Editing Sphere (section)

===Metric spaces===
{{Main|Metric space}}
More generally, in a [[metric space]] {{math|(''E'',''d'')}}, the sphere of center {{mvar|x}} and radius {{math|''r'' > 0}} is the set of points {{mvar|y}} such that {{math|1=''d''(''x'',''y'') = ''r''}}.

If the center is a distinguished point that is considered to be the origin of {{mvar|E}}, as in a [[norm (mathematics)|normed]] space, it is not mentioned in the definition and notation. The same applies for the radius if it is taken to equal one, as in the case of a [[unit sphere]].

Unlike a [[ball (mathematics)|ball]], even a large sphere may be an empty set. For example, in {{math|'''Z'''<sup>''n''</sup>}} with [[Euclidean metric]], a sphere of radius {{math|''r''}} is nonempty only if {{math|''r''<sup>2</sup>}} can be written as sum of {{math|''n''}} squares of [[integer]]s.

An [[octahedron]] is a sphere in [[taxicab geometry]], and a [[cube]] is a sphere in geometry using the [[Chebyshev distance]].