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Ab initio band structure calculations are carried out for the higher borides MB 6 and MB 12 . Highprecision measurements of the elastic constants are performed for the compounds ZrB 12 , HoB 12 , ErB 12 , TmB 12 , LuB 12 , YB 6 and LaB 6 at low temperatures. The bulk properties of the borides are analyzed on the basis of the calculated equations of states and balanced crystal orbital overlap populations. Our calculations indicate that hexaborides with divalent metals, CaB 6 , SrB 6 , BaB 6 , and YbB 6 , are semiconductors with small energy gaps. The metallic MB 6 hexaborides with trivalent M atoms are found to possess larger bulk moduli values. For dodecaborides the bulk moduli are found to be higher for MB 12 with increased filling of the conduction band ͑ZrB 12 , HfB 12 , UB 12 ͒ in comparison with M 3+ B 12 compounds. The total energy calculations for different magnetic configurations in YbB 12 point to the possibility of antiferromagnetic coupling between Yb 3+ ions.