  We exploit the presence of approximate (broken) symmetries to obtain general
scaling laws governing the process of pattern formation in weakly damped
Faraday waves. Specifically, we consider a two-frequency forcing function and
trace the effects of time translation, time reversal and Hamiltonian structure
for three illustrative examples: hexagons, two-mode superlattices, and two-mode
rhomboids. By means of explicit parameter symmetries, we show how the size of
various three-wave resonant interactions depends on the frequency ratio m:n and
on the relative temporal phase of the two driving terms. These symmetry-based
predictions are verified for numerically calculated coefficients, and help
explain the results of recent experiments.
