Finally, we present a new stitch that we invented expressly for use in helical mobius strips. The mobius stitch (Figure 9) has symmetry about both horizontal and vertical axes. Moreover, every row appears exactly the same. These properties allow the construction of a seamless single-helix mobius strip (Figure 10). The strip has no point irregularities except for the start and end of the yarn. In the appendix we discuss how to make this stitch and how to use it to make a mobius strip.
The challenge to knit a better mobius strip has led us to study the underlying topological principles of knitting. In future work, we plan to make precise mathematical definitions of knittable fabric and study symmetries of such fabrics.