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.
> 
>> It is also useful to include matrix+vector for such things as a
>> spherical asymmetric unit from a 72-fold symmetric virus map. If nobody
>> is working on it, maybe I should go ahead and write down a few
>> alternatives and check opinions of other macro-molecular
>> crystallographers.
>>
> This would be useful.  I assume that the existing format could be
> extended using notation such as x/72,y-56/72 etc.  CIF does have
> definitions for symmetry operations in higher dimensions, but not, I
> believe, for non-crystallographic symmetries
> 
I actually meant for the virus example to be one where the equation form
is not an advantage. So, even though it is a simple concise method, it
is not always applicable, and the simple matrix+vector might be better
as a general form. And, I suspect most people would prefer to minimize
variations.

For comparison, mmCIF allows either the Hall symbol or explicit symmetry
operators. In the latter case, they are in equation form:

mmCIF already defines symm-ops as equations:
    _space_group_symop.id
    _space_group_symop.operation_xyz
      1    x,y,z
      2   -x,-y,-z
      3   -x,1/2+y,1/2-z
      4    x,1/2-y,1/2+z


NCS is also part of mmCIF, with matrix+vector, like this:

    _struct_ncs_oper.matrix[1][1]    0.247
    _struct_ncs_oper.matrix[1][2]    0.935
    _struct_ncs_oper.matrix[1][3]    0.256
    _struct_ncs_oper.matrix[2][1]    0.929
    _struct_ncs_oper.matrix[2][2]    0.153
    _struct_ncs_oper.matrix[2][3]    0.337
    _struct_ncs_oper.matrix[3][1]    0.276
    _struct_ncs_oper.matrix[3][2]    0.321
    _struct_ncs_oper.matrix[3][3]   -0.906
    _struct_ncs_oper.vector[1]      -8.253
    _struct_ncs_oper.vector[2]     -11.743
    _struct_ncs_oper.vector[3]      -1.782


Joe