Editing Circumscribed sphere (section)

==Related concepts==
The circumscribed sphere is the three-dimensional analogue of the [[circumscribed circle]].
All [[regular polyhedra]] have circumscribed spheres, but most irregular polyhedra do not have one, since in general not all vertices lie on a common sphere. The circumscribed sphere (when it exists) is an example of a [[bounding sphere]], a sphere that contains a given shape. It is possible to define the smallest bounding sphere for any polyhedron, and compute it in [[linear time]].<ref name="fgk"/>

Other spheres defined for some but not all polyhedra include a [[midsphere]], a sphere tangent to all edges of a polyhedron, and an [[inscribed sphere]], a sphere tangent to all faces of a polyhedron. In the [[regular polyhedra]], the inscribed sphere, midsphere, and circumscribed sphere all exist and are [[Concentric spheres|concentric]].<ref>{{citation|last=Coxeter|first=H. S. M.|authorlink=Harold Scott MacDonald Coxeter|title=[[Regular Polytopes (book)|Regular Polytopes]]|edition=3rd|year=1973|publisher=Dover|isbn=0-486-61480-8|pages=[https://archive.org/details/regularpolytopes0000coxe/page/16 16–17]|contribution=2.1 Regular polyhedra; 2.2 Reciprocation|contribution-url=https://books.google.com/books?id=iWvXsVInpgMC&pg=PA16}}.</ref>

When the circumscribed sphere is the set of infinite limiting points of [[hyperbolic space]], a polyhedron that it circumscribes is known as an [[ideal polyhedron]].