A Point Group Character Tables 485 Table A.27.Character table for the icosahedral group I(icosahedral) I(532) E 12C5 12C号 20C3 15C2 (h=60) A +1 +1 +1 +1 +1 x2+y2+22 +3 +r 1-T 0 -1 (,y,z);(R=,Ry,R:) +3 1-T +1 0 -1 G +4 -1 -1 +1 0 2z2-x2-y2 x2-y2 +5 +1 ty tz yz Table A.28.Character table for Ih(icosahedral) E12C512C号20C315C2 i12S1012S10205615a (h=120) Ag +1 +1 +1 +1 +1 +1 +1 +1 +1+1x2+y2+22 Fis +3 +T1-T 0 -1+3 T 1-T 0-1 R::Ru:R: F +3 1-T 十T 0 -1 +31-T T 0-1 Gg +4 -1 -1 +1 0+4 -1 -1 +1 0 222-x2-y2 x2-y2 Hg +5 0 0 -1 +1 +5 0 0 -1 +1 Ty Tz yz Au +1 +1 +1 +1 +1 -1 -1 -1 -1-1 iu +3 +T1-7 0 -1 -3 -TT-1 0+1 (x,y,2) F2u +31-7 +T 0 -1 -3T-1 一T 0+1 Gu +4-1 -1 +1 -4+1 +1 -1 0 Hu+5 0 0 -1 +1-5 0 0 +1-1 T=(1+v5)/2.Note:Cs and Cs are in different classes,labeled 12Cs and 12C in the character table.Then iCs=So and iCs=Sio are in the classes labeled 12Sio and 12510,respectively.Also iC2=ov and In=Ii Table A.29.Character table for group T (cubic) T(23) E 3C2 4C3 4C3 x2+y2+22 A 1 1 1 1 (x2-2,322-r2) E 1 w2 11 1 (Rz;Ry;R:) (x,,2) T 3 -1 0 0 (yz,zx,xy) w=e2i/3;Th=Ti,(m3)(cubic)A Point Group Character Tables 485 Table A.27. Character table for the icosahedral group I (icosahedral) I (532) E 12C5 12C2 5 20C3 15C2 (h = 60) A +1 +1 +1 +1 +1 x2 + y2 + z2 F1 +3 +τ 1−τ 0 −1 (x, y, z); (Rx, Ry, Rz) F2 +3 1−τ +τ 0 −1 G +4 −1 −1 +1 0 H +5 0 0 −1 +1 ⎧ ⎪⎪⎪⎨ ⎪⎪⎪⎩ 2z2 − x2 − y2 x2 − y2 xy xz yz Table A.28. Character table for Ih (icosahedral) Ih E 12C5 12C2 5 20C3 15C2 i 12S3 10 12S10 20S6 15σ (h = 120) Ag +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 x2 + y2 + z2 F1g +3 +τ 1−τ 0 −1 +3 τ 1 − τ 0 −1 Rx, Ry, Rz F2g +3 1−τ +τ 0 −1 +3 1 − τ τ 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 F1u +3 +τ 1−τ 0 −1 −3 −τ τ − 1 0 +1 (x, y, z) F2u +3 1−τ +τ 0 −1 −3 τ − 1 −τ 0 +1 Gu +4 −1 −1 +1 0 –4 +1 +1 −1 0 Hu +5 0 0 −1 +1 –5 0 0 +1 −1 τ = (1 + √5)/2. Note: C5 and C−1 5 are in different classes, labeled 12C5 and 12C2 5 in the character table. Then iC5 = S−1 10 and iC−1 5 = S10 are in the classes labeled 12S3 10 and 12S10, respectively. Also iC2 = σv and Ih = I ⊗ i Table A.29. Character table for group T (cubic) T (23) E 3C2 4C3 4C 3 x2 + y2 + z2 A 1111 (x2 − y2, 3z2 − r2) E (1 1 1 1 ω ω2 ω2 ω (Rx, Ry, Rz) (x, y, z) (yz, zx, xy)  T 3 −10 0 ω = e2πi/3; Th = T ⊗ i, (m3) (cubic)