  A harmonic mapping is a univalent harmonic function of one complex variable.
We define a family of harmonic mappings on the unit disk whose images are
rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$.
These mappings are analogous to the $n$-cusped hypocycloid, but are modified by
Gauss hypergeometric factors, both in the analytic and co-analytic parts.
Relative rotations by an angle $\beta$ of the analytic and anti-analytic parts
lead to graphs that have cyclic, and in some cases dihedral symmetry of order
$n$. While the graphs for different $\beta$ can be dissimilar, the cusps are
aligned along axes that are independent of $\beta$. For certain isolated values
of $\beta$, the boundary function is continuous with arcs of constancy, and has
nodes of interior angle $\pi/2-\pi/n$.
