  Imposing incommensurable periodicity on the periodic atomic lattice can lead
to complex structural phases consisting of locally periodic structure bounded
by topological defects. Twisted trilayer graphene (TTG) is an ideal material
platform to study the interplay between different atomic periodicities, which
can be tuned by twist angles between the layers, leading to moir\'e-of-moir\'e
lattices. Interlayer and intralayer interactions between two interfaces in TTG
transform this moir\'e-of-moir\'e lattice into an intricate network of domain
structures at small twist angles, which can harbor exotic electronic behaviors.
Here we report a complete structural phase diagram of TTG with atomic scale
lattice reconstruction. Using transmission electron microscopy combined with a
new interatomic potential simulation, we show that a cornucopia of large-scale
moir\'e lattices, ranging from triangular, kagome, and a corner-shared
hexagram-shaped domain pattern, are present. For small twist angles below
0.1{\deg}, all domains are bounded by a network of two-dimensional domain wall
lattices. In particular, in the limit of small twist angles, the competition
between interlayer stacking energy and the formation of discommensurate domain
walls leads to unique spontaneous symmetry breaking structures with nematic
orders, suggesting the pivotal role of long-range interactions across entire
layers. The diverse tessellation of distinct domains, whose topological network
can be tuned by the adjustment of the twist angles, establishes TTG as a
platform for exploring the interplay between emerging quantum properties and
controllable nontrivial lattices.
