  We study some aspects of Gauged Linear Sigma Models corresponding to orbifold
singularities of the form $\BC^r/\Gamma$, for $r=2,3$ and $\Gamma = \BZ_n$ and
$\BZ_n\times \BZ_m$. These orbifolds might be tachyonic in general. We compute
expressions for the multi parameter sigma model Lagrangians for these
orbifolds, in terms of their toric geometry data. Using this, we analyze some
aspects of the phases of generic orbifolds of $\BC^r$.
