Davinci's Polyhedra

Leonardo da Vinci's Polyhedra

Leonardo da Vinci (1452-1519) was the quintessential renaissance man: artist, mathematician, scientist, and engineer.  He was a great lover of geometry, and devoted much time to it starting in his early forties.  His most outstanding polyhedral accomplishment is the illustrations for Luca Pacioli's 1509 book The Divine Proportion.  At right is one of the illustrations from that book. The term Ycocedron Abscisus in the title plaque means truncated icosahedron, and the term Vacuus refers to the fact that the faces are hollow. (The drawings are beautifully hand colored like this in the Ambrosiana manuscript, reprinted by Officina Bodoni, 1956, and also by Silvana Editoriale, 1982.)
These are the first illustrations of polyhedra ever in the form of "solid edges." The solidity of the edges lets one easily see which edges belong to the front and which to the back, unlike simple line drawings where the front and back surfaces may be visually confused.  Yet the hollow faces allow one to see through to the structure of the rear surface.  This is a brilliant new form of geometric illustration, one worthy of Leonardo's genius for insightful graphic display of information.  However, it is not clear whether Leonardo invented this new form or whether he was simply drawing from "life" a series of wooden models with solid edges which Pacioli designed.  If Pacioli designed these models, then he deserves the credit for this new "solid edge" idea, but it is likely that Leonardo designed them.