  In an idealized infinite crystal, the material properties are constrained by
the symmetries of its unit cell. Naturally, the point-group symmetry is broken
by the sample shape of any finite crystal, yet this is commonly unobservable in
macroscopic metals. To sense the shape-induced symmetry lowering in such
metals, long-lived bulk states originating from anisotropic Fermi surfaces are
needed. Here we show how strongly facetted Fermi surfaces and long
quasiparticle mean free paths present in microstructures of PdCoO2 yield an
in-plane resistivity anisotropy that is forbidden by symmetry on an infinite
hexagonal lattice. Bar shaped transport devices narrower than the mean free
path are carved from single crystals using focused ion beam (FIB) milling, such
that the ballistic charge carriers at low temperatures frequently collide with
both sidewalls defining a channel. Two symmetry-forbidden transport signatures
appear: the in-plane resistivity anisotropy exceeds a factor of 2, and
transverse voltages appear in zero magnetic field. We robustly identify the
channel direction as the source of symmetry breaking via ballistic Monte- Carlo
simulations and numerical solution of the Boltzmann equation.
