Abstract
Subgroups of the special orthogonal group SO(3, ℝ) that are generated by two rotations of finite order about axes that are also separated by an angle of finite order are sometimes called generalised dihedral groups. They appear as orientation groups in the theory of tilings of Euclidean 3-space. As our main result, we classify the generalised dihedral subgroups of SO(3, ℚ) as the finite subgroups of SO(3, ℚ) except the alternating group A4.
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