  We analyze the role of dimensionality in the time evolution of discrete time
quantum walks through the example of the three-state walk on a two-dimensional,
triangular lattice. We show that the three-state Grover walk does not lead to
trapping (localization) or recurrence to the origin, in sharp contrast to the
Grover walk on the two dimensional square lattice. We determine the power law
scaling of the probability at the origin with the method of stationary phase.
We prove that only a special subclass of coin operators can lead to recurrence
and there are no coins leading to localization. The propagation for the
recurrent subclass of coins is quasi one-dimensional.
