  A poloidal tilting symmetry of the local nonlinear $\delta f$ gyrokinetic
model is demonstrated analytically and verified numerically. This symmetry
shows that poloidally rotating all the flux surface shaping effects with large
poloidal mode number by a single tilt angle has an exponentially small effect
on the transport properties of a tokamak. This is shown using a generalization
of the Miller local equilibrium model to specify an arbitrary flux surface
geometry. With this geometry specification we find that, when performing an
expansion in large flux surface shaping mode number, the governing equations of
gyrokinetics are symmetric in the poloidal tilt of the high order shaping
effects. This allows us to take the fluxes from a single configuration and
calculate the fluxes in any configuration that can be produced by tilting the
large mode number shaping effects. This creates a distinction between tokamaks
with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which
is expected to have important consequences for generating toroidal rotation
using up-down asymmetry.
