Non-Uniform Polyhedra Described by Daniele Barbaro

Abstract

In La Terza Parte of the treatise La pratica della perspettiva, published in 1568, Daniele Barbaro describes 39 solid bodies between Chapters I and XXXIV through edge unfolding, orthographic projections and/or perspective drawings, some of these in positions that are not the easiest to draw. Barbaro begins with a triangular pyramid and the Platonic Solids before describing the irregular bodies that are born from the regular bodies that he obtains from successive truncations of other bodies. Besides eleven Archimedeans, Barbaro obtains nine convex non-uniform polyhedra most of which are found nowhere before La pratica della perspettiva and are currently identifiable as symmetrohedra, near-miss Johnson Solids and even a Goldberg polyhedra, between others. We will analyse how these and other non-uniform polyhedra were conceived and illustrate them to unveil what Barbaro had in mind and the depth of Barbaro’s research. In spite of the imprecisions recognizable in some of the results, the originality and complexity of Barbaro’s systematic studies on solid geometry deserve our reanalysis, not only because they are intriguingly accurate for his time but because there is still much to learn from his scientific creativity.