  Spherical Proca Stars (PSs) are regarded as the ground state amongst the
family of PSs. In accordance, spherical PSs are thought to have a fundamental
branch of stable solutions. In this Letter, we provide energetic, morphological
and dynamical evidence that spherical PSs are actually excited states. The
ground state is shown to be a family of static, non-spherical, in fact prolate,
PSs. The spherical stars in the fundamental branch, albeit stable against
spherical perturbations, turn out to succumb to non-spherical dynamics,
undergoing an isometry breaking into prolate PSs. We also provide evidence for
the dynamical formation of prolate PSs, starting from spherical dilute initial
data, via gravitational cooling. Consequently, PSs provide a remarkable example
of (possibly compact) relativistic stars, in General Relativity minimally
coupled to a simple, physical, field theory model, where staticity plus
stability implies non-sphericity.
