Susan Goldstine

In our paper "Building a better bracelet: wallpaper patterns in bead crochet," Ellie Baker and I prove that 13 of the 17 wallpaper groups generate designs in bead crochet rope, but two of them only occur in fairly trivial patterns. This seamless necklace smoothly transitions between designs for all 13 groups. The necklace is fastened so that the two boring patterns sit at the back of the neck, the designs with no reflections or glide reflections sit in the inner loop, and the remaining designs sit in the outer loop. The earrings (inner loop), bracelet (outer loop), and clasp (back) are bead woven with planar wallpaper designs that generate the patterns on the necklace. Serpentine Symmetries is hand made and contains over 7700 beads.

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.