Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-22T00:57:02.299Z Has data issue: false hasContentIssue false
  • English
  • Français

A Regular Quaternion Polygon

Published online by Cambridge University Press:  20 November 2018

Donald W. Crowe
Donald W. Crowe*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Repeated application of the unitary reflections

to the point (1,0) and line x + iy = 1 yields 24 points and 24 lines. These are the vertices and edges of the regular complex polygon 4 {3} 4 whose group has the abstract definition R4 = I, RSR = SRS [l]. The purpose of this note is to introduce the notion of regular quaternion polygon and give an example analogous to the preceding one.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 2 , 01 May 1959 , pp. 77 - 79
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Coxeter, H.S.M., The groups of the regular polygons, Can. Math. Congress Newsletter, Sept. 1956.Google Scholar
2. Coxeter, H.S.M. and Moser, W.O.J., Generators and Relations for Discrete Groups, Ergeb. d. Math. 14, (Berlin, 1957).Google Scholar