  We investigate the hexagon formalism in the planar 4d conformal fishnet
theory. This theory arises from N=4 SYM by a deformation that preserves both
conformal symmetry and integrability. Based on this relation, we obtain the
hexagon form factors for a large class of states, including the BMN vacuum,
some excited states, and the Lagrangian density. We apply these form factors to
the computation of several correlators and match the results with direct
Feynman diagrammatic calculations. We also study the renormalisation of the
hexagon form factor expansion for a family of diagonal structure constants and
test the procedure at higher orders through comparison with a known universal
formula for the Lagrangian insertion.
