  We examine Li's double determinantal varieties in the special case that they
are toric. We recover from the general double determinantal varieties case, via
a more elementary argument, that they are irreducible and show that toric
double determinantal varieties are smooth. We use this framework to give a
straighforward formula for their dimension. Finally, we use the smallest
nontrivial toric double determinantal variety to provide some empirical
evidence concerning an open problem in local algebra.
