Probability that a band-gap extremum is located on the irreducible Brillouin-zone contour for the 17 different plane crystallographic lattices

After recalling the first Brillouin zone (BZ) and the first irreducible Brillouin zone (IBZ) of a lattice in terms of its plane crystallographic group, we investigate the danger of restricting a band-gap detection to the contour of the IBZ, instead of its full IBZ. Based on hundreds of porous phononic crystal simulations, we provide for the 17 plane crystallographic groups (i) statistics of the band-gap localizations, (ii) probabilities to get non-full band-gaps, and (iii) averages of the bandwidth error made when only the IBZ contour is considered. It is found that for phononic crystals, the IBZ contour provides accurate results only for highly symmetric lattices.