We introduce HyperFace, a novel framework for generaing synthetic face recognition datasets and increasing the inter-class variation. We formulate the dataset generation as a packing problem on the embedding space (represented on a hypersphere) of a face recognition model and propose a new synthetic dataset generation approach (called HyperFace). We release several synthetic datasets of face images up to 50,000 unique synthetic identities and 3.2 million images.