  A topological defect network (TDN) is formed by a network of topological
defects embedded within a topological quantum field theory (TQFT). TDNs were
introduced recently for the purpose of describing fracton topological phases of
matter using the framework of defect TQFT. Their effectiveness has been
demonstrated through numerous examples, yet a systematic construction was
lacking. Here we solve this problem by formulating a method to construct TDNs
for a wide range of lattice Hamiltonians. Our method takes a lattice
Hamiltonian as input, applies an ungauging procedure, then creates a refined
lattice within each unit cell, followed by regauging the system to produce a
TDN as output. For topological Calderbank-Shor-Steane (CSS) Pauli stabilizer
models, this procedure is guaranteed to produce a phase equivalent TDN. This
provides TDN representations of canonical fracton models for which no such
construction was previously known, including Haah's cubic code and Yoshida's
infinite family of fractal spin liquid models. We demonstrate the applicability
of our method beyond CSS stabilizer models by constructing TDNs for non-CSS
models including Chamon's model and the semionic X-cube model.
