The Symmetries Diagram Themselves

My recent Linear Lace artworks are explorations of the seven frieze symmetry types in traditional knitted lace. In my writing about these works, I use marked knitting charts to illustrate the symmetries in each pattern. Then it occurred to me; why not mark the lace itself?

Here, the glass beads show the symmetries in the seven lace patterns. The white lines are reflection axes, the yellow lines are glide reflection axes, and the bronze beads are centers of rotation. The red beads along the edges of the designs mark their translational symmetries, with the minimal duplication needed to preserve reflections, glide reflections and rotations.

The Symmetries Diagram Themselves was knit by hand on 2.75 mm needles. I placed the beads into the fabric during the knitting process.

For further details, see my Bridges 2018 proceedings paper, Self-Diagramming Lace.