Parametrization of PMNS matrix based on dodeca-symmetry

The dodeca symmetry is designed to obtain the Cabibbo angle $\theta_C^{\rm CKM}$approximately$15^{\rm o}$andthe(11)elementof$\Vp$as$\cos 30^{\rm o}$,leadingto$\theta_1^{\rm PMNS}+\theta_C^{\rm CKM}\simeq 45^{\rm o}$. This leading order dodeca symmetric $\text{Vp}$ is corrected by small parameters, especially as an expansion in terms of a small parameter $\beta$. Neglecting two Majorana phases, the expression of $\text{Vp}$ contains four parameters: a small $\beta$, and three $\text{Od}(1)$ parameters $A,B,$ and $\delta$. From the neutrino oscillation data, we present two parametrizations and estimate their $\beta$’s.