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| physics_chemistry:point_groups:ih [2018/03/22 22:48] – Maurits W. Haverkort | physics_chemistry:point_groups:ih [2018/03/23 00:36] – Maurits W. Haverkort |
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| ^ $ G_u $ | $ G_u $ | $ G_u+H_u+T_{2u} $ | $ G_u+H_u+T_{1u} $ | $ A_u+G_u+H_u+T_{1u}+T_{2u} $ | $ G_u+2 H_u+T_{1u}+T_{2u} $ | $ G_g $ | $ G_g+H_g+T_{2g} $ | $ G_g+H_g+T_{1g} $ | $ A_g+G_g+H_g+T_{1g}+T_{2g} $ | $ G_g+2 H_g+T_{1g}+T_{2g} $ | | ^ $ G_u $ | $ G_u $ | $ G_u+H_u+T_{2u} $ | $ G_u+H_u+T_{1u} $ | $ A_u+G_u+H_u+T_{1u}+T_{2u} $ | $ G_u+2 H_u+T_{1u}+T_{2u} $ | $ G_g $ | $ G_g+H_g+T_{2g} $ | $ G_g+H_g+T_{1g} $ | $ A_g+G_g+H_g+T_{1g}+T_{2g} $ | $ G_g+2 H_g+T_{1g}+T_{2g} $ | |
| ^ $ H_u $ | $ H_u $ | $ G_u+H_u+T_{1u}+T_{2u} $ | $ G_u+H_u+T_{1u}+T_{2u} $ | $ G_u+2 H_u+T_{1u}+T_{2u} $ | $ A_u+2 G_u+2 H_u+T_{1u}+T_{2u} $ | $ H_g $ | $ G_g+H_g+T_{1g}+T_{2g} $ | $ G_g+H_g+T_{1g}+T_{2g} $ | $ G_g+2 H_g+T_{1g}+T_{2g} $ | $ A_g+2 G_g+2 H_g+T_{1g}+T_{2g} $ | | ^ $ H_u $ | $ H_u $ | $ G_u+H_u+T_{1u}+T_{2u} $ | $ G_u+H_u+T_{1u}+T_{2u} $ | $ G_u+2 H_u+T_{1u}+T_{2u} $ | $ A_u+2 G_u+2 H_u+T_{1u}+T_{2u} $ | $ H_g $ | $ G_g+H_g+T_{1g}+T_{2g} $ | $ G_g+H_g+T_{1g}+T_{2g} $ | $ G_g+2 H_g+T_{1g}+T_{2g} $ | $ A_g+2 G_g+2 H_g+T_{1g}+T_{2g} $ | |
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| | ^ Operator ^ Orientation ^ |
| | ^ $\text{E}$ | $\{0,0,0\}$ , | |
| | ^ $C_3$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3}\right\}$ , $\left\{\frac{2}{3},\frac{2}{3},-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(\sqrt{3}-1\right),\frac{1}{3} \left(-1-\sqrt{3}\right),-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(-1-\sqrt{3}\right),\frac{1}{3} \left(\sqrt{3}-1\right),-\frac{1}{3}\right\}$ , $\left\{-\frac{2}{3},-\frac{2}{3},\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3}\right\}$ , | |
| | ^ $C_2$ | $\{1,-1,0\}$ , $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$ , $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$ , $\{1,1,-2\}$ , $\left\{1+\sqrt{3},1-\sqrt{3},4\right\}$ , $\left\{\sqrt{3}-1,-1-\sqrt{3},-4\right\}$ , | |
| | ^ $C_4$ | $\{1,1,1\}$ , $\{-1,-1,-1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{-\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2}-\frac{1}{2},1\right\}$ , $\left\{\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{1}{2}+\frac{\sqrt{3}}{2},-1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , | |
| | ^ $C_2$ | $\{1,1,1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , | |
| | ^ $\text{i}$ | $\{0,0,0\}$ , | |
| | ^ $S_4$ | $\{1,1,1\}$ , $\{-1,-1,-1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{-\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2}-\frac{1}{2},1\right\}$ , $\left\{\frac{1}{2}-\frac{\sqrt{3}}{2},\frac{1}{2}+\frac{\sqrt{3}}{2},-1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , | |
| | ^ $S_6$ | $\{0,0,1\}$ , $\{0,0,-1\}$ , $\left\{\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3}\right\}$ , $\left\{\frac{2}{3},\frac{2}{3},-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(\sqrt{3}-1\right),\frac{1}{3} \left(-1-\sqrt{3}\right),-\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(-1-\sqrt{3}\right),\frac{1}{3} \left(\sqrt{3}-1\right),-\frac{1}{3}\right\}$ , $\left\{-\frac{2}{3},-\frac{2}{3},\frac{1}{3}\right\}$ , $\left\{\frac{1}{3} \left(1-\sqrt{3}\right),\frac{1}{3} \left(1+\sqrt{3}\right),\frac{1}{3}\right\}$ , | |
| | ^ $\sigma _h$ | $\{1,1,1\}$ , $\left\{\frac{\sqrt{3}}{2}-\frac{1}{2},-\frac{1}{2}-\frac{\sqrt{3}}{2},1\right\}$ , $\left\{\frac{1}{2}+\frac{\sqrt{3}}{2},\frac{1}{2}-\frac{\sqrt{3}}{2},-1\right\}$ , | |
| | ^ $\sigma _d$ | $\{1,-1,0\}$ , $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$ , $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$ , $\{1,1,-2\}$ , $\left\{1+\sqrt{3},1-\sqrt{3},4\right\}$ , $\left\{\sqrt{3}-1,-1-\sqrt{3},-4\right\}$ , | |
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