"A mirror pair of (3,2) torus knots embedded on tori"

Knitted bamboo yarn (Southwest Trading Company Twize, in colors twurple and twocean (seriously)), 6.5" x 14.5" x 3", 2009.

A (p,q) torus knot traverses the meridian cycle of a torus p times and the longitudinal cycle q times. Exhibited here are the two chiral versions of the (3,2) torus knot, knitted into their embedding tori. One can represent a (p,q) torus knot on the standard flat torus by drawing a line of slope q/p. The designer of a knit torus must contend with thickening the line to make it visible (and appear continuous), compensating for the curvature of the spatially embedded torus, and discretizing the result onto the non-square grid formed by knit stitches.