  We report on surface wave pattern formation in a Faraday experiment operated
at a very shallow filling level, where modes with a subharmonic and harmonic
time dependence interact. Associated with this distinct temporal behavior are
different pattern selection mechanisms, favoring squares or hexagons,
respectively. In a series of bifurcations running through a pair of
superlattices the surface wave pattern transforms between the two incompatible
symmetries. The close analogy to 2D and 3D crystallography is pointed out.
