“Graziotti was not a professional mathematician. He was an artist, in the style of the masters of the Italian Renaissance: Piero della Francesca, Paolo Uccello, Leonardo da Vinci and many others, big and small.”
Ugo Adriano Graziotti - The Thirteen Duals of the Semi-Regular Archimedean Polyhedra, “Polyhedra:The Realm of Geometric Beauty”, 1962.
In Space, every Figure having Height, Width and Depth, and formed of Planes, Lines and Points, has associated with it another Figure composed of Planes, Lines and Points - its so-called Dual Configuration. In this association lies a far reaching Principle of Mathematics - the Principle of Duality. Each of the Points of the first Body is Transformed into a Plane of the second Body, and a Plane is Transformed into a Point. The new Body thus formed is called the Dual of the first.