  A discrete-time staggered quantum walk was recently introduced as a
generalization that allows to unify other versions, such as the coined and
Szegedy's walk. However, it also produces new forms of quantum walks not
covered by previous versions. To explore their properties, we study here the
staggered walk on a hexagonal lattice. Such a walk is defined using a set of
overlapping tessellations that cover the graph edges, and each tessellation is
a partition of the node set into cliques. The hexagonal lattice requires at
least three tessellations. Each tessellation is associated with a local unitary
operator and the product of the local operators defines the evolution operator
of the staggered walk on the graph. After defining the evolution operator on
the hexagonal lattice, we analyze the quantum walk dynamics with the focus on
the position standard deviation and localization. We also obtain analytic
results for the time complexity of spatial search algorithms with one marked
node using cyclic boundary conditions.
