  Shaken optical lattices permit to coherently modify the tunneling of
particles in a controllable manner. We introduce a general relation between the
geometry of shaken lattices and their admissible effective dynamics. Using
three different examples, we illustrate the symmetries of the emerging
tunneling rates. The results provide a clear framework to understand the
relation between lattice geometry and accessible dynamics, and a tool to
straightforwardly derive truncated effective Hamiltonians on arbitrary
geometries.

Quantum Physics;Quantum Gases