  We provide a systematic and thorough exploration of lepton flavor models in
which the solar mixing angle is related to the golden ratio. For scenarios in
which the solar mixing angle is given by the inverse cotangent of the golden
ratio, we demonstrate that $A_5$ is the smallest non-Abelian finite group that
contains all of the symmetries necessary to enforce this specific lepton mixing
pattern. Within this context, we propose two lepton flavor models that yield
this mixing pattern through the breaking of $A_5$ at leading order to the Klein
four subgroup in the neutrino sector. Both models have triplet embeddings of
the lepton doublets as well as the charged lepton singlets. In the charged
lepton sector, the residual symmetry is $Z_5$ in the first model, while in the
second model, $A_5$ is broken completely at leading order. For the second
model, the reactor mixing angle vanishes at leading order and is of the order
of the square of the Cabibbo angle at next-to-leading order, which is allowed
by the global analysis of current lepton data.
