Circumscribed sphere

[1] The word circumsphere is sometimes used to mean the same thing, by analogy with the term circumcircle.

[2] As in the case of two-dimensional circumscribed circles (circumcircles), the radius of a sphere circumscribed around a polyhedron P is called the circumradius of P,[3] and the center point of this sphere is called the circumcenter of P.[4] When it exists, a circumscribed sphere need not be the smallest sphere containing the polyhedron; for instance, the tetrahedron formed by a vertex of a cube and its three neighbors has the same circumsphere as the cube itself, but can be contained within a smaller sphere having the three neighboring vertices on its equator.

It is possible to define the smallest bounding sphere for any polyhedron, and compute it in linear time.

[7] 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.

on the circumscribed sphere of each Platonic solid with number of the vertices