  We analyse metastable states in the East model, using a recently-proposed
patch-repetition analysis based on time-averaged density profiles. The results
reveal a hierarchy of states of varying lifetimes, consistent with previous
studies in which the metastable states were identified and used to explain the
glassy dynamics of the model. We establish a mapping between these states and
configurations of systems of hard rods, which allows us to analyse both typical
and atypical metastable states. We discuss connections between the complexity
of metastable states and large-deviation functions of dynamical quantities,
both in the context of the East model and more generally in glassy systems.
