Abstract
Let G be a closed, non-transitive subgroup of O(n+1), where n ≥ 2, and let Q = S/G. We will show that for each n there is a lower bound for the diameter of Q. If G is finite then Q is an orbifold of constant curvature one and an explicit lower bound can be given. For Coxeter groups, the resulting lower bound is independent of dimension. Otherwise, Q is a spherical Alexandrov space and we will show existence of a lower bound. In the process, we will compute some examples of quotient spaces and their diameters.
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