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

G. L. Fisher, B. Mellor

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)85-96
Number of pages12
JournalJournal of Mathematics and the Arts
Volume1
Issue number2
DOIs
StatePublished - Jun 1 2007

ASJC Scopus Subject Areas

  • General Mathematics
  • Visual Arts and Performing Arts
  • Computer Graphics and Computer-Aided Design

Keywords

  • 00A06
  • 2000 Mathematics Subject Classifications
  • 20H15
  • 51F25
  • Beaded bead
  • Frieze group
  • Polyhedron
  • Symmetry
  • Three-dimensional finite point group

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