The new Zintl compounds Ba3Al3P5, Ba3Al3As5, and Ba3Ga3P5 have been synthesized using molten metal fluxes. They are isoelectronic and isotypic, crystallizing with a novel rhombohedral structure type in the space group R (3) over barc with unit cell constants a = 14.5886(9) angstrom, c = 28.990(3) angstrom for Ba3Al3P5, a = 14.613(3) angstrom, c = 28.884(8) angstrom for Ba3Ga3P5, and a = 14.9727(13) angstrom, c = 29.689(4) angstrom for Ba3Al3As5, respectively. The structures are based on TrPn(4) (Tr = Al, Ga; Pn = P, As) tetrahedra that share both edges and corners, leading to intricate arrangements embodied in the [Tr(4)Pn(9)](15-) and [Tr(3)Pn(6)](9-) strands, interconnected by dimeric [Tr(2)Pn(6)](12-) units. The Ba2+ cations reside within cylindrical channels within the polyanionic framework and provide the valence electrons needed for Tr-Pn covalent bonding. In spite of the large and complex structure, there are no homoatomic Tr-Tr or Pn-Pn interactions, hence, the structures can be readily rationalized in the context of the Zintl-Klemm formalism as follows [Ba2+](3)[Tr3+](3)[Pn(3-)](5); calculations on their electronic band-structures confirm this reasoning and reveal about 1.4-1.9 eV energy band gaps, that is, semiconducting behavior. Structural parallels with other known Zintl compounds are also presented.