Umkugel
In the circumscribed sphere of a polyhedron is a ball on which all corners are of the given polyhedron. The sphere in spatial geometry is the equivalent of the circumference of a polygon in plane geometry . Not all polyhedra have a sphere.
The center of a sphere must be the same distance from all corners. It must therefore be on all planes of symmetry of two corners each. Since the intersection of these planes is generally empty, only special polyhedra have a sphere, especially all tetrahedra (not just the regular ones!), The five Platonic solids , all Archimedean solids , and all straight triangular prisms .
The smallest sphere that encloses an object (but does not necessarily touch all corner points) is the spherical envelope of the object.
See also
Web links
- Eric W. Weisstein : Circumsphere . In: MathWorld (English).
- Venn diagram for the description of spheres around , in and edge of polyhedra