Abstract: Twisted graphene bilayer has been a hot topic in condensed matter physics.Here，a method

for con- structing the geometric structure of graphene supercells is illustrated，which makes use of

the translational symmetry of crystal and the transformation matrix between the supercell and the

primitive cell. Then，the method is applied to construct the structure of twisted graphene bilayers.

This system can be used as an example in the lecture of solid state physics，which is

helpful for students to achieve a better understanding of the mathmatic method of describing the

geometric structure of crystals.

Key words: twisted graphene bilayer, crystal structure, supercell