Three-dimensional finite point groups and the symmetry of beaded beads

@article{Fisher2007ThreedimensionalFP,
  title={Three-dimensional finite point groups and the symmetry of beaded beads},
  author={Gwen L. Fisher and Blake Mellor},
  journal={Journal of Mathematics and the Arts},
  year={2007},
  volume={1},
  pages={85 - 96}
}
Beaded beads are clusters of beads woven together (usually around one or more large holes). Their groups of symmetries are classified by the three-dimensional finite point groups, i.e. the finite subgroups of the orthogonal group of degree three, O(3). The question we answer is whether every finite subgroup of O(3) can be realized as the group of symmetries of a beaded bead. We show that this is possible, and we describe general weaving techniques we used to accomplish this feat, as well as… 

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References

SHOWING 1-10 OF 12 REFERENCES

The Plato Bead: A Bead Dodecahedron

Creating polyhedra with beads is another way to learn the properties of regular and semi-regular solids. The instructions given below are for the dodecahedron (The Plato Bead). In a bead polyhedron

Symmetry

The word "symmetry" is used in mathematics quite differently from in ordinary speech. In everyday life one applies it mainly to two-sided, right-left symmetry; but not so in mathematics. Admittedly,

Beading with Right Angle Weave (Colorado: Interweave Press)

  • 2004

Sea Anemone Necklace, In: 500 Beaded Objects: New Dimensions in Contemporary Beadwork (New York: Lark Books)

  • 2004

The Art of Beaded Beads: Exploring Design, Color & Technique (New York: Lark Books)

  • 2006

Color coated beads

  • Bead & Button,
  • 2006

Geometric Symmetry (London: Cox & Wyman Ltd)

  • 1978

The Art and Elegance of Beadweaving: New Jewelry Designs with Classic Stitches (North Carolina: Lark Books)

  • 2002

Bead Fantasies

  • 2005