A polyhedron is said to be canonical if all its polyhedron edges touch a sphere
and the center of gravity of their contact points is the center of that sphere.
In other words, a canonical polyhedron is a polyhedron possessing a midsphere.
A dual polyhedron can be constructed from a canonical polyhedron that possesses these properties as well. Moreover, the edges of the canonical
polyhedron and its dual cross at right angles.
Amazingly, there is a unique canonical version (modulo rotations and reflections) for each combinatorial type of (genus zero) convex polyhedron
(Schramm 1992; Ziegler 1995, pp. 117-118; Springborn 2005). Many symmetric polyhedra
are canonical in their "natural" form, including the Platonic
solids as well as the Archimedean solids
and their duals. Equilateral antiprisms
and prisms are also canonical.
