Embedding words from a dictionary as vectors in a space has become an active research field, due to its many uses in several natural language processing applications. Distances between the vectors should reflect the relatedness between the corresponding words. The problem with existing word embedding methods is that they often fail to distinguish between synonymous, antonymous, and unrelated word pairs. Meanwhile, polarity detection is crucial for applications such as sentiment analysis. In this work we propose an embedding approach that is designed to capture the polarity issue. The approach is based on embedding the word vectors into a sphere, whereby the dot product between any vectors represents the similarity. Vectors corresponding to synonymous words would be close to each other on the sphere, while a word and its antonym would lie at opposite poles of the sphere. The approach used to design the vectors is a simple relaxation algorithm. The proposed word embedding is successful in distinguishing between synonyms, antonyms, and unrelated word pairs. It achieves results that are better than those of some of the state-of-the-art techniques and competes well with the others.