## Character table for point group Ih

 Ih E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15 linear functions,rotations quadraticfunctions cubicfunctions Ag +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 - x2+y2+z2 - T1g +3 -2cos(4/5) -2cos(2/5) 0 -1 +3 -2cos(2/5) -2cos(4/5) 0 -1 (Rx, Ry, Rz) - - T2g +3 -2cos(2/5) -2cos(4/5) 0 -1 +3 -2cos(4/5) -2cos(2/5) 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 -2cos(4/5) -2cos(2/5) 0 -1 -3 +2cos(2/5) +2cos(4/5) 0 +1 (x, y, z) - [x(z2+y2), y(z2+x2), z(x2+y2)] T2u +3 -2cos(2/5) -2cos(4/5) 0 -1 -3 +2cos(4/5) +2cos(2/5) 0 +1 - - [x3, y3, z3] Gu +4 -1 -1 +1 0 -4 +1 +1 -1 0 - - [x(z2-y2), y(z2-x2), z(x2-y2), xyz] Hu +5 0 0 -1 +1 -5 0 0 +1 -1 - - -

Information for point groups with fivefold rotational axis

 Cs , Ci , C2 , C3 , C5 , D2 , D3 , D5 , C2v , C3v , C5v , C2h , D2h , D3d , D5d , S6 , S10 , T , Th , I Number of symmetry elements h = 120 Number of irreducible representations n = 10 Abelian group no Number of subgroups 20 Subgroups Optical Isomerism (Chirality) no Polar no

## Reduction formula for point group Ih

Type of representation

general 3N vib

E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15

## Multipoles

dipole (p) T1u Hg T2u+Gu Gg+Hg T1u+T2u+Hu Ag+T1g+Gg+Hg T1u+T2u+Gu+Hu T2g+Gg+2Hg T1u+T2u+2Gu+Hu

First nonvanishing multipole: 64-pole

### Literature

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement