| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} \\ \text{A}_1 & \text{AI} & 1 & 1 & 1 & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{A}_2 & \text{AI} & 1 & 1 & 1 & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \text{A}_3 & \text{AI} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{A}_4 & \text{AI} & 3 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| B | \(\left(0,1,0\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} \\ \text{B}_1 & \text{AI} & 1 & 1 & 1 & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{B}_2 & \text{AI} & 1 & 1 & 1 & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \text{B}_3 & \text{AI} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{B}_4 & \text{AI} & 3 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| C | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} \\ \text{C}_1 & \text{AI} & 1 & -1 \\ \text{C}_2 & \text{AI} & 1 & 1 \\ \end{array} \right)\) |
| D | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} \\ \text{D}_1 & \text{AI} & 1 & 1 & 1 & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{D}_2 & \text{AI} & 1 & 1 & 1 & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \text{D}_3 & \text{AI} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{D}_4 & \text{AI} & 3 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| E | \(\left(\frac{1}{2},\frac{1}{2},-\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} \\ \text{E}_1 & \text{AI} & 1 & 1 & 1 & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{E}_2 & \text{AI} & 1 & 1 & 1 & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \text{E}_3 & \text{AI} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{E}_4 & \text{AI} & 3 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(0,t,0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010}\right\} \\ a_1 & \text{AI} & 1 & -1 \\ a_2 & \text{AI} & 1 & 1 \\ \end{array} \right)\) |
| \(b\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} \\ b_1 & \text{AI} & 1 & -1 \\ b_2 & \text{AI} & 1 & 1 \\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{1}{2},\frac{1}{2},-\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} \\ c_1 & \text{AI} & 1 & -1 \\ c_2 & \text{AI} & 1 & 1 \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{t}{2},\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} \\ d_1 & \text{AI} & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ d_2 & \text{AI} & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ d_3 & \text{AI} & 1 & 1 & 1 \\ \end{array} \right)\) |
| \(e\) | \(\left(\frac{t}{2},\frac{t}{2},-\frac{t}{2}\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} \\ e_1 & \text{AI} & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ e_2 & \text{AI} & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ e_3 & \text{AI} & 1 & 1 & 1 \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{t}{2},1-\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} \\ f_1 & \text{AI} & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ f_2 & \text{AI} & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ f_3 & \text{AI} & 1 & 1 & 1 \\ \end{array} \right)\) |
| \(g\) | \(\left(\frac{t}{2},1-\frac{t}{2},-\frac{t}{2}\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} \\ g_1 & \text{AI} & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ g_2 & \text{AI} & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ g_3 & \text{AI} & 1 & 1 & 1 \\ \end{array} \right)\) |