  Given a toric metrized R-divisor on a toric variety over a global field, we
give a formula for the essential minimum of the associated height function.
Under suitable positivity conditions, we also give formulae for all the
successive minima. We apply these results to the study, in the toric setting,
of the relation between the successive minima and other arithmetic invariants
like the height and the arithmetic volume. We also apply our formulae to
compute the successive minima for several families of examples, including
weighted projective spaces, toric bundles and translates of subtori.
