EMeqvrot

Program: EMeqvrot

This program can be used to list all the rotations that are equivalent to a given rotation for a given rotational point group symmetry. The program also identifies which of the equivalent rotations lies inside the fundamental zone, and lists all 8 representations for that rotation.

This is a command line program that will ask for the point group number, the type of input representation (Rodrigues, axis-angle, quaternion, or Euler), the type of output representation, and an input rotation. For cubic symmetry, input in axis-angle, output in quaternions, and axis-angle pair 30°@[1,0,0], the output is:

Enter the point group number 32
 Input representation: Rodrigues (1), axis-angle (2), quaternion (3), or Euler (4) 2
 Output representation: Rodrigues (1), axis-angle (2), quaternion (3), or Euler (4) 3
 Axis-angle pair (nx, ny, nz, omega°) : 1.0,0.0,0.0,30.0

FZ  0.96592582628906831       0.25881904510252074        0.0000000000000000        0.0000000000000000     
 -0.25881904510252074       0.96592582628906831        0.0000000000000000        0.0000000000000000     
   0.0000000000000000        0.0000000000000000       0.96592582628906831      -0.25881904510252074     
   0.0000000000000000        0.0000000000000000       0.25881904510252074       0.96592582628906831     
  0.50000000000000011       0.86602540378443871        0.0000000000000000        0.0000000000000000     
  0.68301270189221941       0.18301270189221933       0.68301270189221941      -0.18301270189221933     
  0.68301270189221941       0.18301270189221933       0.18301270189221933       0.68301270189221941     
  0.86602540378443871      -0.50000000000000011        0.0000000000000000        0.0000000000000000     
  0.68301270189221941       0.18301270189221933      -0.68301270189221941       0.18301270189221933     
  0.68301270189221941       0.18301270189221933      -0.18301270189221933      -0.68301270189221941     
 -0.18301270189221933       0.68301270189221941       0.68301270189221941      -0.18301270189221933     
  0.18301270189221933      -0.68301270189221941       0.68301270189221941      -0.18301270189221933     
   0.0000000000000000        0.0000000000000000       0.86602540378443871       0.50000000000000011     
   0.0000000000000000        0.0000000000000000      -0.50000000000000011       0.86602540378443871     
 -0.18301270189221933       0.68301270189221941       0.18301270189221933       0.68301270189221941     
  0.18301270189221933      -0.68301270189221941       0.18301270189221933       0.68301270189221941     
  0.35355339059327379       0.61237243569579447       0.61237243569579447       0.35355339059327379     
  0.61237243569579447      -0.35355339059327379      -0.61237243569579447      -0.35355339059327379     
  0.35355339059327379       0.61237243569579447      -0.35355339059327379       0.61237243569579447     
  0.61237243569579447      -0.35355339059327379       0.35355339059327379      -0.61237243569579447     
  0.61237243569579447      -0.35355339059327379       0.61237243569579447       0.35355339059327379     
  0.35355339059327379       0.61237243569579447      -0.61237243569579447      -0.35355339059327379     
  0.61237243569579447      -0.35355339059327379      -0.35355339059327379       0.61237243569579447     
  0.35355339059327379       0.61237243569579447       0.35355339059327379      -0.61237243569579447     

Equivalent representations for the rotation inside the FZ:
Euler angles                     : 180.0000000   30.0000000  180.0000000 
Axis angle pair [n; angle]       :   1.0000000    0.0000000    0.0000000 ;   30.0000000
Rodrigues vector                 :       0.2679492        0.0000000        0.0000000 
Homochoric representation        :   0.2606055    0.0000000    0.0000000 
Cubochoric representation        :   0.2100470    0.0000000    0.0000000 
Quaternion                       :   0.9659258    0.2588190    0.0000000    0.0000000 
Stereographic                       :  0.1317   0.0000   0.0000 
                                   /  1.0000   0.0000   0.0000 \
Orientation Matrix               : |  0.0000   0.8660  -0.5000 |
                                   \  0.0000   0.5000   0.8660 /

 ---> Another one ? (1/0) 0

The output line with FZ at the start represents the rotation inside the fundamental zone.