Three new quaternary polar intermetallic compounds of Eu2.94(2)Ca6.06In8Ge8, Eu3.13(2)Ca5.87In8Ge8, and Sr3.23(3)Ca5.77In8Ge8 have been synthesized by a metal-flux method using molten indium metal as a reactive flux, and the novel isotypic crystal structures have been characterized by both powder and single-crystal X-ray diffractions. All compounds crystallize in the orthorhombic space group Pmmn (Z = 2, Pearson symbol oP50) with 14 crystallographically unique atomic positions in the asymmetric unit. The lattice parameters are refined as follows: a = 36.928(2) Å, b = 4.511(1) Å, and c = 7.506(1) Å for Eu2.94(2)Ca6.06In8Ge8; a = 37.171(19) Å, b = 4.531(2) Å, and c = 7.560(4) Å for Eu3.13(2)Ca5.87In8Ge8; and a = 37.350(2) Å, b = 4.550(3) Å, and c = 7.593(4) Å for Sr3.23(3)Ca5.77In8Ge8. In particular, single crystals of two Eu-containing compounds are obtained as bundles of bar/needle-shaped crystals, and the thicknesses of those crystals can be controlled in the range between ca. 300 μm and ca. <10 μm by adjusting several reaction conditions, including the reaction cooling rate and the centrifugation temperature. The overall crystal structure is illustrated as an assembly of (1) the three-dimensional anionic framework, which is formed by the chains of edge-sharing InGe4 tetrahedra and the annulene-like "12-membered anionic rings" connected via Ge2 dimers, and (2) the cationic mixed sites embedded in the space between the anionic frameworks. Theoretical investigations based on tight-binding linear muffin-tin orbital (TB-LMTO) calculations provide a comprehesive understanding of the overall electronic structure and chemical bonding observed among anionic components and between anions and cations. Electron localization function (ELF) and electron density map present chemical bond strengths and polarization within the anionic framework. Magnetic susceptibility measurement proves an antiferromagnetic (AFM) ordering of Eu atoms below 4 K with a reduced effective magnetic moment of 7.12 μB for the Eu atom.