  Let $K$ be a unit ball of some norm in $R^n$. For an arbitrary direction
$u\in R^n$, there is associated a unit-ball $K_u$, which is rotationally
invariant with respect to rotations keeping $u$ fixed, called the $u$-spin of
$K_u$. It is proved that $K$ is a zonoid if and only if all of its spins are
zonoids.
