The geometrical model of graphene is the flat honeycomb lattice, so the Brillouin zone is also flat honeycomb lattice. However, monolayer of transition metal dichalcogenides is not flat as it consists of three atomic layers. So why is Brilloin zone for TMDs still flat?
I'm not expert in the solid state physics, but, in my understanding, the first Brillouin zone is primarily constructed from a unit (primitive) cell of a crystal. Mathematically it's done if we take a Fourier transform of the unit cell of the crystall in real space (meaning cartesian coordinate system, xyz). So, Fourier transform of the 2D flat graphene geometry in real space produces flat geometry in reciprocal space. However, a monolayer of TMDs is depicted in literature as three layers of atoms, and from geometrical point of view it's not in the plane anymore. So unit cell is no longer flat, but some sort of parallelepiped, I guess (or maybe some other 3D shape). So Fourier transform of a 3D object should also be 3D. That's where I'm confused.