Trigonal Selenium

Selenium possesses space group P3121 with the following struct file:

H    LATTICE,NONEQUIV.ATOMS: 1
MODE OF CALC=RELA  POINTGROUP:32      
 8.2500000 8.2500000  9.369000
ATOM= -1: X= .7746000  Y= .7746000  Z= 0.0000000
          MULT= 3          ISPLIT= 8
ATOM= -1: X= .2254000  Y= .0000000  Z= 0.3333333
ATOM= -1: X= .0000000  Y= .2254000  Z= 0.6666667
Se         NPT=  381  R0=.000100000 RMT=2.100000000  Z:34.0
LOCAL ROT.MATRIX:    0.0       0.5000000 0.8660254
                     0.0000000 -.8660254 0.5000000
                     1.0000000 0.0000000 0.0
   6    IORD OF GROUP G0
......

The output of SYMMETRY reads:

Se         operation #  1     1                   
Se         operation #  9     2 $|$$|$ 110            
  pointgroup is 2 (neg. iatnr!!)
  axis should be: 2 || z
lm: 0 0  1 0  2 0  2 2 -2 2  3 0  3 2 -3 2  4 0  4 2 -4 2 ......

Point group 2 should have its 2-fold rotation axis along z, so the local rotation matrix can be constructed in two steps: firstly interchange x and z (that leads to z $\parallel$ (011) ) and secondly rotate from (011) into (001) (see the struct file given above). Since this is a hexagonal lattice, SYMMETRY uses the hexagonal axes, but the local rotation matrix must be given in cartesian coordinates.