The Cubic Groups
Td
| |
E |
8C3 |
3C2 |
6S4 |
6sd |
|
|
| A1 |
1 |
1 |
1 |
1 |
1 |
|
x2 + y2 + z2 |
| A2 |
1 |
1 |
1 |
-1 |
-1 |
|
|
| E |
2 |
-1 |
2 |
0 |
0 |
|
(2z2 - x2 - y2, x2 - y2) |
| T1 |
3 |
0 |
-1 |
1 |
-1 |
(Rx, Ry, Rz) |
|
| T2 |
3 |
0 |
-1 |
-1 |
1 |
(x, y, z) |
(xy, xz, yz) |
Oh
| |
E |
8C3 |
6C2 |
6C4 |
3C2ºC42 |
i |
6S4 |
8S6 |
3sh |
6sd |
|
|
| A1g |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
x2 + y2 + z2 |
| A2g |
1 |
1 |
-1 |
-1 |
1 |
1 |
-1 |
1 |
1 |
-1 |
|
|
| Eg |
2 |
-1 |
0 |
0 |
2 |
2 |
0 |
-1 |
2 |
0 |
|
(2z2 - x2 - y2, x2 - y2) |
| T1g |
3 |
0 |
-1 |
1 |
-1 |
3 |
1 |
0 |
-1 |
-1 |
(Rx, Ry, Rz) |
|
| T2g |
3 |
0 |
1 |
-1 |
-1 |
3 |
-1 |
0 |
-1 |
1 |
|
(xy, xz, yz) |
| A1u |
1 |
1 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
-1 |
|
|
| A2u |
1 |
1 |
-1 |
-1 |
1 |
-1 |
1 |
-1 |
-1 |
1 |
|
|
| Eu |
2 |
-1 |
0 |
0 |
2 |
-2 |
0 |
1 |
-2 |
0 |
|
|
| T1u |
3 |
0 |
-1 |
1 |
-1 |
-3 |
-1 |
0 |
1 |
1 |
(x, y, z) |
|
| T2u |
3 |
0 |
1 |
-1 |
-1 |
-3 |
1 |
0 |
1 |
-1 |
|
|