We will explain our proof of the existence of \( \varepsilon >0 \) such that every quotient of the unit sphere \( S^n (n\geq 2) \) by a isometric group action has diameter zero or at least \( \varepsilon \). The novelty is the independence of \( \varepsilon \) from \( n \). The classification of finite simple groups is used in the proof. (Joint work with C. Lange, A. Lytchak and R. A. E. Mendes.)