  The hoppings of non-interacting particles in the optical dice lattice result
in the gapless dispersions in the band structure formed by the three lowest
minibands. In our research, we find that once a periodic driving force is
applied to this optical dice lattice, the original spectral characteristics
could be changed, forming three gapped quasi-energy bands in the quasi-energy
Brillouin zone. The topological phase diagram containing the Chern number of
the lowest quasi-energy band shows that when the hopping strengths of the
nearest-neighboring hoppings are isotropic, the system persists in the
topologically non-trivial phases with Chern number $C=2$ within a wide range of
the driving strength. Accompanied by the anisotropic nearest-neighboring
hopping strengths, a topological phase transition occurs, making Chern number
change from $C=2$ to $C=1$. This transition is further verified by our
analytical method. Our theoretical work implies that it is feasible to realize
the non-trivially topological characteristics of optical dice lattices by
applying the periodic shaking, and that topological phase transition can be
observed by independently tuning the strength of a type of nearest-neighbor
hopping.
