Quote by meopemuk
The shape of the 1st BZ is determined by the lattice periodicity. Positions of k points in the Brillouin zone are determined by the size and shape of the crystal. Usually, periodic boundary conditions are applied on the crystal boundary, so the crystal as a whole is assumed to form a periodic unit cell. The size of this unit cell is huge, so the distance between kpoints is very small. For all practical purposes one can assume that the crystal is infinite, and that actual positions of the kpoints have no physical significance, and summations over kpoints can be replaced by integrations in the kspace.
Eugene.

I am now constructing a crystal of theoretically finite size. Can I understand as that, for a triangular lattice, the positions of k points exactly form a "triangular lattice" too in the 1st BZ? Thanks a lot!