Circumscribed sphere

In the circumscribed sphere of a polyhedron is a sphere on which lie all corners of the given polyhedron. The circumscribed sphere in the space geometry is the equivalent of the area of a polygon in the plane geometry.

The center of a circumscribed sphere must be equidistant from all corners. He therefore must be on all planes of symmetry of any two vertices. Since the intersection of these planes is generally empty, only special polyhedra have a circumscribed sphere, in particular, all tetrahedron (not just the regular! ) And the five Platonic solids.

The smallest sphere that encloses an object (but not necessarily all vertices touched), the spherical envelope body of the object.