Conceptual spaces are geometric representations of meaning that were proposed by G ̈ardenfors (2000). They share many similarities with the vector space embeddings that are commonly used in natural language processing. However, rather than representing entities in a single vector space, conceptual spaces are usually decomposed into several facets, each of which is then modelled as a relatively low dimensional vector space. Unfortunately, the problem of learning such conceptual spaces has thus far only received limited attention. To address this gap, we analyze how, and to what extent, a given vector space embedding can be decomposed into meaningful facets in an unsupervised fashion. While this problem is highly challenging, we show that useful facets can be discovered by relying on word embeddings to group semantically related features.