English

Subgroups of SO(3) Associated with Tilings

Group Theory 2018-07-11 v1 Metric Geometry

Abstract

We give a thorough analysis of those subgroups of SO(3) generated by rotations about perpendicular axes by 2\pi/p and 2\pi/q. A corollary is that such a group is the free product of the cyclic groups of rotations about the separate axes if and only if p,q\ge 3 and are both odd. These groups are naturally associated with a family of hierarchical tilings of Euclidean 3-space.

Keywords

Cite

@article{arxiv.math/9601202,
  title  = {Subgroups of SO(3) Associated with Tilings},
  author = {Charles Radin and Lorenzo Sadun},
  journal= {arXiv preprint arXiv:math/9601202},
  year   = {2018}
}

Comments

Plain TeX; 20 pages of text plus 4 postscript figures

R2 v1 2026-07-22T17:55:57.629Z