No. # | Coset Representative | Geometrical Interpretation |
Transformed WP |
1 | x,y,z | | 1 0 0 0
0 1 0 0
0 0 1 0 | |
| 1 | a b c d |
2 | x+2/3,y+1/3,z | | 1 0 0 2/3
0 1 0 1/3
0 0 1 0 | |
| t (2/3,1/3,0) | b c a d |
3 | x+1/3,y+2/3,z | | 1 0 0 1/3
0 1 0 2/3
0 0 1 0 | |
| t (1/3,2/3,0) | c a b d |
4 | -x,-y,-z | | -1 0 0 0
0 -1 0 0
0 0 -1 0 | |
| -1 0,0,0 | a c b d |
5 | -x+2/3,-y+1/3,-z | | -1 0 0 2/3
0 -1 0 1/3
0 0 -1 0 | |
| -1 1/3,1/6,0 | c b a d |
6 | -x+1/3,-y+2/3,-z | | -1 0 0 1/3
0 -1 0 2/3
0 0 -1 0 | |
| -1 1/6,1/3,0 | b a c d |
7 | -x,-y,z | | -1 0 0 0
0 -1 0 0
0 0 1 0 | |
| 2 0,0,z | a c b d |
8 | -x+2/3,-y+1/3,z | | -1 0 0 2/3
0 -1 0 1/3
0 0 1 0 | |
| 2 1/3,1/6,z | c b a d |
9 | -x+1/3,-y+2/3,z | | -1 0 0 1/3
0 -1 0 2/3
0 0 1 0 | |
| 2 1/6,1/3,z | b a c d |
10 | x,y,-z | | 1 0 0 0
0 1 0 0
0 0 -1 0 | |
| m x,y,0 | a b c d |
11 | x+2/3,y+1/3,-z | | 1 0 0 2/3
0 1 0 1/3
0 0 -1 0 | |
| g (2/3,1/3,0) x,y,0 | b c a d |
12 | x+1/3,y+2/3,-z | | 1 0 0 1/3
0 1 0 2/3
0 0 -1 0 | |
| g (1/3,2/3,0) x,y,0 | c a b d |