Daniele Barbaro

BARBARO’S CONVEX NON-UNIFORM POLYHEDRA

This webpage summarizes some of my research on the solid bodies Daniele Barbaro (1514-1570) described in the treatise La Pratica della Perspettiva [1, 2], published in 1568 (more details in the paper Materializing Daniele Barbaro’s Creativity with 3D Printing [3] and the book chapter Non-Uniform Polyhedra Described by Daniele Barbaro [4]). The following links direct to a brief description of each polyhedron, an interactive 3D model, and the STL file for anyone who wishes to 3D print them. The models are around 100 to 110 mm diameter and were edited for stereolithographic printing.

Chapter XVI: Rectified Truncated Octahedron
Chapter XVIII: Rectified truncated Icosahedron
Chapter XIX: Truncated Pentakis Dodecahedron
Chapter XX: Twice-Truncated Icosahedron
Chapter XXII: Twice-Truncated Octahedron
Chapter XXV: Truncated Rectified Truncated Octahedron
Chapter XXXIV: Elongated Truncated Octahedron
Chapter XXXIV: Chamfered Cube
Chapter XXXIV: (no name yet)
Chapter XXXIV: Truncated Rectified Truncated Icosahedron

Chapter XVI (1568: 90–93): Rectified Truncated Octahedron

On page 91 of [1], Barbaro explains that, by dividing into two equal parts the edges of the body of 6 squares and 8 hexagons (the truncated octahedron) and taking away the solid angles where these parts finish, he obtained another body of 24 triangles, 6 squares and 8 hexagons, which is the rectified truncated octahedron.

Wentzel Jamnitzer (1507/08–1585) drew a similar body on Perspectiva Corporum Regularium [4, Plates B. II and B. IV], published in the same year as Pratica della Perspettiva. There is no evidence that Barbaro ever knew Jamnitzer’s book, but since their approaches to solid geometry were so different, they probably found the rectified truncated octahedron independently.

3D print it with this STL file

Chapter XVIII (1568: 97): Rectified Truncated Icosahedron