  Symmetry arguments are used to describe all possible two-dimensional periodic
corrugations of graphene ("nanomeshes") capable of inducing tangible
semiconducting gap. Such nanomeshes or superlattices break the initial graphene
translational symmetry in a way that produces mixing and subsequent splitting
of the Dirac K and K' states. All of them have hexagonal Bravais lattice and
are described by space groups that are subgroups of the graphene group. The
first-principles calculations show that the gaps of about 0.5 eV can be induced
at strains safely smaller than the graphene failure strain.
