Five new polar intermetallic compounds in the Ae-Ga-Au system (Ae = Ba, Eu), BaAu(5)Ga(2) (I), BaAu(4.3)Ga(2.7) (II), Ba(1.0)Au(4.5)Ga(2.4 )(III), EuAu(4.8)Ga(2.2) (IV), and Eu(1.1)Au(4.4)Ga(2.2) (V), have been synthesized and their crystal structures determined by single-crystal X-ray diffraction. I crystallizes in the orthorhombic crystal system with a large unit cell [Pearson symbol oP64; Pnma, Z = 8, a = 8.8350(5) Å, b = 7.1888(3)Å, c = 20.3880(7) Å], whereas all other compounds are hexagonal [hP24; P6̅2m, Z = 3, a = 8.54-8.77(1) Å, c = 7.19-7.24(1) Å]. Both structures contain mutually orthogonal layers of Au(6) hexagons in chair and boat conformations, resulting in a hexagonal diamond-like network. Ae atoms and additional (Au/Ga)(3) groups are formally encapsulated by (Au(6))(2) distorted hexagonal prisms formed of three edge-sharing hexagons in the boat conformation or, alternatively, lie between two Au(6) hexagons in the chair conformation. The (Au/Ga)(3) groups can be substituted by Ae atoms in some of the hexagonal structures with no change to the structural symmetry. Tight-binding electronic structure calculations using linear-muffin-tin-orbital methods on idealized models "BaAu(5)Ga(2)" and "BaAu(4)Ga(3)" show both compounds to be metallic with evident pseudogaps near the corresponding Fermi levels. The integrated crystal orbital Hamilton populations are dominated by Au-Au and Au-Ga orbital interactions, although Ba-Au and Ba-Ga contributions are significant. Furthermore, Au-Au interactions vary considerably along different directions in the unit cells, with the largest values for the hexagons in the boat conformation and the lowest values for those in the chair conformation. II revealed that partial substitution of Au atoms in the hexagonal diamond net by a post-transition element (Ga) may occur in this family, whereas the sizes of the (Au/Ga)(3) groups and strong Ba-Au covalent interactions allow for their mutual replacement in the voids.