  For any $n\in \mathbb{N}$, $n\geq 2$, we construct a real analytic,
one-parameter family of compact embedded CMC annuli with free boundary in the
unit ball $\mathbb{B}^3$ of $\mathbb{R}^3$ with a prismatic symmetry group of
order $4n$. These examples give a negative answer to the uniqueness problem by
Nitsche and Wente of whether any annular solution to the partitioning problem
in the ball should be rotational.
