Editing Circumscribed sphere (section)

{{short description|Sphere touching all of a polyhedron's vertices}}
[[File:Вписанный куб.gif|right|thumb|Circumscribed sphere of a [[cube]]]]

In [[geometry]], a '''circumscribed sphere''' of a [[polyhedron]] is a [[sphere]] that contains the polyhedron and touches each of the polyhedron's [[Vertex (geometry)|vertices]].<ref>{{citation|title=The Mathematics Dictionary|first=R. C.|last=James |author-link=Robert C. James |publisher=Springer|year=1992|isbn=9780412990410|page=62|url=https://books.google.com/books?id=UyIfgBIwLMQC&pg=PA62}}.</ref>  The word '''circumsphere''' is sometimes used to mean the same thing, by analogy with the term ''[[circumcircle]]''.<ref>{{citation|title=Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere|first=Edward S.|last=Popko|publisher=CRC Press|year=2012|isbn=9781466504295|page=144|url=https://books.google.com/books?id=WLAFlr1_2S4C&pg=PA144}}.</ref> As in the case of two-dimensional circumscribed circles (circumcircles), the [[radius]] of a sphere circumscribed around a polyhedron {{mvar|P}} is called the [[circumradius]] of {{mvar|P}},<ref>{{citation|title=Methods of Geometry|first=James T.|last=Smith|publisher=John Wiley & Sons|year=2011|isbn=9781118031032|page=419|url=https://books.google.com/books?id=B0khWEZmOlwC&pg=PA419}}.</ref> and the center point of this sphere is called the [[circumcenter]] of {{mvar|P}}.<ref>{{citation|title=Modern pure solid geometry|first=Nathan|last=Altshiller-Court|edition=2nd|publisher=Chelsea Pub. Co.|year=1964|page=57}}.</ref>