  Let $\rho:\mathbb{Z}/k \mathbb{Z}\rightarrow \text{SL}(2,\mathbb{C})$ be a
representation of a finite abelian group and let $\Theta^{\text{gen}}\subset
\text{Hom}_\mathbb{Z}(R(\mathbb{Z}/k\mathbb{Z}),\mathbb{Q})$ be the space of
generic stability conditions on the set of $G$-constellations. We provide a
combinatorial description of all the chambers $C\subset\Theta^{\text{gen}}$ and
prove that there are $k!$ of them. Moreover, we introduce the notion of simple
chamber and we show that, in order to know all toric $G$-constellations, it is
enough to build all simple chambers. We also prove that there are $k\cdot
2^{k-2} $ simple chambers. Finally, we provide an explicit formula for the
tautological bundles $\mathscr{R}_C$ over the moduli spaces $\mathscr{M} _C$
for all chambers $C\subset \Theta^{\text{gen}}$ which only depends upon the
chamber stair which is a combinatorial object attached to the chamber $C$.
