From:   GORDON::COCKCROFT    "Jeremy Karl Cockcroft" 10-JAN-2001 20:32:34.86
To:     SMTP%"Fraser.Rowan@awe.co.uk"
CC:     COCKCROFT
Subj:   RE: PD00 Assignment

Dear Fraser,

I was doing a PhD viva all day yesterday so am now catching up again on email
etc.

>                Sorry to be bothering you again, but I have a query about an
>example which is set in the course notes. Release 5, Symmetry I, Rotation
>Symmetry sub-sect.II Symmetry operators, third last paragraph ending "Thus
>the symmetry operator for a twofold rotation axis at, for example, (0,1/4,z)
>is -x,1/2-y,z."
>
>                When proving a symmetry operator I would plug in values of a
>hypothetical position (e.g. 1,1,1). If, however, you perform a two fold
>rotation about point (0,1/4,z) originating from (1,1,1) the final point will
>be (-1,-3/4,1), however, the symmetry operator dictates that the final point
>should be (-1,-1/2,1). Is this is typo in the course notes or have I
>completely got the wrong end of the stick? (As you may have gathered I am
>having big troubles with question 5 - I put it down to not being able to
>think in 3-dimensions.)

(1,1,1) => (-1,-1/2,1) is correct (as dictated by the symmetry operator).

The reason is as follows: If the y coordinate is at 1 and the axis is
at 1/4, then the difference is 3/4. Applying the twofold rotation implies
that the difference should be -3/4 and so the y-coordinate becomes
1/4 - 3/4, which is equal to -1/2.

I think you are getting the idea - but have just made a numerical error here.

Best regards,
                        Jeremy

Back