Serpentine Symmetries

In our Journal of Mathematics and the Arts 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.

For a less technical account than the aforementioned journal paper, see Chapter 6 of of my book with Ellie Baker, Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist.