The isostructural compounds Sr4Bi3, Ba4Bi3, and Ba4Assimilar to2.60 were prepared by direct reactions of the corresponding elements and their structures determined from single-crystal X-ray diffraction data as anti-Th3P4 type in the cubic space group I (4) over bar 3d, Z = 4 (a = 10.101(1) Angstrom, 10.550(1) Angstrom, 9.973(1) Angstrom, respectively). The two bismuth compounds are stoichiometric, and the arsenide refines as Ba4As2.60(2). Only unrelated phases are obtained for all binary combinations among the title components for either Ca or Sb. The magnetic susceptibility and resistivities of Ba4Bi3 and Eu4Bi3 show that they are good metallic conductors (similar to40 muQ.cm at 298 K), whereas Ba4As2.60 exhibits rho(150) > 1000 muQ.cm. The electronic structures of Sr4Bi3, Ba4Bi3, and Ba4As3 were calculated by TB-LMTO-ASA methods. Mixing of cation d states into somewhat disperse valence p bands on Bi results in empty bands at E-F and metallic behavior, whereas the narrower valence band in the electron-deficient Ba4As3 leads to vacancies in about 11% of the anion sites and a valence compound.