S20 | E | 2S20 | 2C10 | 2(S20)3 | 2C5 | 2S4 | 2(C10)3 | 2(S20)7 | 2(C5)2 | 2(S20)9 | C2 |
---|---|---|---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
E1* | 2 | 2cos(π/10) | 2cos(π/5) | 2cos(3π/10) | 2cos(2π/5) | 0 | -2cos(2π/5) | -2cos(3π/10) | -2cos(π/5) | -2cos(π/10) | -2 |
E2* | 2 | 2cos(π/5) | 2cos(2π/5) | -2cos(2π/5) | -2cos(π/5) | -2 | -2cos(π/5) | -2cos(2π/5) | 2cos(2π/5) | 2cos(π/5) | 2 |
E3* | 2 | 2cos(3π/10) | -2cos(2π/5) | -2cos(π/10) | -2cos(π/5) | 0 | 2cos(π/5) | 2cos(π/10) | 2cos(2π/5) | -2cos(3π/10) | -2 |
E4* | 2 | 2cos(2π/5) | -2cos(π/5) | -2cos(π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | -2cos(π/5) | -2cos(π/5) | 2cos(2π/5) | 2 |
E5* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 |
E6* | 2 | -2cos(2π/5) | -2cos(π/5) | 2cos(π/5) | 2cos(2π/5) | -2 | 2cos(2π/5) | 2cos(π/5) | -2cos(π/5) | -2cos(2π/5) | 2 |
E7* | 2 | -2cos(3π/10) | -2cos(2π/5) | 2cos(π/10) | -2cos(π/5) | 0 | 2cos(π/5) | -2cos(π/10) | 2cos(2π/5) | 2cos(3π/10) | -2 |
E8* | 2 | -2cos(π/5) | 2cos(2π/5) | 2cos(2π/5) | -2cos(π/5) | 2 | -2cos(π/5) | 2cos(2π/5) | 2cos(2π/5) | -2cos(π/5) | 2 |
E9* | 2 | -2cos(π/10) | 2cos(π/5) | -2cos(3π/10) | 2cos(2π/5) | 0 | -2cos(2π/5) | 2cos(3π/10) | -2cos(π/5) | 2cos(π/10) | -2 |
Number of symmetry elements | h = 20 |
Number of classes, irreps | n = 20 |
Number of real-valued irreducible representations | n = 11 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |