  We study fishnet Feynman diagrams defined by a certain triangulation of a
planar n-gon, with massless scalars propagating along and across the cuts. Our
solution theory uses the technique of Separation of Variables, in combination
with the theory of symmetric polynomials and Mellin space. The n-point
split-ladders are solved by a recursion where all building blocks are made
fully explicit. In particular, we find an elegant formula for the coefficient
functions of the light-cone leading logs. When the diagram grows into a
fishnet, we obtain new results exploiting a Cauchy identity decomposition of
the measure over separated variables. This leads to an elementary proof of the
Basso-Dixon formula at 4-points, while at n-points it provides a natural
OPE-like stratification of the diagram. Finally, we propose an independent
approach based on ``stampede" combinatorics to study the light-cone behaviour
of the diagrams as the partition function of a certain vertex model.
