Spherical Designs

If, moreover, dimHarmG(t + 1) = 1 and HarmG(k) = 0 for t + 1 < k ≤ t′, then some orbit of G of a point on Ωd forms a spherical t′-design.

54.9 Table Examples of finite groups G ⊂ O(d,R) satisfying the hypotheses of Theorem 54.8.