This study addresses the interpretability of word representations through an investigation of a count-based co-occurrence matrix. Employing the mathematical methodology of Formal Concept Analysis, we reveal an underlying structure that is amenable to human interpretation. Furthermore, we unveil the emergence of hierarchical and geometrical structures within word vectors as consequences of word usage. Our experiments on the PPMI matrix demonstrate that the formal concepts that we identified align with interpretable categories, as shown in the category completion task.