  We consider Diagram algebras, $\Dg(G)$ (generalized Temperley-Lieb algebras)
defined for a large class of graphs $G$, including those of relevance for cubic
lattice Potts models, and study their structure for generic $Q$. We find that
these algebras are too large to play the precisely analogous role in three
dimensions to that played by the Temperley-Lieb algebras for generic $Q$ in the
planar case. We outline measures to extract the quotient algebra that would
illuminate the physics of three dimensional Potts models.
