  Majorana stars, the $2S$ spin coherent states that are orthogonal to a
spin-$S$ state, offer an elegant method to visualize quantum states, disclosing
their intrinsic symmetries. These states are naturally described by the
corresponding multipoles. These quantities can be experimentally determined and
allow for an SU(2)-invariant analysis. We investigate the relationship between
Majorana constellations and state multipoles, thus providing insights into the
underlying symmetries of the system. We illustrate our approach with some
relevant and informative examples.
