  The paper is devoted to the convex-set counterpart of the theory of weak$^*$
derived sets initiated by Banach and Mazurkiewicz for subspaces. The main
result is the following: For every nonreflexive Banach space $X$ and every
countable successor ordinal $\alpha$, there exists a convex subset $A$ in $X^*$
such that $\alpha$ is the least ordinal for which the weak$^*$ derived set of
order $\alpha$ coincides with the weak$^*$ closure of $A$. This result extends
the previously known results on weak$^*$ derived sets by Ostrovskii (2011) and
Silber (2021).
