  Three-dimensional (3D) gapped topological phases with fractional excitations
are divided into two subclasses: one has topological order with point-like and
loop-like excitations fully mobile in the 3D space, and the other has fracton
order with point-like excitations constrained in lower-dimensional subspaces.
These exotic phases are often studied by exactly solvable Hamiltonians made of
commuting projectors, which, however, are not capable of describing those
exhibiting surface states with gapless chiral dispersion. Here we introduce a
systematic way, based on cellular construction recently proposed for 3D
topological phases, to construct another type of exactly solvable models in
terms of coupled quantum wires with given inputs of cellular structure,
two-dimensional Abelian topological order, and their gapped interfaces. We show
that our models can describe both 3D topological and fracton orders (and even
their hybrid) and study their universal properties such as quasiparticle
statistics and topological ground-state degeneracy. We also apply this
construction to two-dimensional coupled-wire models with ordinary topological
orders and translation-symmetry-enriched topological orders. Our results pave
the way for effective quantum field theory descriptions or microscopic model
realizations of fracton orders with chiral gapless surface states.
