Abstract: Graphene has become one of the most widely used new materials because of its unique hexagonal lattice

structure，which has excellent mechanical， thermal，optical and electrical properties.From the point of view of

solid state physics teaching， taking the lattice structure of single-layer graphene as an example， this paper describes

the normal lattice primitive cell and base vector， inverted lattice primitive cell and base vector，wave vector space

and first Brillouin region of two-dimensional hexagonal lattice in the form of images，and derives the vibration mode

of two-dimensional hexagonal lattice.

Key words: hexagonal lattice, lattice structure, lattice vibration, graphene