  We put forth a Fierzed hopping expansion for strong coupling Wilson fermions.
As an application, we show that the strong coupling Schwinger model on
parallelogram lattices with nonbacktracking Wilson fermions span, as a function
of the lattice skewness angle, the $\Delta = -1$ critical line of $6$-vertex
models. This Fierzed formulation also applies to backtracking Wilson fermions,
which as we describe apparently correspond to richer systems. However, we have
not been able to identify them with exactly solved models.
