  For a given graph $G=(V,E)$ and permutation $\pi:V\mapsto V$ the prism $\pi
G$ of $G$ is defined as follows: $V(\pi G)=V(G)\cup V(G')$, where $G'$ is a
copy of $G$, and $E(\pi G)=E(G)\cup E(G')\cup M_{\pi}$, where $M_{\pi}=\{uv':
u\in V(G), v=\pi(u)\}$ and $v'$ denotes the copy of $v$ in $G'$.
  We study and compare the properties of convex and weakly convex dominating
sets in prism graphs. In particular, we characterize prism
$\gamma_{con}$-fixers and -doublers. We also show that the differences
$\gamma_{wcon}(G)-\gamma_{wcon}(\pi G)$ and $\gamma_{wcon}(\pi G) -
2\gamma_{wcon}(G)$ can be arbitrarily large, and that the convex domination
number of $\pi G$ cannot be bounded in terms of $\gamma_{con}(G).$
