  We introduce a toric code model on the dice lattice which is exactly solvable
and displays topological order at zero temperature. In the presence of a
magnetic field, the flux dynamics is mapped to the highly frustrated transverse
field Ising model on the kagome lattice. This correspondence suggests an
intriguing disorder by disorder phenomenon in a topologically ordered system
implying that the topological order is extremely robust due to the geometric
frustration. Furthermore, a connection between fully frustrated transverse
field Ising models and topologically ordered systems is demonstrated which
opens an exciting physical playground due to the interplay of topological
quantum order and geometric frustration.
