Periodic Boundary Conditions on non sq lattice

[cmphys1]

Is it possible to impose boundary conditions on the other 2d lattices like
a rhombic lattice?
a hexagonal lattice?
an oblique lattice?

How does one typically index such lattices?

 

[olgranpappy]

Yes, and in the same way as for a square lattice. In any lattice you still have basis vectors. For example, in the hexagonal lattice the basis vectors can be chosen to look like they point along two sides of a triangle. Call one of these \vec R_1 and the other \vec R_2. You can pick some N_1 tending to infinity and identify the lattice point N_1 \vec R_1 with 0. Also pick some N_2 tending to infinity and identify the lattice point N_2 \vec R_2 with 0. Then you have periodic boundary conditions.