Crystallography Online: the website of the International Union of Crystallography

David Brown wrote:
> Joe Krahn wrote:
> 
>> What about equation forms? It is important to define more than just the
>> space group, because non-standard settings can be useful in some cases.
>>
> The Hall symbol is a space group name (symbol) that specifies all
> possible settings of the 230 regular space groups.  It can easily be
> expanded into the list of the expressions of symmetry operations.
> 
I was looking over the Hall notation. If I understand it right, it only
defines origin choices which are symmetry equivalents of the normal
origin choice. There are cases where it is useful to shift a C2221
origin to align symmetry operators with those of P212121. I don't think
the standard Hall notation handles this sort of case, at least not as
tabulated in the International tables.

The other issue is that interactions may need to define a specific
symmetry operation. Is there a standard way to derive the symmetry
operators in a specific order from Hall notation?

Joe