### Super Right Angle Weave: 18 Patches in 3 Colors and 3 Sizes

or

RAW Diamonds

Materials and Methods: Seed beads in sizes 15°, 11°, 8°, Nymo nylon thread, cotton and silk fabric, batting

Designer & Artist: Gwen Fisher

Year: 2013

This is a study in color for Super Right Angle Weave (SRAW), a bead weave based upon the regular tiling by squares. Each patch is 6 squares high by 5 squares across. Loops of four beads in each square face are woven and attached across edges with a single bead between the loops. Three bead types are used for coloring---two types for the faces and one type for the edges. Three colors in each of three sizes were chosen for a total of nine different bead types. This set of 18 patches answers the question: What are all possibilities of SRAW woven with three colors, one color in each of three sizes, where the colors are arranged as shown? The patches are arranged in sets of three, where each set has all of the same bead colors and sizes, but arranged differently.

The patches form sets like those in the game SET. Moreover, the patches can be thought of as representing elements of a group of order 18, where each patch corresponds to one group element, up to automorphisms. The group has two complete copies of 9 elements. Each set of 9 can be partitioned vertically, horizontally, and along both diagonals. Mathematician Tom Davis identified this group as the generalized dihedral group for E9. Read more about this on Gwen's blog.