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Any of a set of objects resulting from the generalization of a two-dimensional circle and a three-dimensional sphere to n dimensions. In n-dimensional space, a hypersphere is the set of all points that are a given distance, called the radius, from a given point, called the center.
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n]) is digital n-sphere, n [member of] {1,2} and [[kappa].
2](I) denotes the radius of circumscribed n-sphere and V(I) denotes the set of vertices.
In [C] Cheng proved that d(M) = [Pi] if and only if M is isometric to the unit n-sphere Sn in [R.