1. The radical subgroups represent the inverse operation to an extended symmetry operation . 2. The symmetry operation between sequential vertices is glide reflection. 3. The symmetry operations of a molecule determine the specific point group for this molecule. 4. The Bravais lattices may be considered as representing "'translational "'symmetry operations . 5. All but the two rightmost columns correspond to the symmetry operations which are invariant in the group. 6. The mental operations are the same as the symmetry operations are the same as the logical operations. 7. Since both rotations mentioned are symmetry operations , A'and B'must both be lattice points. 8. Specifically, symmetry operation column headers 2S 8 and 2S 8 3 were reversed in the older references. 9. The atom positions within the unit cell can be calculated through application of symmetry operations to the asymmetric unit. 10. Combinations of operations of the crystallographic point groups with the addition symmetry operations produce the 230 crystallographic space groups.
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