Circumscribed polyhedra

A circumscribed polyhedron is a polyhedron that has a sphere touching all its faces. This sphere is called the inscribed sphere or the incircle (in 3D, the 'insphere'). Each face of the polyhedron is tangent to the sphere at exactly one point.

Important properties

• The center of the inscribed sphere is the same distance from every face of the polyhedron.

• Not all polyhedra can have an inscribed sphere. For example, all faces must be able to touch the sphere at a single point each.

• Regular polyhedra (like the cube, tetrahedron, octahedron, dodecahedron, icosahedron) can be circumscribed about a sphere.