We investigate several models of coupled scalar fields that present discret
e Z(2), Z(2) x Z(2), Z(3) and other symmetries. These models support topolo
gical domain wall solutions of the BPS and non-BPS type. The BPS solutions
are stable, but the stability of the non-BPS solutions may depend on the pa
rameters that specify the models. The BPS and non-BPS states give rise to b
ags, and also to three-junctions that may allow the presence of networks of
topological defects. In particular, we show that the non-BPS defects of a
specific model that engenders the Z(3) symmetry give rise to a stable regul
ar hexagonal network of domain walls.