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A hypersphere is a highly-symmetric object in each respective dimension. Hyperspheres are not polytopes, as they are round objects with no vertices or other flat elements. The surface of the hypersphere in n dimensions is the set of all points a fixed distance away from a given point (its center)
It is the most common practice to refer to a hypersphere by the dimensionality of its surface, which is one less than the space it occupies. For example, a 3-sphere refers to the hypersphere in 4D space (a glome).
Examples[edit | edit source]
Excluding the point, the hyperspheres up to 10D are the following: