The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere
does not always exist, but when it does, its radius is called the circumradius
and its center the circumcenter. The circumsphere
is the 3-dimensional generalization of the circumcircle.

The figures above depict the circumspheres of the Platonic
solids.

The circumsphere is implemented in the Wolfram Language as Circumsphere[pts],
where pts is a list of points, or Circumsphere[poly],
where poly is a Polygon (giving a two-dimensional circumcircle)
or Polyhedron (giving a three-dimensional circumsphere) object.