Combinatorial Reid's recipe for consistent dimer models

Reid's recipe for a finite abelian subgroup G⊂ SL(3,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-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. Comment: 29 pages, published version