Lebedev quadrature

The Lebedev grid or Lebedev angular mesh is a set of grid points on the unit sphere, and their corresponding weights, usually used to numerically integrate scalar functions defined on the angular spherical coordinates, ($\theta$ and $\phi$). These grids have octahedral symmetry, and are defined such that spherical harmonic functions can be integrated exactly up to a certain threshold. In practice, this means that highly accurate numerical integrations can be performed with fewer grid points. Their main drawbacks are that they are not defined to arbitrary accuracy, and the $\theta$ and $\phi$ integrals are not performed separately. In other cases, numerical integration can be performed over a Gauss-Legendre angular mesh instead.