Domain wall networks on solitons

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)xZ(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.