The cluster units obtained by the capping of all faces of a tetrahedron (tetrahedral star, TS) and a trigonal bipyramid (double tetrahedral star, DTS) are used as building units to describe and rationalize framework structures found in the intermetallic structure types NaBa, NaZn13, Th6Mn23, Ba2Li4.21Al4.79, BaHg11, BaCd11, Cr23C6, beta-Mn, Ba3Li3Ga4.1, BaLi4, CaZn3, EuMg5.2, ErZn5, Sr3Mg13, and Sr9Li17.5Al25.5. The electronic requirements for optimum structural stability of these frameworks in the case of sp-bonding have been investigated with the simple tight-binding Huckel model. As a result the networks exhibit a pronounced maximum of stability in the range of 2.1-2.6 electrons per atom with the particular optimum values slightly depending on the kind of basis cluster and its connectivity. Considering the sp-bonded representatives of the above mentioned structure types, the frameworks described by the basis clusters TS and DTS are usually formed by the divalent metals Be, Mg, Zn, Cd, and Hg or a combination of a mono-and a trivalent metal, e.g., (Li,AI), (Cu,AI), or(Ag,AI). More electropositive atoms, Like the heavier alkaline earth metals Ca, Sr, and Ba, are embedded in such frameworks. When applying a formal electron transfer from these atoms to the slightly more electronegative framework forming atoms, the obtained values for the framework valence electron concentration are very close to the calculated optimum ones. Therefore it is argued that this family of intermetallic compounds can still be interpreted as electron compounds following the Zintl-Klemm concept. The new representative BaLi7Al6, which has been synthesized by fusion of the elements and characterized by single-crystal X-ray diffraction methods, supports this idea. BaLi7Al6 is isotypic to NaZn13 (Fm (3) over bar c, a = 12.9377 (9) Angstrom, Z = 8) with the Zn sites mixed occupied by Li and Al atoms.