Why Polygons are Mostly Pointless

When performing materials calculations, one of the most computationally expensive calculations is performing an integral of the electronic band structure of a material. For reasons explained in the talk, integration techniques that rely on non-uniform sampling cannot utilize the full symmetry of the system. To ensure optimal symmetry reduction, calculations should be performed in the symmetrically irreducible Brillouin zone (IBZ). We present an algorithm for finding the IBZ for an arbitrary lattice.