Danny Litvin has introduced the use of Seitz notation into the space group tables, something which I strongly support. I understand this has already been done in Volume E and that it is considered for ITA (see Acta Cryst., A67, 415, 2011). Now as usual there are many notations used for the Seitz symbol or operator and each has its own advantages and disadvantages. There are two issues I would like to raise for discussion, one small and one larger. Let me start with the larger one.

Issue 1:

The Seitz operator contains two parts, first the rotational/inversion point operation and the second translations. Now there is a problem in specifying the first part in relation to denoting directions. Let me take a particular example. Suppose we have a mirror perpendicular to the a-axis. You will see that this is often written by physicists as

mx

where the x is subscripted, although some use a numerical system to denote the direction. Now despite the fact that this is used by physicists, it seems to me that as crystallographers we already have a system of axes denoted a, b and c. The use of the letter x to a crystallographer, especially in the IT, denotes a coordinate not a direction. So perhaps we should write instead

ma

in this case. Now consider a mirror at along x,x,z in th hexagonal system. How do we denote this? I believe that Danny writes this as

m3

so that one now has a numerical subscript, which personally I find confusing, and not obvious. Now, we crystallographers already have an excellent system for denoting directions in real space, namely the use of [uvw]. So, I would like to propose that this is used instead (yes, I know that many will say this is not in use by physicists in general, although it was introduced in Burns and Glazer, but the compilers of the IT do have the chance and sufficient status to define new international symbols e.g. the new glide denoted by the letter e.). So in my two examples above we would have

m[100] and m[1-10] the – sign being a bar

Note that a mirror on xxz is perpendicular to the [1-10] direction. This is natural for a crystallographer and does not need one to reach out for a table of notations in order to understand.

Issue 2.

Danny and many others use the parentheses () for the Seitz operator. However, others, including myself, prefer to us braces {}. Apart from the possible confusion with symbols for planes, I do this because braces emphasise that the Seitz symbol is actually the symbol of an operator. So for instance the Seitz operator for a c-glide perpendicular to b would be

{m[010]|0,0,1/2}

Thus writing the operator equation that this symbol describes we have

{m[010]|0,0,1/2}r = {m[010]}r + (0,0,1/2)

where r is a position vector. Note that in this equation we see that the braces encompass an operator {m[010]} whereas the parentheses encompass a translation (0,0,1/2) , making a natural distinction between operator and symbol.

## Seitz symbols and operators

The Commission on Crystallographic Nomenclature comprises an elected Chairperson and

*ex officio*members. Nomenclature problems arising in specific fields of crystallography that come to the attention of, and are recognised as important by, the Commission are studied by*ad hoc*committees of experts appointed by the Commission.
**Moderators:** AndreAuthier, glazer

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