The electronic structure of inorganic solids such as Li2Ga and Li9Al4 containing infinite zigzag homoatomic chains is discussed. It is shown that Li2Ga, a solid for which a Zintl-type electron-counting approach would suggest that a half-filled pi-type band occurs as in trans-polyacetylene, is really a three-dimensional solid with strong covalent interchain connections and small effective charge transfer. The zigzag chains do not play a dominant role as far as the electronic structure near the Fermi level is concerned, and there is no reason for the occurrence of a Peierls distortion despite the possible analogy with trans-polyacetylene. It is suggested that even assuming that a Zintl-type approach is appropriate for electron counting purposes, the infinite zigzag chains in this compound and those in trans-polyacetylene are not isolobal. The bonding in Li9Al4 and Li2Ga is very similar, and both phases are predicted to be stable three-dimensional metals.