This paper deals with a polymer version of the topological pi-spin polarization interrelated to the topological superdegeneracy of crystal orbitals of infinite or extended polymeric spin systems and also with a VB picture of their spin structure in terms of simple electronic band calculations. We stress that the theoretical models (traveling wave approach) introduced predict essential features of magnetic properties of polymeric systems which yield crucial aspects for their materials design. The model calculation has also been made for various types of inter-polymer interactions in order to understand the topological spin polarization of higher-dimensional infinite or extended polymeric spin systems and the topological nature of inter-polymer contacts (inter-polymer connectedness). The results have shown that the connectedness gives rise to the prominent modulation of band structures and pi spin polarizations which is highly dependent on the topology of the contacts. Thus, the results serve for molecular designs for novel intriguing organic magnetic systems such as multifunctionality molecular magnetic materials. The VB representation in the k space has disclosed such a physical picture for the infinite spin system that can not be expected from the simple or intuitive extension obtained for a finite system. Naturally, in the VB picture the contributing weight of a particular spin structure undergoes fluctuation in the k space as the physical consequence of the intersegment interaction in the infinite system.