| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{6_{001}\right\} & \left\{3_{001}\right\} & \left\{2_{001}\right\} & \left\{3^-{}_{001}\right\} & \left\{6^-{}_{001}\right\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{6}_{001}\right\} & \left\{\bar{3}_{001}\right\} & \left\{m_{001}\right\} & \left\{\bar{3}^-{}_{001}\right\} & \left\{\bar{6}^-{}_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{A}_1 & \text{AI} & 2 & -\sqrt{3} & 1 & 0 & -1 & \sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & -2 & \sqrt{3} & -1 & 0 & 1 & -\sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_2 & \text{AI} & 2 & -\sqrt{3} & 1 & 0 & -1 & \sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & 2 & -\sqrt{3} & 1 & 0 & -1 & \sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_3 & \text{AI} & 2 & 0 & -2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & 2 & 0 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_4 & \text{AI} & 2 & 0 & -2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & -2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_5 & \text{AI} & 2 & \sqrt{3} & 1 & 0 & -1 & -\sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & -2 & -\sqrt{3} & -1 & 0 & 1 & \sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_6 & \text{AI} & 2 & \sqrt{3} & 1 & 0 & -1 & -\sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & 2 & \sqrt{3} & 1 & 0 & -1 & -\sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| B | \(\left(0,\frac{1}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{B}_1 & \text{AI} & 2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 \\ \text{B}_2 & \text{AI} & 2 & 0 & 0 & 0 & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| C | \(\left(\frac{1}{3},\frac{1}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{001}\right\} & \left\{3^-{}_{001}\right\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{\bar{6}_{001}\right\} & \left\{m_{001}\right\} & \left\{\bar{6}^-{}_{001}\right\} & \left\{m_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{C}_1 & \text{CI} & 2 & -2 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{C}_2 & \text{AI} & 2 & 1 & -1 & 0 & 0 & 0 & -\sqrt{3} & 0 & \sqrt{3} & 0 & 0 & 0 \\ \text{C}_3 & \text{AI} & 2 & 1 & -1 & 0 & 0 & 0 & \sqrt{3} & 0 & -\sqrt{3} & 0 & 0 & 0 \\ \end{array} \right)\) |
| D | \(\left(0,0,\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{6_{001}\right\} & \left\{3_{001}\right\} & \left\{2_{001}\right\} & \left\{3^-{}_{001}\right\} & \left\{6^-{}_{001}\right\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{6}_{001}\right\} & \left\{\bar{3}_{001}\right\} & \left\{m_{001}\right\} & \left\{\bar{3}^-{}_{001}\right\} & \left\{\bar{6}^-{}_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{D}_1 & \text{BDI} & 2 & -\sqrt{3} & 1 & 0 & -1 & \sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\mathrm{i} &\mathrm{i}\sqrt{3} & -2\mathrm{i}&\mathrm{i}\sqrt{3} & -\mathrm{i} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{D}_2 & \text{BDI} & 2 & -\sqrt{3} & 1 & 0 & -1 & \sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 &\mathrm{i}& -\mathrm{i} \sqrt{3} & 2\mathrm{i}& -\mathrm{i} \sqrt{3} &\mathrm{i}& 0 & 0 & 0 & 0 & 0 & 0 \\ \text{D}_3 & \text{BDI} & 2 & 0 & -2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2\mathrm{i}& 0 & 2\mathrm{i}& 0 & -2\mathrm{i}& 0 & 0 & 0 & 0 & 0 & 0 \\ \text{D}_4 & \text{BDI} & 2 & 0 & -2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2\mathrm{i}& 0 & -2\mathrm{i}& 0 & 2\mathrm{i}& 0 & 0 & 0 & 0 & 0 & 0 \\ \text{D}_5 & \text{BDI} & 2 & \sqrt{3} & 1 & 0 & -1 & -\sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\mathrm{i} & -\mathrm{i} \sqrt{3} & -2\mathrm{i}& -\mathrm{i} \sqrt{3} & -\mathrm{i} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{D}_6 & \text{BDI} & 2 & \sqrt{3} & 1 & 0 & -1 & -\sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 &\mathrm{i}&\mathrm{i}\sqrt{3} & 2\mathrm{i}&\mathrm{i}\sqrt{3} &\mathrm{i}& 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| E | \(\left(0,\frac{1}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{E}_1 & \text{BDI} & 2 & 0 & 0 & 0 & 0 & -2\mathrm{i}& 0 & 0 \\ \text{E}_2 & \text{BDI} & 2 & 0 & 0 & 0 & 0 & 2\mathrm{i}& 0 & 0 \\ \end{array} \right)\) |
| F | \(\left(\frac{1}{3},\frac{1}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{001}\right\} & \left\{3^-{}_{001}\right\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{\bar{6}_{001}\right\} & \left\{m_{001}\right\} & \left\{\bar{6}^-{}_{001}\right\} & \left\{m_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{F}_1 & \text{AIII} & 1 & -1 & 1 &\mathrm{i}& -\mathrm{i} & -\mathrm{i} & -\mathrm{i} &\mathrm{i}& -\mathrm{i} & -1 & 1 & 1 \\ \text{F}_2 & \text{AIII} & 1 & -1 & 1 &\mathrm{i}& -\mathrm{i} & -\mathrm{i} &\mathrm{i}& -\mathrm{i} &\mathrm{i}& 1 & -1 & -1 \\ \text{F}_3 & \text{AIII} & 1 & -1 & 1 & -\mathrm{i} &\mathrm{i}&\mathrm{i}& -\mathrm{i} &\mathrm{i}& -\mathrm{i} & 1 & -1 & -1 \\ \text{F}_4 & \text{AIII} & 1 & -1 & 1 & -\mathrm{i} &\mathrm{i}&\mathrm{i}&\mathrm{i}& -\mathrm{i} &\mathrm{i}& -1 & 1 & 1 \\ \text{F}_5 & \text{BDI} & 2 & 1 & -1 & 0 & 0 & 0 & -\mathrm{i} & -2\mathrm{i}& -\mathrm{i} & 0 & 0 & 0 \\ \text{F}_6 & \text{BDI} & 2 & 1 & -1 & 0 & 0 & 0 &\mathrm{i}& 2\mathrm{i}&\mathrm{i}& 0 & 0 & 0 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(\frac{t}{3},\frac{t}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ a_1 & \text{CI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(b\) | \(\left(0,\frac{t}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} \\ b_1 & \text{CI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{3},\frac{1}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ c_1 & \text{CI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{t}{3},\frac{t}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ d_1 & \text{AIII} & 1 &\mathrm{i}& -\mathrm{i} & 1 \\ d_2 & \text{AIII} & 1 &\mathrm{i}&\mathrm{i}& -1 \\ d_3 & \text{AIII} & 1 & -\mathrm{i} & -\mathrm{i} & -1 \\ d_4 & \text{AIII} & 1 & -\mathrm{i} &\mathrm{i}& 1 \\ \end{array} \right)\) |
| \(e\) | \(\left(0,\frac{t}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} \\ e_1 & \text{AIII} & 1 &\mathrm{i}& -\mathrm{i} & 1 \\ e_2 & \text{AIII} & 1 &\mathrm{i}&\mathrm{i}& -1 \\ e_3 & \text{AIII} & 1 & -\mathrm{i} & -\mathrm{i} & -1 \\ e_4 & \text{AIII} & 1 & -\mathrm{i} &\mathrm{i}& 1 \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{t}{3},\frac{1}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ f_1 & \text{AIII} & 1 &\mathrm{i}& -\mathrm{i} & -1 \\ f_2 & \text{AIII} & 1 &\mathrm{i}&\mathrm{i}& 1 \\ f_3 & \text{AIII} & 1 & -\mathrm{i} & -\mathrm{i} & 1 \\ f_4 & \text{AIII} & 1 & -\mathrm{i} &\mathrm{i}& -1 \\ \end{array} \right)\) |
| \(g\) | \(\left(0,0,\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{6_{001}\right\} & \left\{3_{001}\right\} & \left\{2_{001}\right\} & \left\{3^-{}_{001}\right\} & \left\{6^-{}_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{110},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ g_1 & \text{BDI} & 2 & -\sqrt{3} & 1 & 0 & -1 & \sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 \\ g_2 & \text{BDI} & 2 & 0 & -2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ g_3 & \text{BDI} & 2 & \sqrt{3} & 1 & 0 & -1 & -\sqrt{3} & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(h\) | \(\left(0,\frac{1}{\sqrt{3}},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} \\ h_1 & \text{BDI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(i\) | \(\left(\frac{1}{3},\frac{1}{\sqrt{3}},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{001}\right\} & \left\{3^-{}_{001}\right\} & \left\{m_{210},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{010},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{m_{-110},\left\{0,0,\frac{1}{2}\right\}\right\} \\ i_1 & \text{AIII} & 1 & -1 & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ i_2 & \text{AIII} & 1 & -1 & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ i_3 & \text{BDI} & 2 & 1 & -1 & 0 & 0 & 0 \\ \end{array} \right)\) |