# Gwen Fisher

I weave beads to appeal to people's affinity for organization in design. I use geometry, symmetry, and topology as inspiration for the structures of my creations. Across cultures and continents, people show a natural affinity towards the aesthetics of pattern and order, and my art appeals to these aesthetics in tactile, tangible forms. I have found that people often recognize the repetition and order in my art. So my art appeals to their sense of discovery of the familiar in the unfamiliar.

A remarkable feature of bead weaving is its scalability, where most of my pieces lie at the small end of the scale. I use beads as little as 1.5 mm by 1 mm to build clusters of beads, tiny enough to be worn as jewelry, or just to be carried in a pocket, like a good luck charm. While most of my beaded pieces can be held in one hand, their designs have the potential to be scaled up into large sculptures; so, within their miniature frameworks is the potentiality of skyscrapers.

These Beaded Borromean Links are part of my larger body of mathematical artwork in beaded beads. A beaded bead is a cluster of smaller beads, woven together with a needle and thread, to form a composite cluster with one or more holes running though the center of the finished beaded bead.

The Borromean link is a set of three rings, which are woven together into a single symmetric piece of art. The three rings are linked collectively, despite the fact that no two of them are linked to each other.

Each component is woven using cubic right-angle weave (CRAW), which is the three-dimensional version of right angle weave (RAW). RAW corresponds to arranging beads on the edges of the regular tiling by squares, and CRAW corresponds to arranging beads on the edges of a rectangular array of cubes. I stitched rows of cubes, and I used larger beads where I turned corners. A second layer of seed beads embellishes and buttresses the CRAW to make the pieces stiffer.

These three pieces combine Vi Hart's idea of beading a hyperbolic tiling with the idea of strategic tacking, as in Daina Taimina’s crocheted hyperbolic planes. Instead of tacking the edges together, however, I used larger beads within the folds of the hyperbolic surfaces to help them hold their forms. Also, instead of using edge-only angle weaves as Hart has done, I used across-edge angle weaves because they are tighter weaves that make the bead work more rigid.

This set includes two different patches of the uniform hyperbolic tiling that goes by many names, including (4.5.4.5), which describes its arrangement of squares and pentagons. These two different patches of this hyperbolic tiling identify different subgroups of symmetries of the tiling.

The order (4.3.3) dual tiling is composed entirely of hexagons. While the center has four hexagons meeting at a point, and there are also places where just three hexagons meet at a point.