hdrotations
functions
functions
| Oh | E | 8C3 | 6C2 | 6C4 | 3C2 =(C4)2 | i | 6S4 | 8S6 | 3h |
6d |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 | - | (xz, yz, xy) | - |
| A1u | +1 | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | -1 | - | - | - |
| A2u | +1 | +1 | -1 | -1 | +1 | -1 | +1 | -1 | -1 | +1 | - | - | xyz |
| 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) | - | (x3, y3, z3) [x(z2+y2), y(z2+x2), z(x2+y2)] |
| T2u | +3 | 0 | +1 | -1 | -1 | -3 | +1 | 0 | +1 | -1 | - | - | [x(z2-y2), y(z2-x2), z(x2-y2)] |
| Number of symmetry elements | h = 48 |
| Number of irreducible representations | n = 10 |
| Abelian group | no |
| Number of subgroups | 31 |
| Number of distinct subgroups | 23 |
| Subgroups
(Number of different orientations) |
Cs (2) , Ci , C2 (2) , C3 , C4 , D2 (2) , D3 , D4 , C2v (3) , C3v , C4v , C2h (2) , C4h , D2h (2) , D4h , D2d (2) , D3d , S4 , S6 , T , Th , Td , O |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Sulfurhexafluoride | [B6H6]2--Ion | Tungstenhexacarbonyl |
|---|---|---|
| Cubane | Octamethylsilsesquioxane |
| dipole (p) | T1u |
|---|---|
| quadrupole (d) | Eg+T2g |
| octopole (f) | A2u+T1u+T2u |
| hexadecapole (g) | A1g+Eg+T1g+T2g |
| 32-pole (h) | Eu+2T1u+T2u |
| 64-pole (i) | A1g+A2g+Eg+T1g+2T2g |
| 128-pole (j) | A2u+Eu+2T1u+2T2u |
| 256-pole(k) | A1g+2Eg+2T1g+2T2g |
| 512-pole (l) | A1u+A2u+Eu+3T1u+2T2u |
