[phenixbb] phenix.explore_metric_symmetry

[vincent Chaptal]

Dear all,

I ran "phenix.explore_metric_symmetry" with the command:

phenix.explore_metric_symmetry --unit_cell="97,97,225,78,78,68" 
--space_group=P1

It output:
...
-------------------------
Transforming point groups
-------------------------
 From P 1   to  C 1 2 1 (x-y,x+y,z)  using :
   *  -k,-h,-l
...

I understand that going from P1 to C2, one needs to apply the 
transformation matrix (x-y, x+y,z) on the P1 cell to form the C2 cell, 
and (-k, -h, -l) on the reflections.

Naive question: why aren't the two matrices similar?
The reciprocal space is the fourier transform of the real space; i was 
thinking that a reorientation matrix in the real space would be kept in 
the reciprocal space. My maths are not that good, and in P1 it is more 
complex than other space groups. Can someone tell me why the matrices 
are different?

Also, in C2 there is a 2-fold axis parallel to b, so reflections (h,k,l) 
are equivalent to (-h, k, -l).
In P1, they are not. Applying the above transformation matrix on the 
reflections would give (hP1, kP1, lP1) transforms into (-kP1, -hP1, 
-lP1), and these are equivalent to (kP1, -hP1, lP1)? Is this correct?

thank you
vincent