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Let $S^n$ be the $n$-sphere with the geodesic metric, and of diameter $\\pi$, and let $\\delta > 0$. Suppose that the first nontrivial homotopy group of the Vietoris-Rips complex $\\mathrm{VR}(S^n;\\pi-\\delta)$ of the $n$-sphere at scale $\\pi-\\delta$ occurs in dimension $k$, i.e., suppose that the connectivity is $k-1$. 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Afterwards, we show how to control the homotopy connectivity of Vietoris-Rips complexes of spheres in terms of coverings of spheres and projective spaces. Let $S^n$ be the $n$-sphere with the geodesic metric, and of diameter $\\pi$, and let $\\delta > 0$. Suppose that the first nontrivial homotopy group of the Vietoris-Rips complex $\\mathrm{VR}(S^n;\\pi-\\delta)$ of the $n$-sphere at scale $\\pi-\\delta$ occurs in dimension $k$, i.e., suppose that the connectivity is $k-1$. 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