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What does hypersphere mean?

Looking for the meaning or definition of the word hypersphere? Here's what it means.

Noun
  1. (geometry) The set of all points in a given hyperspace that are at a given distance from a given point.
  2. (sports) A zorb; the act of zorbing, entering a zorbing ball, strapping into a harness, and rolling down a hill.
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Examples
Sasaki has obtained also a result on the structure of a conformally connected space whose group of holonomy fixes a point or a hypersphere.
The first just gives the large dimensionality of hypersphere, the second the flat diffusive landscape.
It fits in with some thoughts I've been having which map our consciousness as a hypersphere in a twisted six dimensional universe.

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