Susan Goldstine

(See my other submissions for the description of the collection, The Symmetry Completist.) Fourteen Ciphers: In the most common forms of two-color hand knitting, the knitter carries the two colors of yarn at the same time and stitches from each color as dictated by the pattern, which is physically challenging. In the 1970’s, Barbara Walker introduced mosaic knitting, a less intimidating two-color technique in which only one yarn is carried and worked at a time. The simplicity for the knitter comes at a cost for the designer: an unusual set of restrictions on color placement unique to mosaic knitting. As Carolyn Yackel and I have discovered in our current research, the rules of mosaic knitting allow for all of the symmetry groups compatible with a square grid. However, if we consider two-color symmetry groups, in which there are both symmetries that preserve colors and symmetries that swap colors, some groups are excluded. Of the seventeen two-color frieze groups (the possible two-color symmetry types of a patterns that repeat in a single direction), only fourteen are possible in mosaic knitting. In this rectangular wrap, designs for twelve of those groups run along the length of the shawl, and designs for the other two appear at either end, an arrangement partially forced by the constraints of mosaic knitting.