Intrinsically multilayer moiré heterostructures

We introduce trilayer and multilayer moir\'e heterostructures that cannot be viewed from the ``moir\'e-of-moir\'e'' perspective of helically twisted graphene. These ``intrinsically trilayer'' systems feature periodic modulation a local quasicrystalline structure. They open door to realizing with vastly more material constituents because they do not constrain lattice constants layers. In this manuscript, we define intrinsically patterns, provide recipe for their construction, derive configuration space, connect visual patterns physical observables in systems.