  Many of the interesting patterns seen in recent multi-frequency Faraday
experiments can be understood on the basis of three-wave interactions (resonant
triads). In this paper we consider two-frequency forcing and focus on a
resonant triad that occurs near the bicritical point where two pattern-forming
modes with distinct wavenumbers emerge simultaneously. This triad has been
observed directly (in the form of rhomboids) and has also been implicated in
the formation of quasipatterns and superlattices. We show how the symmetries of
the undamped unforced problem (time translation, time reversal, and Hamiltonian
structure) can be used, when the damping is weak, to obtain general scaling
laws and additional qualitative properties of the normal form coefficients
governing the pattern selection process near onset; such features help to
explain why this particular triad is seen only for certain "low" forcing
ratios, and predict the existence of drifting solutions and heteroclinic
cycles. We confirm the anticipated parameter dependence of the coefficients and
investigate its dynamical consequences using coefficients derived numerically
from a quasipotential formulation of the Faraday problem due to Zhang and
Vinals.
