  When two periodic potentials compete in materials, one may adopt the other,
which straightforwardly generates topological defects. Of particular interest
are domain walls in charge-, dipole-, and spin-ordered systems, which govern
macroscopic properties and important functionality. However, detailed atomic
and electronic structures of domain walls have often been uncertain and the
microscopic mechanism of their functionality has been elusive. Here, we clarify
the complete atomic and electronic structures of the domain wall network, a
honeycomb network connected by Z$_{3}$ vortices, in the nearly commensurate
Mott charge-density wave (CDW) phase of 1T-TaS$_{2}$. Scanning tunneling
microscopy resolves characteristic charge orders within domain walls and their
vortices. Density functional theory calculations disclose their unique atomic
relaxations and the metallic in-gap states confined tightly therein. A generic
theory is constructed, which connects this emergent honeycomb network of
conducting electrons to the enhanced superconductivity.
