John Deere

George W. Hart

This is a paper sculpture, almost a foot in diameter, made of 120 thin pieces. There are two shapes, the green and the yellow, sixty of each. When I first designed the parts, they reminded me somehow of the Pitman arm on a hay cutter I once knew, and of a scythe:

This reminded me of pleasant hours riding around on a tractor cutting a hay field.  So I made the parts green and yellow and called it John Deere.  The tabs at the ends of the parts fit into the slots shown, though it is a bit complex to fathom it all from just a 2D photograph.

Each part is flat, i.e., it lies in a plane as it wiggles around its neighbors.  This computer rendering with thicker parts might make the form clearer:

But the most interesting thing about the design is that at every joint the connection is 90 degrees. This means every tab fits perpendicularly into its mating slot.  How can so many planes be perpendicular to so many other planes? The answer derives from the fact that the green parts lie in the face planes of a rhombic triacontahedron (which contains the planes of five cubes) while the yellow parts lie in the face planes of a regular dodecahedron (which are each orthogonal to ten of the planes of the triacontahedron). The sculpture design uses each of these many orthogonalities. The image below is centered on a 3-fold axis, where three planes come together like the corners of a cube:

So far, I have only made this design in paper.  It is possible to make it with a stiff metal, similar to Spaghetti Code, which also uses only 90 degree joints.  There is a high-resolution image available here.

copyright 2008, George W. Hart