  A discrete-time Quantum Walk (QW) is essentially an operator driving the
evolution of a single particle on the lattice, through local unitaries. Some
QWs admit a continuum limit, leading to well-known physics partial differential
equations, such as the Dirac equation. We show that these simulation results
need not rely on the grid: the Dirac equation in $(2+1)$--dimensions can also
be simulated, through local unitaries, on the honeycomb or the triangular
lattice. The former is of interest in the study of graphene-like materials. The
latter, we argue, opens the door for a generalization of the Dirac equation to
arbitrary discrete surfaces.
