  We generalize the Majorana stellar representation of spin-$s$ pure states to
mixed states, and in general to any hermitian operator, defining a bijective
correspondence between three spaces: the spin density-matrices, a projective
space of homogeneous polynomials of four variables, and a set of equivalence
classes of points (constellations) on spheres of different radii. The
representation behaves well under rotations by construction, and also under
partial traces where the reduced density matrices inherit their constellation
classes from the original state $\rho$. We express several concepts and
operations related to density matrices in terms of the corresponding
polynomials, such as the anticoherence criterion and the tensor representation
of spin-$s$ states described in [1].
