Three Dimensional Finite Point Groups and the Symmetries of Beaded Beads
Document Type
Article
Publication Date
2007
Abstract
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 examples of a beaded bead realizing each finite subgroup of O(3) or, in the case of the seven infinite classes of finite subgroups, at least one representative beaded bead for each class.
Recommended Citation
Fisher, G. L., and B. Mellor. “Three-Dimensional Finite Point Groups and the Symmetry of Beaded Beads.” Journal of Mathematics and the Arts 1, no. 2 (June 1, 2007): 85–96. https://doi.org/10.1080/17513470701416264.
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