| Ih | E | 12C5 | 12C5² | 20C3 | 15C2 | i | 12S10 | 12S10³ | 20S6 | 15σ | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y²+z² | |
| T1g | 3 | ½(1+√5) | ½(1−√5) | 0 | −1 | 3 | ½(1−√5) | ½(1+√5) | 0 | −1 | (Rx, Ry, Rz) | |
| T2g | 3 | ½(1−√5) | ½(1+√5) | 0 | −1 | 3 | ½(1+√5) | ½(1−√5) | 0 | −1 | ||
| Gg | 4 | −1 | −1 | 1 | 0 | 4 | −1 | −1 | 1 | 0 | ||
| Hg | 5 | 0 | 0 | −1 | 1 | 5 | 0 | 0 | −1 | 1 | (2z²−x²−y², x²−y², xy, xz, yz) | |
| Au | 1 | 1 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | −1 | ||
| T1u | 3 | ½(1+√5) | ½(1−√5) | 0 | −1 | −3 | −½(1−√5) | −½(1+√5) | 0 | 1 | (x, y, z) | |
| T2u | 3 | ½(1−√5) | ½(1+√5) | 0 | −1 | −3 | −½(1+√5) | −½(1−√5) | 0 | 1 | ||
| Gu | 4 | −1 | −1 | 1 | 0 | −4 | 1 | 1 | −1 | 0 | ||
| Hu | 5 | 0 | 0 | −1 | 1 | −5 | 0 | 0 | 1 | −1 |
| 阶 hOrder h | 120 |
|---|---|
| 类数Classes | 10 |
| 所属族Family | 二十面体 Icosahedral |
| 代表分子Examples | C₆₀, [B₁₂H₁₂]²⁻, 十二面体烷C₆₀, [B₁₂H₁₂]²⁻, dodecahedrane |
在 3D 中查看并做对称操作Open in 3D and try the symmetry operationsC₆₀ →
约化可约表示Reduce a representation
输入可约表示在各类上的特征标，按约化公式 \(n_i = \frac{1}{h}\sum_R g_R\,\chi(R)\,\chi_i(R)^{*}\) 求出各不可约表示出现的次数。
Enter the characters of a reducible representation; the reduction formula gives how many times each irreducible representation occurs.