A general formula W ∞= d/[3( v+ μ 0)] is derived for the normalized Wiener index of infinite polymers, W ∞. It makes possible the calculation of this important polymer descriptor directly from simple structural information: the number of atoms ( ν) and rings (μ 0) in the repeating polymer cell, and the topological distance d (the number of bonds along the shortest path) between the corresponding pairs of equivalent atoms in two neighboring monomer units. In view of the previously shown ([1] D. Bonchev, O. Mekenyan, A topological approach to the calculation of the π-electron energy and energy gap of infinite conjugated polymers, Z. Naturforsch. 35a (1980) 739–747; [2] D. Bonchev, O. Mekenyan, O.E. Polansky, A topological approach to the predicting of the electron energy characteristics of conjugated infinite polymers. II. PPP-calculations. Z. Naturforsch. 36a (1981) 643–646; [3] D. Bonchev, O. Mekenyan, O.E. Polansky, A topological approach to the predicting of the electron energy characteristics of conjugated infinite polymers. III. The influence of some structural modifications of polymers, Z. Naturforsch. 36a (1981) 647–650; [4] O. Mekenyan, S. Dimitrov, D. Bonchev, Graph-theoretical approach to the calculation of physicohemical properties of polymers, Eur. Polym. J. 19 (1963) 1185–1193; [5] D. Bonchev, O. Mekenyan, V. Kamenska, A topological approach to the modeling of polymer properties (the TEMPO method), J. Math. Chem. 11 (1992) 107–132) high correlation of W ∞ with the total π-electron energy and physicochemical properties of polymers, this result might be regarded as a step towards the design of polymers with tailored properties. The approach is illustrated with examples of acyclic polymers, and of polymers with isolated rings, with cata-condensed or peri-condensed rings. The reciprocal relationship with the similar index J ∞ is pointed out and an approximate hyperbolic dependence is presented between these two indices.