# Hypersphere

Jump to navigation
Jump to search

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:

Rank | Name | Picture | Rank | Name | Picture | |
---|---|---|---|---|---|---|

1 | Dyad | 6 | Hexasphere | |||

2 | Circle | 7 | Heptasphere | |||

3 | Sphere | 8 | Octasphere | |||

4 | Glome | 9 | Enneasphere | |||

5 | Pentasphere | 10 | Decasphere |