A few months ago, this column showed a cut-and-fold paper version of Escher’s Relativity. Here’s a new version, made of nylon by selective laser sintering on a 3D printing machine. The 3D file for this was designed by Oded Fuhrmann and Gershon Elber, who present a number of Escher-inspired objects. I scaled this instance of it to be 9 cm across.
Escher’s design is based on three walls of a cube, with the six axis directions (+/- X, Y, or Z) each understandable as the Up direction in some part of the structure. So it is confusing, but not an “impossible object” or trick of perspective. Below is a view from another angle, which may help make the structure clear.
If you have access to a 3D printing machine and would like to make your own copy of Relativity, the stl file is available here, (c) Oded Fuhrmann (of Google) and Gershon Elber (of the Technion).
More: See all of George Hart’s Math Monday columns