Subgroups of SO(3) Associated with Tilings
Abstract
We give a thorough analysis of those subgroups of SO(3) generated by rotations about perpendicular axes by 2π/p and 2π/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 3 and are both odd. These groups are naturally associated with a family of hierarchical tilings of Euclidean 3-space.
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