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