Since the introduction of the angular segmentation or Sn method some 60 years ago, there have been many advances in the understanding of the method and many improvements to it. Indeed, the Sn method is now a widely used technique for deterministic solution of the transport equation. For three-dimensional (3-D) calculations, the method relies on numerical quadratures for the sphere, which integrate certain subspaces of spherical harmonics. The construction of such quadratures can be difficult. Here we report the development of new, highly efficient quadratures for the sphere that are invariant under the icosahedral rotation group. We compare the efficiency of the standard level-symmetric quadratures commonly used for 3-D Sn calculations and see that the new quadratures can be as much as 70% more efficient than the standard quadratures.