Charles Radin, Lorenzo Sadun
SUBGROUPS OF SO(3) ASSOCIATED WITH TILINGS
(279K, postscript)
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.