  In this paper, we first find an estimate for the range of polyharmonic
mappings in the class $HC_{p}^{0}$. Then, we obtain two characterizations in
terms of the convolution for polyharmonic mappings to be starlike of order
$\alpha$, and convex of order $\beta$, respectively. Finally, we study the
radii of starlikeness and convexity for polyharmonic mappings, under certain
coefficient conditions.
