Before revision:  More generally, our algorithm succeeds for mixtures of any distribution that satisfies two well-studied analytic assumptions - certifiable hypercontractivity and anti-concentration . Thus, they extend to clustering mixtures of arbitrary affine transforms of the uniform distribution on the d-dimensional unit sphere.
After revision:  More generally, our algorithm succeeds for mixtures of any distribution that satisfies two well-studied analytic assumptions - certifiable hypercontractivity and anti-concentration - that are necessary and sufficient for mixture models to be (efficiently) clusterable. As a consequence, our results extend to clustering mixtures of arbitrary affine transforms of the uniform distribution on the d-dimensional unit sphere.