  Third order amplitude equations on hexagonal lattices can be used for
predicting the existence and stability of stripes, up- and down-hexagons in
pattern forming systems. These amplitude equations predict the nonexistence of
bistable ranges between up- and down-hexagons and tristable ranges between
stripes, up- and down-hexagons. In the present work we use fifth order
amplitude equations for finding such bistable and tristable ranges for a
generalized Swift-Hohenberg equation and discuss stationary front connections
between up- and down-hexagons.
