Abstract
We provide relevant math and detailed sewing instructions for constructing a toroidal scarf that reverses three ways and whose design uses the unique inversion properties of a particular torus geometry and particular 3-component link. We explain how the scarf’s sewing instructions are guided by the mathematics underlying its construction.
GRAPHICAL ABSTRACT
![](/cms/asset/c25241f0-2507-4656-8ee6-66af9e5bc12a/tmaa_a_2200897_uf0001_oc.jpg)
Acknowledgments
We would like to thank the editors and anonymous reviewers for their many helpful suggestions. The torus knot images in Figures 9 and 20 were produced using Robert Scharein’s KnotPlot (1998–2023), which is a marvellous tool. Thank you to Kent Christman for helping diagnose the misstep the first time Ellie tried to sew a torus knot seam on a rhombus layout, and for his excellent active listening in general.
Disclosure statement
No potential conflict of interest was reported by the author(s).