Although t-designs may be formulated for an arbitrary number of spatial dimensions, we are only interested in three dimensional Euclidean space R 3 and will limit our discussion to the unit 2-sphere with S 2 = {s ∈ R 3 : |s| = 1}. For any spherical polynomial of degree at most t on the 2-sphere, P t (S 2 ), Womersley has developed 24 spherical t-designs, which are sets of M points x 1 , ..., x M on S 2 for which equal weight cubature using these nodes is exact: