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The analogous question was investigated by the authors in the hyperbolic $\\bH^2$ and elliptic $\\cE^2$ planes (see \\cite{CsSz1}, \\cite{CsSz2}, \\cite{CsSz5}), but in the higher dimensional spaces there are only a few result in this topic.\n  In \\cite{CsSz4} we gave a natural extension of the notion of the isoptic curves to the $n$-dimensional Euclidean space $\\bE^n$ $(n\\ge 3)$ which are called isoptic hypersurfaces. 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