close to the experimental best-fit value of $34.43\,^{\circ}$. In Refs.[@Datta:2003qg; @Kajiyama:2007gx] the solar mixing angle is related to the golden ratio $\phi=(1+\sqrt{5})/2$ [@ratio] via $\theta_{12} = \tan^{-1}(\frac{1}{\phi}) = 31.72\,^{\circ}$ which is $2\sigma$ below the experimental best-fit value. The icosahedral group $I$, isomorphic to the permutation group $A_{5}$, has also been utilized in lepton flavor symmetry in Refs. [@Cummins:1988dr; @shirai; @Luhn:2007yr] (also see recent reviews in  [@Ludl:2009ft; @Ishimori:2010au]) where the golden ratio also shows up naturally. This suggests a possible connection to $A_5$ as shown in Ref. [@Everett:2008et]. Another interesting parameterization involving the golden ratio is ${\theta_{12}} = {\frac{\pi}{5}} = 
\cos^{-1} (\frac{\phi}{2})$ and $\theta_{\rm cabibbo} = \frac{\pi}{12}$ introduced in Ref. [@Rodejohann:2008ir] for both the lepton and quark sectors. This might have connection with the $A_5$ group as well.

In this paper we propose the four generation lepton sector fit into the context of an $A_{5}\times Z_{2}\times Z_{3}$ symmetry where $A_5$ subsequently breaks into $A_{4}$, with the goal of retaining the tribimaximal mixing as well as the lepton mass pattern (three hierarchical charged leptons and three tiny neutrino masses). In Section 2 we begin with a brief introduction of the discrete group $A_{5}$ (for more details see Appendix A) and then utilize 