point_groups:d8|8]]</sub> | |
| | ^C<sub>nv</sub> groups | [[physics_chemistry:point_groups:c2v|C]]<sub>[[physics_chemistry:point_groups:c2v|2v]]</sub> | [[physics_chemistry:point_groups:c3v|C]]<sub>[[physics_chemistry:point_groups:c3v|3v]]</sub> | [[physics_chemistry:point_groups:c4v|C]]<sub>[[physics_chemistry:point_groups:c4v|4v]]</sub> | [[physics_chemistry:point_groups:c5v|C]]<sub>[[physics_chemistry:point_groups:c5v|5v]]</sub> | [[physics_chemistry:point_groups:c6v|C]]<sub>[[physics_chemistry:point_groups:c6v|6v]]</sub> | [[physics_chemistry:point_groups:c7v|C]]<sub>[[physics_chemistry:point_groups:c7v|7v]]</sub> | [[physics_chemistry:point_groups:c8v|C]]<sub>[[physics_chemistry:point_groups:c8v|8v]]</sub> | |
| | ^C<sub>nh</sub> groups | [[physics_chemistry:point_groups:c2h|C]]<sub>[[physics_chemistry:point_groups:c2h|2h]]</sub> | [[physics_chemistry:point_groups:c3h|C]]<sub>[[physics_chemistry:point_groups:c3h|3h]]</sub> | [[physics_chemistry:point_groups:c4h|C]]<sub>[[physics_chemistry:point_groups:c4h|4h]]</sub> | [[physics_chemistry:point_groups:c5h|C]]<sub>[[physics_chemistry:point_groups:c5h|5h]]</sub> | [[physics_chemistry:point_groups:c6h|C]]<sub>[[physics_chemistry:point_groups:c6h|6h]]</sub> | | | |
| | ^D<sub>nh</sub> groups | [[physics_chemistry:point_groups:d2h|D]]<sub>[[physics_chemistry:point_groups:d2h|2h]]</sub> | [[physics_chemistry:point_groups:d3h|D]]<sub>[[physics_chemistry:point_groups:d3h|3h]]</sub> | [[physics_chemistry:point_groups:d4h|D]]<sub>[[physics_chemistry:point_groups:d4h|4h]]</sub> | [[physics_chemistry:point_groups:d5h|D]]<sub>[[physics_chemistry:point_groups:d5h|5h]]</sub> | [[physics_chemistry:point_groups:d6h|D]]<sub>[[physics_chemistry:point_groups:d6h|6h]]</sub> | [[physics_chemistry:point_groups:d7h|D]]<sub>[[physics_chemistry:point_groups:d7h|7h]]</sub> | [[physics_chemistry:point_groups:d8h|D]]<sub>[[physics_chemistry:point_groups:d8h|8h]]</sub> | |
| | ^D<sub>nd</sub> groups | [[physics_chemistry:point_groups:d2d|D]]<sub>[[physics_chemistry:point_groups:d2d|2d]]</sub> | [[physics_chemistry:point_groups:d3d|D]]<sub>[[physics_chemistry:point_groups:d3d|3d]]</sub> | [[physics_chemistry:point_groups:d4d|D]]<sub>[[physics_chemistry:point_groups:d4d|4d]]</sub> | [[physics_chemistry:point_groups:d5d|D]]<sub>[[physics_chemistry:point_groups:d5d|5d]]</sub> | [[physics_chemistry:point_groups:d6d|D]]<sub>[[physics_chemistry:point_groups:d6d|6d]]</sub> | [[physics_chemistry:point_groups:d7d|D]]<sub>[[physics_chemistry:point_groups:d7d|7d]]</sub> | [[physics_chemistry:point_groups:d8d|D]]<sub>[[physics_chemistry:point_groups:d8d|8d]]</sub> | |
| | ^S<sub>n</sub> groups | [[physics_chemistry:point_groups:S2|S]]<sub>[[physics_chemistry:point_groups:S2|2]]</sub> | [[physics_chemistry:point_groups:S4|S]]<sub>[[physics_chemistry:point_groups:S4|4]]</sub> | [[physics_chemistry:point_groups:S6|S]]<sub>[[physics_chemistry:point_groups:S6|6]]</sub> | [[physics_chemistry:point_groups:S8|S]]<sub>[[physics_chemistry:point_groups:S8|8]]</sub> | [[physics_chemistry:point_groups:S10|S]]<sub>[[physics_chemistry:point_groups:S10|10]]</sub> | [[physics_chemistry:point_groups:S12|S]]<sub>[[physics_chemistry:point_groups:S12|12]]</sub> | | |
| | ^Cubic groups | [[physics_chemistry:point_groups:T|T]] | [[physics_chemistry:point_groups:Th|T]]<sub>[[physics_chemistry:point_groups:Th|h]]</sub> | [[physics_chemistry:point_groups:Td|T]]<sub>[[physics_chemistry:point_groups:Td|d]]</sub> | [[physics_chemistry:point_groups:O|O]] | [[physics_chemistry:point_groups:Oh|O]]<sub>[[physics_chemistry:point_groups:Oh|h]]</sub> | [[physics_chemistry:point_groups:I|I]] | [[physics_chemistry:point_groups:Ih|I]]<sub>[[physics_chemistry:point_groups:Ih|h]]</sub> | |
| | ^Linear groups | [[physics_chemistry:point_groups:cinfv|C]]<sub>[[physics_chemistry:point_groups:cinfv|$\infty$v]]</sub> | [[physics_chemistry:point_groups:cinfv|D]]<sub>[[physics_chemistry:point_groups:dinfh|$\infty$h]]</sub> | | | | | | |
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| | ### |
