  We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt
distance to the convex hull of spin coherent states. We derive its analytic
expression in the case of pure states as a function of the smallest eigenvalue
of the Bloch matrix and give explicitly the closest classical state for an
arbitrary pure state. Numerical evidence is provided that the exact formula for
pure states provides an upper bound on the quantumness of mixed states. Due to
the connection between quantumness and entanglement we obtain new insights into
the geometry of symmetric entangled states.
