The title phases were synthesized via high-temperature reactions of the elements in welded Ta tubes and characterized by single-crystal X-ray diffraction methods and band calculations. BaIrIn4 adopts the LaCoAl4-type structure: Pmma, Z = 2, a = 8.642(2), b = 4,396(1), and c = 7.906(2) angstrom. Ba2Ir4In13 exhibits a new structure type: Cmc2(1), Z = 4, a = 4.4856(9), b = 29.052(6), and c = 13.687(3) angstrom. BaIrIn4 is constructed from a single basic unit, a Ba-centered pentagonal prism of indium on which two adjacent and the opposed rectangular faces are capped by In and Ir, respectively. The three capping atoms are coplanar with Ba and represent the only augmentation of the pentagonal prism. The relatively large proportions of Ba:Ir, In, and of In:Ir lead to the condensation of homoatomic pentagonal prisms into zigzag chains through the sharing of the two uncapped faces. The cation proportion is much lower in Ba2Ir4In13, and Ba atoms are surrounded by a more anionic Ir/In network without any condensation between prisms. This and the greater Ir proportion lead to a network of formal augmented pentagonal Ba@Ir5In15 and hexagonal Ba@Ir7In15 prisms with overall 5-10-5 and 6-10-6 arrangements of parallel planar rings, respectively, although most Ir is not well bound to the prisms. The latter prism, with alternating Ir/In atoms in the basal faces, is novel for Ae-T-In phases (Ae = alkaline-earth metal, T = Co, Rh, Ir). Band structure calculation results (linear-muff in-tin-orbital method in the atomic sphere approximation) emphasize the greater overlap populations (similar to strengths) of the Ir-In bonds and confirm expectations that both compounds are metallic. The Ir 5d bands are narrower and lie higher in energy than those for Au in analogous phases.