  In this paper we generalize some results in \cite{Yu2021} concerning stacked
central configurations. We can deal with the general homogeneous potential
$U_{\alpha}$ (containing the vortex case) in $\mathbb{R}^3$. We give the
admissible set of $\alpha$ for a convex central configuration (with respect to
the Newtonian potential i.e. $\alpha=3$). We discuss some properties of the
regular $n$-gon co-circular central configurations. We also find that the
stacked property is particular for central configurations by studying the
S-balanced configuration case.
