  Methylammonium lead iodide, as related organometal halide perovskites,
emerged recently as a particularly attractive material for photovoltaic
applications. The origin of its appealing properties is sometimes assigned to
its potential ferroelectric character, which remains however a topic of intense
debate. Here, we rationalize from first-principles calculations how the spatial
arrangement of methylammonium polar molecules is progressively constrained by
the subtle interplay between their tendency to bond with the inorganic
framework and the appearance of iodine octahedra rotations inherent to the
perovskite structure. The disordered tetragonal phase observed at room
temperature is paraelectric. We show that it should a priori become
ferroelectric but that iodine octahedra rotations drive the system toward an
antipolar orthorhombic ground state, making it a missed ferroelectric.
