Notes on TQFT Wire Models and Coherence Equations for $SU(3)$ Triangular Cells

After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for $SU(3)$ spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of $SU(3)$ at level $k$. We show how to solve these equations in a number of examples.