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:

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And in 3D:

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The insphere of the regular octahedron:

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Its surface area:

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Scope  (17)

Applications  (3)

Properties & Relations  (2)

Neat Examples  (1)

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