  Recent experiments by Kudrolli, Pier and Gollub on surface waves,
parametrically excited by two-frequency forcing, show a transition from a small
hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We
show that generically the hexagons and the superlattice wave patterns bifurcate
simultaneously from the flat surface state as the forcing amplitude is
increased, and that the experimentally-observed transition can be described by
considering a low-dimensional bifurcation problem. A number of predictions come
out of this general analysis.
