# Insphere

Insphere[{p1,,pn+1}]

gives the sphere that can be inscribed in the simplex defined by points pi in .

Insphere[poly]

gives the insphere of a polyhedron or polygon poly.

# Details • Insphere is also known as incircle, inscribed circle, or inscribed disk.
• Insphere gives the Sphere of largest measure (arc length, area, etc.) that can be inscribed in the simplex (triangle, tetrahedron, etc.) defined by points pi.
• Insphere evaluates to a Sphere[c,r], where the center c is known as the incenter and radius r is known as the inradius for the related simplex.
• • Insphere is defined for and affinely independent.
• For polyhedra, Insphere[poly] returns a sphere that is contained within the polyhedron poly and tangent to each of the polyhedron faces.
• For polygons, Insphere[poly] returns a sphere that is contained within the polygon poly and tangent to each of the polygon edges.
• Insphere can be used with symbolic points in GeometricScene.

# Examples

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## Basic Examples(2)

An insphere in 2D:

 In:= Out= And in 3D:

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

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

 In:= Out= ## Neat Examples(1)

Introduced in 2015
(10.2)
|
Updated in 2019
(12.0)