  Recent experiments have observed hints of hydrodynamic electron flow in a
number of materials, not all of which have an isotropic Fermi surface. We
revisit these experiments in $\mathrm{PdCoO}_2$, a quasi-two-dimensional
material whose Fermi surface is a rounded hexagon, and observe that the data
appears quantitatively consistent with a non-hydrodynamic interpretation.
Nevertheless, motivated by such experiments, we develop a simple model for the
low temperature kinetics and hydrodynamics of a two-dimensional Fermi liquid
with a polygonal Fermi surface. A geometric effect leads to a finite number of
additional long-lived quasihydrodynamic "imbalance" modes and corresponding
qualitative changes in transport at the ballistic-to-hydrodynamic crossover. In
the hydrodynamic limit, we find incoherent diffusion and a new dissipative
component of the viscosity tensor arising from the explicit breaking of
rotational invariance by the Fermi surface. Finally, we compute the conductance
of narrow channels across the ballistic-to-hydrodynamic crossover and
demonstrate a modification of the Gurzhi effect that allows for non-monotonic
temperature and width dependence in the channel conductance.
