  Van der Waals heterostructures form a massive interdisciplinary research
field, fueled by the rich material science opportunities presented by layer
assembly of artificial solids with controlled composition, order and relative
rotation of adjacent atomic planes. Here we use atomic resolution transmission
electron microscopy and multiscale modeling to show that the lattice of MoS$_2$
and WS$_2$ bilayers twisted to a small angle, $\theta<3^{\circ}$, reconstructs
into energetically favorable stacking domains separated by a network of
stacking faults. For crystal alignments close to 3R stacking, a tessellated
pattern of mirror reflected triangular 3R domains emerges, separated by a
network of partial dislocations which persist to the smallest twist angles.
Scanning tunneling measurements show that the electronic properties of those 3R
domains appear qualitatively different from 2H TMDs, featuring layer-polarized
conduction band states caused by lack of both inversion and mirror symmetry. In
contrast, for alignments close to 2H stacking, stable 2H domains dominate, with
nuclei of an earlier unnoticed metastable phase limited to $\sim$ 5nm in size.
This appears as a kagome-like pattern at $\theta\sim 1^{\circ}$, transitioning
at $\theta\rightarrow 0$ to a hexagonal array of screw dislocations separating
large-area 2H domains.
