Christopher Bingham, An Antipodally Symmetric Distribution on the Sphere, The Annals of Statistics, Vol. 2, No. 6 (Nov., 1974), pp. 1201-1225 ...

For a spherically symmetric multivariate normal random sample, the asymptotic distribution of the largest interpoint Euclidean distance is derived. The number of interpoint distances exceeding a high ...

The dice example from Figure 1 clearly shows the appearance of the data as more bell-shaped, unimodal, symmetric, and “normal” as the sample size increased.