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By George Hart for the Museum of Mathematics


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).

See all of George Hart’s Math Monday columns

Sean Michael Ragan

Sean Michael Ragan

I am descended from 5,000 generations of tool-using primates. Also, I went to college and stuff. I am a long-time contributor to MAKE magazine and My work has also appeared in ReadyMade, c’t – Magazin für Computertechnik, and The Wall Street Journal.