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A Polyhedron is said to be canonical if all its Edges touch a Sphere and the center of gravity of their contact points is the center of that Sphere. Each combinatorial type of (Genus zero) polyhedron contains just one canonical version. The Archimedean Solids and their Duals are all canonical.
References
Conway, J. H. ``Re: polyhedra database.'' Posting to geometry.forum newsgroup, Aug. 31, 1995.