Circumsphere

Circumsphere[{p1,,pn+1}]

gives the sphere that circumscribes the points pi in .

Circumsphere[poly]

gives the circumsphere of a polyhedron or polygon poly.

Details • Circumsphere is also known as circumcircle, circumscribed circle, or circumscribed disk.
• Circumsphere gives the Sphere of smallest measure (arc length, area, etc.) that circumscribes the points pi.
• Circumsphere evaluates to a Sphere[c,r] where the center c is known as the circumcenter, and radius r is known as the circumradius for the Simplex[{p1,,pn+1}].
• • Circumsphere is defined for and is affinely independent.
• For polyhedra, Circumsphere[poly] is equivalent to .
• For polygons, Circumsphere[poly] is equivalent to Circumsphere[PolygonCoordinates[poly]].
• Circumsphere can be used with symbolic points in GeometricScene.

Examples

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Basic Examples(2)

A circumsphere in 2D:

 In:= Out= And in 3D:

 In:= Out= The circumsphere of the regular octahedron:

 In:= Out= In:= Out= Its surface area:

 In:= Out= Properties & Relations(1)

Introduced in 2014
(10.0)
|
Updated in 2019
(12.0)