  Domain wall networks on the surface of a soliton are studied in a simple
theory. It consists of two complex scalar fields, in (3+1)-dimensions, with a
global U(1) x Z_n symmetry, where n>2. Solutions are computed numerically in
which one of the fields forms a Q-ball and the other field forms a network of
domain walls localized on the surface of the Q-ball. Examples are presented in
which the domain walls lie along the edges of a spherical polyhedron, forming
junctions at its vertices. It is explained why only a small restricted class of
polyhedra can arise as domain wall networks.
