The isostructural compounds Sr(4)Bi(3), Ba(4)Bi(3), and Ba(4)As( approximately )(2.60) were prepared by direct reactions of the corresponding elements and their structures determined from single-crystal X-ray diffraction data as anti-Th(3)P(4) type in the cubic space group I43d, Z = 4 (a = 10.101(1) A, 10.550(1) A, 9.973 (1) A, respectively). The two bismuth compounds are stoichiometric, and the arsenide refines as Ba(4)As(2.60(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 Ba(4)Bi(3) and Eu(4)Bi(3) show that they are good metallic conductors ( approximately 40 microomega.cm at 298 K), whereas Ba(4)As(2.60) exhibits rho(150) > 1000 microomega.cm. The electronic structures of Sr(4)Bi(3), Ba(4)Bi(3), and Ba(4)As(3) 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 Ba(4)As(3) leads to vacancies in about 11% of the anion sites and a valence compound.