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 R 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.
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