Katherine Seaton

Adjunct Associate Professor of Mathematics
Department of Mathematics and Statistics, La Trobe University
Melbourne, Australia
I am a mathematician, university lecturer and some-time fiber artist. I delight in the mathematics that can be experienced in the construction, by hand, of pieces of knitting, crochet and embroidery, and in the thought that our grandmothers and great-grandmothers constructed mathematics this way, too. I frequently, but not exclusively, use recycled or remnant materials. Sashiko is a stitching technique born of frugality. Its domestic origin, together with its geometry and symmetry, instantly appealed to me when I became aware of this embroidery style.

10 x 25 x 25 cm
cotton thread, Aida cloth
This work comprises eleven biscornu, which roughly translates as "irregular". Each one is made from two offset squares and has the symmetry of a square antiprism. By embroidering each with a different hitomezashi (one-stitch sashiko) design, a complete three-dimensional symmetry sampler of the axial point group $D_{4d}$, and its ten subgroups, has been created. The whole group is depicted using a fractal (a Fibonacci snowflake), the trivial subgroup design is aleatoric, and traditional motifs with rotational and reflection symmetries have been combined to decorate the other nine biscornu.