  We discuss a particularly symmetric model of neutrino mixings where, with
good accuracy, the atmospheric mixing angle theta_{23} is maximal, theta_{13}=0
and the solar angle satisfies sin^2(theta_{12})=1/3 (Harrison-Perkins-Scott
(HPS) matrix). The discrete symmetry A_4 is a suitable symmetry group for the
realization of this type of model. We construct a model where the HPS matrix is
exactly obtained in a first approximation without imposing ad hoc relations
among parameters. The crucial issue of the required VEV alignment in the scalar
sector is discussed and we present a natural solution of this problem based on
a formulation with extra dimensions. We study the corrections from higher
dimensionality operators allowed by the symmetries of the model and discuss the
conditions on the cut-off scales and the VEVs in order for these corrections to
be completely under control. Finally, the observed hierarchy of charged lepton
masses is obtained by assuming a larger flavour symmetry. We also show that,
under general conditions, a maximal theta_{23} can never arise from an exact
flavour symmetry.
