Gwen Fisher
"Various symmetric beaded beads"
GWEN L. FISHER California Polytechnic State University, San Luis Obispo, USA
Weavers of beads use a needle and thread to sew beads together to make decorative objects including jewelry, wall hangings, and baskets. Some bead weave designers weave beads into composite clusters, usually with at least one large hole, called beaded beads. Their groups of symmetries are classified by the 14 three-dimensional finite point groups, i.e. the finite subgroups of the orthogonal group of degree three, O(3). The beaded beads in this sample show representatives of 11 of the 14 classes. All of the beaded beads here measure between 17mm and 33mm. Mathematically, many beaded beads can be viewed as polyhedra, with each bead (or, more precisely, the hole through the middle of each bead, which provides its orientation) corresponding to an edge of the polyhedron. Different weaving patterns will bring different numbers of these "edges" together to form the vertices of the polyhedron. So it is very natural to use various polyhedra as the inspiration for beaded bead designs. In a sense, any polyhedron can be modelled as a beaded bead - more specifically, given any polyhedron, one can weave a beaded bead with the same set of symmetries. The challenge is to create the designs to accomplish this so that the beaded beads are objects of beauty in their own right. In meeting this challenge, I developed many new designs that may not have been created otherwise.