Leonardo Project

George W. Hart

Leonardo da Vinci drew the illustrations for Luca Pacioli's 1509 book De Divina Proportione (The Divine Proportion). Never has an author had a more able illustrator. For the 500th anniversary of the book I am recreating wooden models similar to those which Leonardo must have had when making these drawings from "life."  Above is my "speculative reconstruction" in cherry of one of the most beautiful and complex models in the book.  This is the Duodecedron Abscisus Elevatus Vacuus, consisting of 120 equilateral triangles, made from 360 pieces of wood.  It is about 17 inches in diameter. (No one knows how large Leonardo's models were.) The plaque is aspen with a cherry frame and they are connected with a suspension of brass wire. A hi-res version of the image is available.

Above is the illustration from the manuscript version of the book, on which my reconstruction is based.  The drawings are beautifully hand colored like this in the Ambrosiana manuscript, reprinted by Officina Bodoni, 1956, and also by Silvana Editoriale, 1982.  There are roughly sixty similar illustrations in the book. 

When the book was printed, woodcuts were produced for each of the images. Here is the woodcut based on the drawing, which appeared in the printed version of the book. Mathematically, the shape derives from an icosidodecahedron by erecting a pyramid of equilateral triangles on each face.

Above is a second example: the truncated icosahedron or soccer ball shape, which Leonardo called Ycocedron Abscisus Vacuus. My speculative reconstruction is made of cherry, about 14 inches in diameter.  A total of 180 pieces of wood were cut and assembled to make it.  This sculpture is in the collection of Wendy Petti, creator of Math Cats.

Leonardo's drawing of the truncated icosahedron, from the manuscript of the book.

There ought to be a commemorative exhibition celebrating the 500th anniversary of the Pacioli/Leonardo book in 2009. The exhibit should include reconstructions of some or all of the wooden models and illustrations of their influence on other artists. For more information on Leonardo's polyhedra, Luca Pacioli's book, and other mathematically sophisticated artwork of the Renaissance, see the Art section of my online Encyclopedia of Polyhedra. I have also made my own forms in this style.

Copyright 1999, George W. Hart