In geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices. The word circumsphere is sometimes used to mean the same thing. 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. All regular polyhedra have circumscribed spheres, but most irregular polyhedra do not have all vertices lying on a common sphere, although it is still possible to define the smallest containing sphere for such shapes.

The radius of sphere circumscribed around a polyhedron P is called the circumradius of P.

Contents 1 Volume 2 Surface area 3 Circumscribed hemisphere 3.1 Volume 3.2 Surface area 4 See also 5 External links

VolumeEdit

The volume of sphere circumscribed around a polyhedron is therefore:

Surface areaEdit

The surface area of sphere circumscribed around a polyhedron is therefore:

Circumscribed hemisphereEdit

VolumeEdit

The volume of the hemisphere circumscribed in a polyhedron is therefore:

Surface areaEdit

The surface area of the hemisphere circumscribed in a polyhedron is therefore:

See also Edit

• Circumscribed circle
• Midsphere
• Inscribed sphere

External links Edit

• Weisstein, Eric W., "Circumscribed sphere" from MathWorld.

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