  Symmetry-protected and symmetry-enriched topological (SPT/SET) phases in
three dimensions are quantum systems that support non-trivial two-dimensional
surface states. These surface states develop finite excitation energy gaps when
the relevant symmetries are broken. On the other hand, one-dimensional gapless
modes can populate along interfaces that separate adjacent gapped surface
domains with distinct symmetry-breaking orders. A surface strip pattern in
general reduces the low-energy SPT/SET surface degrees of freedom onto a 2D
array of gapless 1D channels. These channels can be coupled to one another by
quasiparticle tunneling, and these inter-wire interactions collectively provide
an effective description of the surface state. In this paper, we study a
general class of symmetry-preserving or breaking SPT/SET surface states that
admit finite excitation energy gaps and Abelian topological orders via the
coupled wire construction. In particular, we focus on the prototype Abelian
surface topological orders that fall under the $ADE$ classification of
simply-laced Lie algebras. We also elaborate on the emergent symmetry and
duality properties of the coupled wire models.
