Fusion Ring
\[ \begin{array}{llll} \htmlTitle{1\otimes 1}{1} & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1 \oplus 4} & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{3 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 4} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.618\) | \( \frac{1}{2} + \frac{\sqrt{5}}{2} \) |
| \( 4\) | \(1.618\) | \( \frac{1}{2} + \frac{\sqrt{5}}{2} \) |
| \( D^2\) | 7.236 | \(\sqrt{5} + 5\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{3}{2}} & \htmlTitle{\theta_{3}}{\frac{3}{10}} & \htmlTitle{\theta_{4}}{\frac{4}{5}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llll} \htmlTitle{S_{1; 1}}{1} & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{-1} & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{40}^{12} + \zeta_{40}^{8} + 1} & \htmlTitle{S_{3; 2}}{\zeta_{40}^{12} - \zeta_{40}^{8} - 1} & \htmlTitle{S_{3; 3}}{1} & \\ \htmlTitle{S_{4; 1}}{-\zeta_{40}^{12} + \zeta_{40}^{8} + 1} & \htmlTitle{S_{4; 2}}{-\zeta_{40}^{12} + \zeta_{40}^{8} + 1} & \htmlTitle{S_{4; 3}}{-1} & \htmlTitle{S_{4; 4}}{-1}\end{array}\right) \]
Central Charge
\[c = \frac{9}{5} \]