Chiral icositetrachoric symmetry, [3,4,3], () is generated by 3 of 6 rotations: S 0,1, S 1,2, S 2,3, S 0,2, S 1,3, and S 0,3. Ionic diminished [3,4,3 ] group, () is generated by reflection R 0 and rotations S 1,2 and S 2,3. A 12-fold double rotation is generated by W 0,1,2,3, the product of all 4 reflections.