  The Hubbard model on the honeycomb lattice is a well known model for
graphene. Equally well known is the Peierls type of instability of the lattice
bond lengths. In the context of these two approximations we ask and answer the
question of the possible lattice distortions for graphene in zero magnetic
field. The answer is that in the thermodynamic limit only periodic,
reflection-symmetric distortions are allowed and these have at most six atoms
per unit cell as compared to two atoms for the undistorted lattice.
