| I | E | 12C5 | 12C5² | 20C3 | 15C2 | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | 1 | x²+y²+z² | |
| T1 | 3 | ½(1+√5) | ½(1−√5) | 0 | −1 | (x, y, z), (Rx, Ry, Rz) | |
| T2 | 3 | ½(1−√5) | ½(1+√5) | 0 | −1 | ||
| G | 4 | −1 | −1 | 1 | 0 | ||
| H | 5 | 0 | 0 | −1 | 1 | (2z²−x²−y², x²−y², xy, xz, yz) |
| 阶 hOrder h | 60 |
|---|---|
| 类数Classes | 5 |
| 所属族Family | 二十面体 Icosahedral |
| 代表分子Examples | 少见（手性病毒衣壳）rare (chiral virus capsids) |
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.