Sphericity, h, of a sample of rotating anisotropic clusters, as defined in Appendix F, from N-body simulations for N​ = ​10⁵. Each case has been averaged over 50 realisations. We represent radially anisotropic clusters (q​ = ​1) in red, isotropic clusters (q​ = ​0) in yellow, and tangentially anisotropic ones (q​ = ​ − 6) in blue. For each anisotropy, we consider three rotating parameters α​ = ​0.1, 0.25, 0.5 (ordered from dark to light colors). In agreement with Rozier et al. (2019), some of these clusters are unstable – namely (q, α)​ = ​(1, 0.5), and in a smaller fashion (q, α)​ = ​(1, 0.25) – while the others are linearly stable and remain spherically symmetric.