Subgroups ofSO(3) Associated with Tilings

✍ Scribed by Charles Radin; Lorenzo Sadun

• Book ID: 102577077
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 284 KB
• Volume: 202
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1997.7320

✦ Synopsis

We give a thorough analysis of those subgroups of SO 3 generated by rotations about perpendicular axes by 2rp and 2rq. 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 G 3 and are both odd. These groups are naturally associated with a family of hierarchical tilings of Euclidean 3-space.