Susan Goldstine

Collection: The Symmetry Completist Each of the pieces in this collection catalogs all the symmetries of a particular mathematical type that are possible in a particular form of knitting color work. The three unifying design principles are as follows: the designs in each garment fall into one or several visually compatible families of patterns with shared motifs; each possible symmetry type appears exactly once in the garment; the resulting garment has a pattern that an experienced knitter can easily reproduce. Crystalline: Double knitting is a form of two-color knitting that yields color-reversed versions of the same pattern on the front and the back. Its thick, reversible fabric is particularly suited to scarves. Of the seventeen wallpaper groups (the possible symmetry types for designs in the plane that repeat in multiple directions), exactly nine are compatible with the regular grid of a double-knitting design. Crystalline contains each of these nine symmetry types. The nine designs fall into three families of three; a family with heart motifs with reflection symmetry, a family with scroll motifs with rotational symmetry, and a family with vine motifs with glide-reflection symmetry. The pattern for Crystalline appears in the Deep Fall 2016 issue of the popular online magazine Knitty. Sneaking an account of symmetry groups into a general knitting magazine is one of my proudest feats of stealth mathematics.