Library/Geometry/Solid geometry/Polyhedra and spatial polygons/Inscribed polyhedra

Inscribed polyhedra

Overview
Important

An inscribed polyhedron is a polyhedron whose vertices all lie on the surface of a sphere. This sphere is called the circumscribed sphere of the polyhedron.

Important properties

  • Not every polyhedron can be inscribed in a sphere.

  • Regular polyhedra (Platonic solids) can always be inscribed in a sphere.

  • The sphere that passes through all the vertices of the polyhedron is unique if it exists.

  • Inscribed polyhedra have special symmetry properties.