  We construct a statistical model that reproduces the BPS partition function
of D4-D2-D0 bound states on a class of toric Calabi-Yau three-folds. The
Calabi-Yau three-folds we consider are obtained by adding a compact two-cycle
to $A_{N-1}$-ALE $\times \mathbb{C}$. We show that in the small radii limit of
the Calabi-Yau the D4-D2-D0 partition function is correctly reproduced by
counting the number of triangles and parallelograms.
