  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 Z_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 scalar
fields that describes the remaining Z_3 symmetry. If the host domain wall bends
to the spherical form, in the thin wall approximation there may appear
non-topological structures hosting networks that accept diverse patterns. If
Z_3 is also broken, the model may generate a buckyball containing sixty
junctions, a fullerene-like structure. Applications to cosmology are outlined.
