Sentence embeddings play an important role in tasks such as clustering, semantic search, and retrieval-augmented generation, yet they generally lack interpretability. We propose a framework for decomposing embeddings into interpretable components, which we define as semantic regions, i.e. connected subsets on the embedding hypersphere. These regions reveal both the internal semantic structure of individual embeddings and the set-theoretical relationships between them. We further show that these regions exhibit a hierarchical organization that reflects semantic inclusion, including hypernymy and hyponymy relations. Empirical results across both synthetic and real-world datasets validate the existence of these regions and demonstrate their utility for sentence embedding interpretability.