  For $n\geq 4$ (even), the function
$\varphi_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps the unit disk
$\mathbb{D}$ onto a domain bounded by an epicycloid with $n-1$ cusps. In this
paper, the class $\mathcal{S}^*_{n\mathcal{L}} =
\mathcal{S}^*(\varphi_{n\mathcal{L}})$ is studied and various inclusion
relations are established with other subclasses of starlike functions. The
bounds on initial coefficients is also computed. Various radii problems are
also solved for the class $\mathcal{S}^*_{n\mathcal{L}}$.
