The crystallochemistry of and the bonding in the orthorhombic four-connected nets of BaIn2 (CeCu2 structure) and of CaPtSn (TiNiSi structure, a derivative of the CeCu2 structure) are analyzed with approximate molecular orbital calculations. Following the Zintl concept, in BaIn2 the In- ions are isoelectronic with group IV tin and should adopt a four-connected structure. In contrast to alpha-tin, which has a cubic diamond structure, the indium ions in BaIn2 build up an orthorhombic three-dimensional four-connected net containing distorted tetrahedra and ladder polymers of four-membered rings. In the CeCu2 structure (space group Imma) two bond angles in these distorted tetrahedra are fixed at 90 degrees. The four-connected net in the CeCu2 structure is topologically related to the layers in black phosphorus (space group Cmca). In CaPtSn (TiNiSi structure) the orthorhombic four-connected net is formed by (PtSn)(2-) ions in an ordered arrangement. Calculations on BaIn2 and CaPtSn show that the four-connected nets are increasingly stabilized as the valence electron count is increased from 16 to 30 valence electrons per 4 formula units. For more than 30e, the nets are destabilized due to filling of M-E antibonding states. Structural data obtained by precise single crystal investigations for the TiNiSi series CaPdIn (20e), CaPdSn (24e), CaPdSb (28e), and CaAgSb (32e), confirm the results of the extended Huckel calculations. We find an interesting and understandable angular asymmetry of the tetrahedral sites in these ternary compounds.