Rather unexpected spin-symmetry breakings of mean-field single determinants occur in singlet ground states of many families of alternating conjugated hydrocarbons which accept a full on-bond electron pairing. These symmetry breakings may be seen as an indication of the existence of unpaired electrons. Although qualitative, the concept of disjoint electronic sextets proposed by Clar (hereafter called CS) is at least a heuristic tool for predicting various features of fused polybenzenic hydrocarbons. The present work shows that identifying the preferred CS distribution enables one to rationalize the existence of one or several spin-symmetry breakings, i.e., the existence and the number of unpaired electrons in altemant fused polycyclic hydrocarbons via a simple recipe for the prediction of these features. This recipe is based on comparison between various distributions of CS on the molecular frame, subject to a restriction concerning the fragments of the graph that do not belong to the CS. This rule is successfully confronted to UDFT calculations and to a recently proposed criterion predicting the possible occurrence of spin-symmetry breaking from the topological Huckel Hamiltonian. The confrontation runs on series of rhombuses, periacenes, anthenes, and other graphene flakes or nanoribbons. The CS distribution definitely offers a qualitative guide to look at the possible occurrence of (multiple) symmetry breakings in polycyclic architectures which are commonly seen as closed-shell singlets.