Editing Inscribed sphere (section)

{{Short description|Sphere tangent to every face of a polyhedron}}
[[File:01 Tetraeder-Größen.png|thumb|[[Tetrahedron]] with insphere in red (also midsphere in green, circumsphere in blue)]]
[[File:Kepler-solar-system-1.png|right|thumb|In his 1597 book ''[[Mysterium Cosmographicum]]'', [[Johannes Kepler|Kepler]] modelled of the [[Solar System]] with its then known six planets' orbits by nested [[platonic solid]]s, each circumscribed and inscribed by a sphere.]]
In [[geometry]], the '''inscribed sphere''' or '''insphere''' of a [[convex polyhedron]] is a [[sphere]] that is contained within the polyhedron and [[tangent]] to each of the polyhedron's faces. It is the largest sphere that is contained wholly within the polyhedron, and is [[Duality (mathematics)|dual]] to the [[dual polyhedron]]'s [[circumsphere]].

The radius of the sphere inscribed in a polyhedron ''P'' is called the '''inradius''' of ''P''.