Lanthanum hexaboride is one of the cathode materials most used in high-power electronics technology, but the many experimental results do not provide a consistent picture of the surface properties. Therefore, we report the first ab initio calculations of the work functions and surface energies of the (001), (011), (111), (112), and (012) surfaces by considering the different surface terminations and structural relaxation. Either the (111)B- or the (001) La-terminated surface is the most stable, depending on La chemical potential. The work function of the latter is the lowest (2.07 eV) of the surfaces considered. Both the work function and surface energy decrease further when surface La is replaced by Ba and become, respectively, 1.43 and 7.7 eV/nm(2) at the chemical potentials of elemental lanthanum and barium bulk. These results compare favorably with previous work on the intermetallics BaAl4, CaAl4, and BaAuIn3. Their most stable surfaces possess the lowest work function. Now, we study a compound with a decidedly different crystal type and with its constituting elements from column 3 of the periodic table, of which one is nonmetallic.