Inscribed sphere

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In geometry, an inscribed sphere of a polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's facets. The word insphere is sometimes used to mean the same thing. When it exists, an inscribed sphere must be the largest sphere contained within the polyhedron. All regular polyhedra have inscribed spheres, but some irregular polyhedra do not have all facets tangent to a common sphere, although it is still possible to define the largest contained sphere for such shapes.

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