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ih - Tablice symetrii grup punktowych

Ih grupa punktowa

nieabelowe, nieredukowalne reprezentacje 10(32)

Tabela charakterów dla grupy punktowej Ih

E12C512(C5)220C315C2i12S1012(S10)320S615σlinear,
rotations
quadratic
Ag1111111111x2+y2+z2
T1g3-2cos(4π/5)-2cos(2π/5)0-13-2cos(2π/5)-2cos(4π/5)0-1(Rx, Ry, Rz)
T2g3-2cos(2π/5)-2cos(4π/5)0-13-2cos(4π/5)-2cos(2π/5)0-1
Gg4-1-1104-1-110
Hg500-11500-11[2z2-x2-y2, x2-y2, xy, xz, yz]
Au11111-1-1-1-1-1
T1u3-2cos(4π/5)-2cos(2π/5)0-1-32cos(2π/5)2cos(4π/5)01(x, y, z)
T2u3-2cos(2π/5)-2cos(4π/5)0-1-32cos(4π/5)2cos(2π/5)01
Gu4-1-110-411-10
Hu500-11-5001-1

Tabela mnożenia grupy punktowej Ih

 AgT1gT2gGgHgAuT1uT2uGuHu
AgAgT1gT2gGgHgAuT1uT2uGuHu
T1gT1gAg+T1g+HgGg+HgT2g+Gg+HgT1g+T2g+Gg+HgT1uAu+T1u+HuGu+HuT2u+Gu+HuT1u+T2u+Gu+Hu
T2gT2gGg+HgAg+T2g+HgT1g+Gg+HgT1g+T2g+Gg+HgT2uGu+HuAu+T2u+HuT1u+Gu+HuT1u+T2u+Gu+Hu
GgGgT2g+Gg+HgT1g+Gg+HgAg+T1g+T2g+Gg+HgT1g+T2g+Gg+2HgGuT2u+Gu+HuT1u+Gu+HuAu+T1u+T2u+Gu+HuT1u+T2u+Gu+2Hu
HgHgT1g+T2g+Gg+HgT1g+T2g+Gg+HgT1g+T2g+Gg+2HgAg+T1g+T2g+2Gg+2HgHuT1u+T2u+Gu+HuT1u+T2u+Gu+HuT1u+T2u+Gu+2HuAu+T1u+T2u+2Gu+2Hu
AuAuT1uT2uGuHuAgT1gT2gGgHg
T1uT1uAu+T1u+HuGu+HuT2u+Gu+HuT1u+T2u+Gu+HuT1gAg+T1g+HgGg+HgT2g+Gg+HgT1g+T2g+Gg+Hg
T2uT2uGu+HuAu+T2u+HuT1u+Gu+HuT1u+T2u+Gu+HuT2gGg+HgAg+T2g+HgT1g+Gg+HgT1g+T2g+Gg+Hg
GuGuT2u+Gu+HuT1u+Gu+HuAu+T1u+T2u+Gu+HuT1u+T2u+Gu+2HuGgT2g+Gg+HgT1g+Gg+HgAg+T1g+T2g+Gg+HgT1g+T2g+Gg+2Hg
HuHuT1u+T2u+Gu+HuT1u+T2u+Gu+HuT1u+T2u+Gu+2HuAu+T1u+T2u+2Gu+2HuHgT1g+T2g+Gg+HgT1g+T2g+Gg+HgT1g+T2g+Gg+2HgAg+T1g+T2g+2Gg+2Hg

C1 Cs Ci
C2 C3 C4 C5 C6
C2v C3v C4v C5v C6v
C2h C3h C4h C5h C6h
D2 D3 D4 D5 D6
D2h D3h D4h D5h D6h
D2d D3d D4d D5d D6d
S4 S6 S8 S10
Td Oh Ih
C∞v D∞h

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