  We construct embeddings of Bers slices of ideal polygon reflection groups
into the classical family of univalent functions $\Sigma$. This embedding is
such that the conformal mating of the reflection group with the
anti-holomorphic polynomial $z\mapsto\overline{z}^d$ is the Schwarz reflection
map arising from the corresponding map in $\Sigma$. We characterize the image
of this embedding in $\Sigma$ as a family of univalent rational maps. Moreover,
we show that the limit set of every Kleinian reflection group in the closure of
the Bers slice is naturally homeomorphic to the Julia set of an
anti-holomorphic polynomial.
