Combinatorial Reid's recipe for consistent dimer models

Reid’s recipe for a finite abelian subgroup $G\subset $\text{SL}$(3,$\mathbb{C}$)$ is a combinatorial procedure that marks the toric fan of the $G$-Hilbert scheme with irreducible representations of $G$. The geometric McKay correspondence conjecture of Cautis–Logvinenko that describes certain objects in the derived category of $G\text{-Hilb}$ in terms of Reid’s recipe was later proved by Logvinenko et al. We generalise Reid’s recipe to any consistent dimer model by marking the toric fan of a crepant resolution of the vaccuum moduli space in a manner that is compatible with the geometric correspondence of Bocklandt–Craw–Quintero-V'{e}lez. Our main tool generalises the jigsaw transformations of Nakamura to consistent dimer models.