D∞h Point Group
not Abelian, ∞ irreducible representationsCharacter table for D∞h point group
| E | 2C∞ | ... | ∞σv | i | 2S∞ | ... | ∞C'2 | linear functions, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|
| A1g=Σ+g | 1 | 1 | ... | 1 | 1 | 1 | ... | 1 | x2+y2, z2 | |
| A2g=Σ-g | 1 | 1 | ... | -1 | 1 | 1 | ... | -1 | Rz | |
| E1g=Πg | 2 | 2cos(φ) | ... | 0 | 2 | -2cos(φ) | ... | 0 | (Rx, Ry) | (xz, yz) |
| E2g=Δg | 2 | 2cos(2φ) | ... | 0 | 2 | 2cos(2φ) | ... | 0 | (x2-y2, xy) | |
| E3g=Φg | 2 | 2cos(3φ) | ... | 0 | 2 | -2cos(3φ) | ... | 0 | ||
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ||
| A1u=Σ+u | 1 | 1 | ... | 1 | -1 | -1 | ... | -1 | z | |
| A2u=Σ-u | 1 | 1 | ... | -1 | -1 | -1 | ... | 1 | ||
| E1u=Πu | 2 | 2cos(φ) | ... | 0 | -2 | 2cos(φ) | ... | 0 | (x, y) | |
| E2u=Δu | 2 | 2cos(2φ) | ... | 0 | -2 | -2cos(2φ) | ... | 0 | ||
| E3u=Φu | 2 | 2cos(3φ) | ... | 0 | -2 | 2cos(3φ) | ... | 0 | ||
| ... | ... | ... | ... | ... | ... | ... | ... | ... |
| C1 | Cs | Ci | ||
| C2 | C3 | C4 | C5 | C6 |
| C2v | C3v | C4v | C5v | C6v |
| C2h | C3h | C4h | C5h | C6h |
| D2 | D3 | D4 | D5 | D6 |
| D2h | D3h | D4h | D5h | D6h |
| D2d | D3d | D4d | D5d | D6d |
| S4 | S6 | S8 | S10 | |
| Td | Oh | Ih | ||
| C∞v | D∞h |
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