Fusion Ring
\[ \begin{array}{llll} \htmlTitle{1\otimes 1}{1} & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1 \oplus 3} & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4 \oplus 2} & \htmlTitle{3\otimes 3}{1 \oplus 4 \oplus 3} & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{4 \oplus 3} & \htmlTitle{4\otimes 3}{4 \oplus 2 \oplus 3} & \htmlTitle{4\otimes 4}{1 \oplus 4 \oplus 2 \oplus 3} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} \) |
| \( 3\) | \(2.532\) | \( - \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( 4\) | \(2.879\) | \( \cos{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} + 1 \) |
| \( D^2\) | 19.234 | \(6 \cos{\left(\frac{2 \pi}{9} \right)} + 6 \cos{\left(\frac{\pi}{9} \right)} + 9\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{4}{3}} & \htmlTitle{\theta_{3}}{\frac{14}{9}} & \htmlTitle{\theta_{4}}{\frac{2}{3}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llll} \htmlTitle{S_{1; 1}}{1} & & & \\ \htmlTitle{S_{2; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4}} & \htmlTitle{S_{2; 2}}{\zeta_{72}^{20} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{3; 2}}{-\zeta_{72}^{16} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{3; 3}}{0} & \\ \htmlTitle{S_{4; 1}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4} + 1} & \htmlTitle{S_{4; 2}}{-1} & \htmlTitle{S_{4; 3}}{\zeta_{72}^{16} - \zeta_{72}^{8} - \zeta_{72}^{4} - 1} & \htmlTitle{S_{4; 4}}{-\zeta_{72}^{20} + \zeta_{72}^{8} + \zeta_{72}^{4}}\end{array}\right) \]
Central Charge
\[c = \frac{14}{3} \]