Key to modeling the topology of a material are the special points along k-vector of the Brillouin zone, accounting for the accurate depiction of the density of states emerging from the electronics of the material. Density functional theory (DFT) analyses predicted an indirect band gap of 0.158 eV in the β-BiI phase with the valence and conduction band maxima localized at the Γ and M k-space points, respectively. Interestingly enough, the major contributors to the band structure around the Fermi level are bismuth's p orbitals of even and odd parity, thus giving the gerade and ungerade points of symmetry.