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3. Hermann-Mauguin space-group symbols

The characters appearing after the lattice letter in the Hermann-Mauguin (HM) symbol of a space group were originally meant to represent generating operations of the group. For instance, b was a b-glide reflection in a plane oriented according to its position in the HM symbol.

In practice, the popular though ill-defined symmetry elements took over from the operations. Thus, b came to be seen as a glide plane, Eb in our present terminology. There is no harm in that re-interpretation except when the operation belongs to an Ee-glide plane. If this holds, for instance, for the above b-glide reflection, then there is an Ee but no Eb-glide plane in the corresponding orientation. In this case, b becomes a very misleading character. Apart from this, the bias (given to b over a or c) is just as disturbing as in the case of the symmetry-element symbols treated in §1.

Therefore, it is proposed to replace such misleading letters a or b by e in all five HM symbols in which they occur:

 

Space group No. 39 41 64 67 68

Symbol in ITA83: Abm2 Aba2 Cmca Cmma Ccca

New symbol: Aem2 Aea2 Cmce Cmme Ccce.

A further advantage of the proposed new symbols is that e - unlike a or b - is neutral and is therefore not changed upon axis permutation.

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