  Let $H$ be a semisimple Hopf algebra acting on an Artin-Schelter regular
algebra $A$, homogeneously, inner-faithfully, preserving the grading on $A$,
and so that $A$ is an $H$-module algebra. When the fixed subring $A^H$ is also
AS regular, thus providing a generalization of the Chevalley-Shephard-Todd
Theorem, we say that $H$ is a reflection Hopf algebra for $A$. We show that
each of the semisimple Hopf algebras $H_{2n^2}$ of Pansera, and
$\mathcal{A}_{4m}$ and $\mathcal{B}_{4m}$ of Masuoka is a reflection Hopf
algebra for an AS regular algebra of dimension 2 or 3.
