I_{h} |
E |
12C_{5} |
12(C_{5})^{2} |
20C_{3} |
15C_{2} |
i |
12S_{10} |
12(S_{10})^{3} |
20S_{6} |
15 |
linear functions, rotations |
quadratic functions |
cubic functions |
A_{g} |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
- |
x^{2}+y^{2}+z^{2} |
- |
T_{1g} |
+3 |
-2cos(4/5) |
-2cos(2/5) |
0 |
-1 |
+3 |
-2cos(2/5) |
-2cos(4/5) |
0 |
-1 |
(R_{x}, R_{y}, R_{z}) |
- |
- |
T_{2g} |
+3 |
-2cos(2/5) |
-2cos(4/5) |
0 |
-1 |
+3 |
-2cos(4/5) |
-2cos(2/5) |
0 |
-1 |
- |
- |
- |
G_{g} |
+4 |
-1 |
-1 |
+1 |
0 |
+4 |
-1 |
-1 |
+1 |
0 |
- |
- |
- |
H_{g} |
+5 |
0 |
0 |
-1 |
+1 |
+5 |
0 |
0 |
-1 |
+1 |
- |
[2z^{2}-x^{2}-y^{2}, x^{2}-y^{2}, xy, xz, yz] |
- |
A_{u} |
+1 |
+1 |
+1 |
+1 |
+1 |
-1 |
-1 |
-1 |
-1 |
-1 |
- |
- |
- |
T_{1u} |
+3 |
-2cos(4/5) |
-2cos(2/5) |
0 |
-1 |
-3 |
+2cos(2/5) |
+2cos(4/5) |
0 |
+1 |
(x, y, z) |
- |
[x(z^{2}+y^{2}), y(z^{2}+x^{2}), z(x^{2}+y^{2})] |
T_{2u} |
+3 |
-2cos(2/5) |
-2cos(4/5) |
0 |
-1 |
-3 |
+2cos(4/5) |
+2cos(2/5) |
0 |
+1 |
- |
- |
[x^{3}, y^{3}, z^{3}] |
G_{u} |
+4 |
-1 |
-1 |
+1 |
0 |
-4 |
+1 |
+1 |
-1 |
0 |
- |
- |
[x(z^{2}-y^{2}), y(z^{2}-x^{2}), z(x^{2}-y^{2}), xyz] |
H_{u} |
+5 |
0 |
0 |
-1 |
+1 |
-5 |
0 |
0 |
+1 |
-1 |
- |
- |
- |