We explore the idea of a network of defects to live inside a domain wall in
models of three real scalar fields, engendering the Z(2)X(3) symmetry. The
field that governs the Z(2) symmetry generates a domain wall, and entraps
the hexagonal network formed by the three junctions of the model of two sca
lar fields that describes the remaining Z(3) symmetry. If the host domain w
all bends to spherical form, in the thin wall approximation there may appea
r nontopological structures hosting networks that accept diverse patterns.
If Z(3) is also broken, the model may generate a buckyball containing 60 ju
nctions, a fullerenelike structure. Applications to cosmology are outlined.