From symmetry arguments and the conceptual phase diagrams previously developed, it is shown that the gross features of the energy bands can be rationalized for compounds crystallizing in the pyrite, marcasite and arsenopyrite structures. The structure-determining interactions are argued to be cation-anion interactions, not cation-cation interactions. With the exception of the MnX 2 chalcogenides and CrSb 2, the 3d electrons appear to be itinerant, not localized; and the crystallographic determinant is not the conventional Jahn-Teller mechanism. Even the arsenopyrite structure, which would appear to reflect cation-cation homopolar bonding, may have a larger electron density in the larger cation-cation separations because the cation-anion interactions are dominant. Finally, the measured physical properties are shown to satisfy not only the requirements of the band schemes for these structures, but also the constraints of the periodic table in comparison with other transition-metal compounds.