Four remarks on spin coherent states

Abstract: We discuss how to recognize the constellations seen in the Majorana representation of quantum states. Then we give explicit formulas for the metric and symplectic form on SU(2) orbits containing general number states. Their metric and symplectic areas differ unless the states are coherent. Finally we discuss some patterns that arise from the Lieb-Solovej map, and for dimensions up to nine we find the location of those states that maximize the Wehrl-Lieb entropy.