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Home > 2017 Mathematical Art Exhibition
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"Borromean racks," by Saul Schleimer (University of Warwick, Coventry, UK) and Henry Segerman (Oklahoma State University, Stillwater, OK)

10 x 10 x 10 cm, 3D printed nylon plastic, 2013

This sculpture consists of three identical pieces. Each has two identical rods; each rod is a rectangular prism with racks on three of its four sides. These racks mesh with one or two racks on the other pieces, for a total of 12 meshings. The pieces interlink in the fashion of the Borromean rings; their long axes form a standard orthogonal frame. When we take the directions of the racks into account, the sculpture has a handedness. At its middle position it realizes its maximal symmetry, a dihedral group of order six. Curiously, the Borromean Racks give an example of a triple of gears that mesh pairwise, but are not frozen. Challenge: Does this pattern of racks extend to tile three-space? If so, how many degrees of freedom does it have? --- Saul Schleimer and Henry Segerman


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American Mathematical Society