A mathematical analysis of mosaic knitting: constraints, combinatorics, and colour-swapping symmetries

Mosaic knitting is a method of two-colour knitting that has become popular in recent decades. Our analysis begins with the mathematical rules that govern stitch patterns in mosaic knitting. Through this characterization, we find the total number of mosaic patterns possible in a given size of fabric and bound the number of patterns that are practical to knit. We proceed to a classification of the symmetry types that are compatible with mosaic designs, including theorems that enumerate which one- and two-colour frieze and wallpaper groups are and are not attainable in mosaic knitting. Our discussion includes practical information for knitwear designers and a multitude of sample patterns. GRAPHICAL ABSTRACT