D60h E 2 C60 2 C30 2 C20 2 C15 2 C12 2 C10 2 C60^7 2 C15^2 2 C20^3 2 C6 2 C60^11 2 C5 2 C60^13 2 C30^7 2 C4 2 C15^4 2 C60^17 2 C10^3 2 C60^19 2 C3 2 C20^7 2 C30^11 2 C60^23 2 C5^2 2 C12^5 2 C30^13 2 C20^9 2 C15^7 2 C60^29 C2 30 C2' 30 C2" i 2 S60 2 S30 2 S20 2 S15 2 S12 2 S10 2 S60^7 2 S15^2 2 S20^3 2 S6 2 S60^11 2 S5 2 S60^13 2 S30^7 2 S4 2 S15^4 2 S60^17 2 S10^3 2 S60^19 2 S3 2 S20^7 2 S30^11 2 S60^23 2 S5^2 2 S12^5 2 S30^13 2 S20^9 2 S15^7 2 S60^29 sh 30 sv 30 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ... ....T ....... ........T ........... ............T A2g 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. B1g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2g 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1g 2.00000 1.98904 1.95630 1.90211 1.82709 1.73205 1.61803 1.48629 1.33826 1.17557 1.00000 0.81347 0.61803 0.41582 0.20906 0.00000 -0.20906 -0.41582 -0.61803 -0.81347 -1.00000 -1.17557 -1.33826 -1.48629 -1.61803 -1.73205 -1.82709 -1.90211 -1.95630 -1.98904 -2.00000 0.00000 0.00000 2.00000 -1.98904 -1.95630 -1.90211 -1.82709 -1.73205 -1.61803 -1.48629 -1.33826 -1.17557 -1.00000 -0.81347 -0.61803 -0.41582 -0.20906 0.00000 0.20906 0.41582 0.61803 0.81347 1.00000 1.17557 1.33826 1.48629 1.61803 1.73205 1.82709 1.90211 1.95630 1.98904 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g 2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 -2.00000 -1.95630 -1.82709 -1.61803 -1.33826 -1.00000 -0.61803 -0.20906 0.20906 0.61803 1.00000 1.33826 1.61803 1.82709 1.95630 2.00000 0.00000 0.00000 2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 -2.00000 -1.95630 -1.82709 -1.61803 -1.33826 -1.00000 -0.61803 -0.20906 0.20906 0.61803 1.00000 1.33826 1.61803 1.82709 1.95630 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3g 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 0.00000 0.00000 2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4g 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 0.00000 0.00000 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5g 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 0.00000 0.00000 2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6g 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 0.00000 0.00000 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7g 2.00000 1.48629 0.20906 -1.17557 -1.95630 -1.73205 -0.61803 0.81347 1.82709 1.90211 1.00000 -0.41582 -1.61803 -1.98904 -1.33826 0.00000 1.33826 1.98904 1.61803 0.41582 -1.00000 -1.90211 -1.82709 -0.81347 0.61803 1.73205 1.95630 1.17557 -0.20906 -1.48629 -2.00000 0.00000 0.00000 2.00000 -1.48629 -0.20906 1.17557 1.95630 1.73205 0.61803 -0.81347 -1.82709 -1.90211 -1.00000 0.41582 1.61803 1.98904 1.33826 0.00000 -1.33826 -1.98904 -1.61803 -0.41582 1.00000 1.90211 1.82709 0.81347 -0.61803 -1.73205 -1.95630 -1.17557 0.20906 1.48629 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8g 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 0.00000 0.00000 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9g 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 0.00000 0.00000 2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10g 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 0.00000 0.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11g 2.00000 0.81347 -1.33826 -1.90211 -0.20906 1.73205 1.61803 -0.41582 -1.95630 -1.17557 1.00000 1.98904 0.61803 -1.48629 -1.82709 0.00000 1.82709 1.48629 -0.61803 -1.98904 -1.00000 1.17557 1.95630 0.41582 -1.61803 -1.73205 0.20906 1.90211 1.33826 -0.81347 -2.00000 0.00000 0.00000 2.00000 -0.81347 1.33826 1.90211 0.20906 -1.73205 -1.61803 0.41582 1.95630 1.17557 -1.00000 -1.98904 -0.61803 1.48629 1.82709 0.00000 -1.82709 -1.48629 0.61803 1.98904 1.00000 -1.17557 -1.95630 -0.41582 1.61803 1.73205 -0.20906 -1.90211 -1.33826 0.81347 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12g 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.00000 0.00000 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13g 2.00000 0.41582 -1.82709 -1.17557 1.33826 1.73205 -0.61803 -1.98904 -0.20906 1.90211 1.00000 -1.48629 -1.61803 0.81347 1.95630 0.00000 -1.95630 -0.81347 1.61803 1.48629 -1.00000 -1.90211 0.20906 1.98904 0.61803 -1.73205 -1.33826 1.17557 1.82709 -0.41582 -2.00000 0.00000 0.00000 2.00000 -0.41582 1.82709 1.17557 -1.33826 -1.73205 0.61803 1.98904 0.20906 -1.90211 -1.00000 1.48629 1.61803 -0.81347 -1.95630 0.00000 1.95630 0.81347 -1.61803 -1.48629 1.00000 1.90211 -0.20906 -1.98904 -0.61803 1.73205 1.33826 -1.17557 -1.82709 0.41582 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14g 2.00000 0.20906 -1.95630 -0.61803 1.82709 1.00000 -1.61803 -1.33826 1.33826 1.61803 -1.00000 -1.82709 0.61803 1.95630 -0.20906 -2.00000 -0.20906 1.95630 0.61803 -1.82709 -1.00000 1.61803 1.33826 -1.33826 -1.61803 1.00000 1.82709 -0.61803 -1.95630 0.20906 2.00000 0.00000 0.00000 2.00000 0.20906 -1.95630 -0.61803 1.82709 1.00000 -1.61803 -1.33826 1.33826 1.61803 -1.00000 -1.82709 0.61803 1.95630 -0.20906 -2.00000 -0.20906 1.95630 0.61803 -1.82709 -1.00000 1.61803 1.33826 -1.33826 -1.61803 1.00000 1.82709 -0.61803 -1.95630 0.20906 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15g 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000 2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16g 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 0.00000 0.00000 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17g 2.00000 -0.41582 -1.82709 1.17557 1.33826 -1.73205 -0.61803 1.98904 -0.20906 -1.90211 1.00000 1.48629 -1.61803 -0.81347 1.95630 0.00000 -1.95630 0.81347 1.61803 -1.48629 -1.00000 1.90211 0.20906 -1.98904 0.61803 1.73205 -1.33826 -1.17557 1.82709 0.41582 -2.00000 0.00000 0.00000 2.00000 0.41582 1.82709 -1.17557 -1.33826 1.73205 0.61803 -1.98904 0.20906 1.90211 -1.00000 -1.48629 1.61803 0.81347 -1.95630 0.00000 1.95630 -0.81347 -1.61803 1.48629 1.00000 -1.90211 -0.20906 1.98904 -0.61803 -1.73205 1.33826 1.17557 -1.82709 -0.41582 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18g 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 0.00000 0.00000 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19g 2.00000 -0.81347 -1.33826 1.90211 -0.20906 -1.73205 1.61803 0.41582 -1.95630 1.17557 1.00000 -1.98904 0.61803 1.48629 -1.82709 0.00000 1.82709 -1.48629 -0.61803 1.98904 -1.00000 -1.17557 1.95630 -0.41582 -1.61803 1.73205 0.20906 -1.90211 1.33826 0.81347 -2.00000 0.00000 0.00000 2.00000 0.81347 1.33826 -1.90211 0.20906 1.73205 -1.61803 -0.41582 1.95630 -1.17557 -1.00000 1.98904 -0.61803 -1.48629 1.82709 0.00000 -1.82709 1.48629 0.61803 -1.98904 1.00000 1.17557 -1.95630 0.41582 1.61803 -1.73205 -0.20906 1.90211 -1.33826 -0.81347 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20g 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21g 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 0.00000 0.00000 2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22g 2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 -2.00000 1.33826 0.20906 -1.61803 1.95630 -1.00000 -0.61803 1.82709 -1.82709 0.61803 1.00000 -1.95630 1.61803 -0.20906 -1.33826 2.00000 0.00000 0.00000 2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 -2.00000 1.33826 0.20906 -1.61803 1.95630 -1.00000 -0.61803 1.82709 -1.82709 0.61803 1.00000 -1.95630 1.61803 -0.20906 -1.33826 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E23g 2.00000 -1.48629 0.20906 1.17557 -1.95630 1.73205 -0.61803 -0.81347 1.82709 -1.90211 1.00000 0.41582 -1.61803 1.98904 -1.33826 0.00000 1.33826 -1.98904 1.61803 -0.41582 -1.00000 1.90211 -1.82709 0.81347 0.61803 -1.73205 1.95630 -1.17557 -0.20906 1.48629 -2.00000 0.00000 0.00000 2.00000 1.48629 -0.20906 -1.17557 1.95630 -1.73205 0.61803 0.81347 -1.82709 1.90211 -1.00000 -0.41582 1.61803 -1.98904 1.33826 0.00000 -1.33826 1.98904 -1.61803 0.41582 1.00000 -1.90211 1.82709 -0.81347 -0.61803 1.73205 -1.95630 1.17557 0.20906 -1.48629 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24g 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 0.00000 0.00000 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E25g 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 0.00000 0.00000 2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26g 2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 -2.00000 1.82709 -1.33826 0.61803 0.20906 -1.00000 1.61803 -1.95630 1.95630 -1.61803 1.00000 -0.20906 -0.61803 1.33826 -1.82709 2.00000 0.00000 0.00000 2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 -2.00000 1.82709 -1.33826 0.61803 0.20906 -1.00000 1.61803 -1.95630 1.95630 -1.61803 1.00000 -0.20906 -0.61803 1.33826 -1.82709 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27g 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 0.00000 0.00000 2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E28g 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 0.00000 0.00000 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29g 2.00000 -1.98904 1.95630 -1.90211 1.82709 -1.73205 1.61803 -1.48629 1.33826 -1.17557 1.00000 -0.81347 0.61803 -0.41582 0.20906 0.00000 -0.20906 0.41582 -0.61803 0.81347 -1.00000 1.17557 -1.33826 1.48629 -1.61803 1.73205 -1.82709 1.90211 -1.95630 1.98904 -2.00000 0.00000 0.00000 2.00000 1.98904 -1.95630 1.90211 -1.82709 1.73205 -1.61803 1.48629 -1.33826 1.17557 -1.00000 0.81347 -0.61803 0.41582 -0.20906 0.00000 0.20906 -0.41582 0.61803 -0.81347 1.00000 -1.17557 1.33826 -1.48629 1.61803 -1.73205 1.82709 -1.90211 1.95630 -1.98904 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. A1u 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. 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B1u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. B2u 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E1u 2.00000 1.98904 1.95630 1.90211 1.82709 1.73205 1.61803 1.48629 1.33826 1.17557 1.00000 0.81347 0.61803 0.41582 0.20906 0.00000 -0.20906 -0.41582 -0.61803 -0.81347 -1.00000 -1.17557 -1.33826 -1.48629 -1.61803 -1.73205 -1.82709 -1.90211 -1.95630 -1.98904 -2.00000 0.00000 0.00000 -2.00000 1.98904 1.95630 1.90211 1.82709 1.73205 1.61803 1.48629 1.33826 1.17557 1.00000 0.81347 0.61803 0.41582 0.20906 0.00000 -0.20906 -0.41582 -0.61803 -0.81347 -1.00000 -1.17557 -1.33826 -1.48629 -1.61803 -1.73205 -1.82709 -1.90211 -1.95630 -1.98904 2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2u 2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 -2.00000 -1.95630 -1.82709 -1.61803 -1.33826 -1.00000 -0.61803 -0.20906 0.20906 0.61803 1.00000 1.33826 1.61803 1.82709 1.95630 2.00000 0.00000 0.00000 -2.00000 -1.95630 -1.82709 -1.61803 -1.33826 -1.00000 -0.61803 -0.20906 0.20906 0.61803 1.00000 1.33826 1.61803 1.82709 1.95630 2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 -2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3u 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 0.00000 0.00000 -2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4u 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 0.00000 0.00000 -2.00000 -1.82709 -1.33826 -0.61803 0.20906 1.00000 1.61803 1.95630 1.95630 1.61803 1.00000 0.20906 -0.61803 -1.33826 -1.82709 -2.00000 -1.82709 -1.33826 -0.61803 0.20906 1.00000 1.61803 1.95630 1.95630 1.61803 1.00000 0.20906 -0.61803 -1.33826 -1.82709 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5u 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 0.00000 0.00000 -2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6u 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 0.00000 0.00000 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E7u 2.00000 1.48629 0.20906 -1.17557 -1.95630 -1.73205 -0.61803 0.81347 1.82709 1.90211 1.00000 -0.41582 -1.61803 -1.98904 -1.33826 0.00000 1.33826 1.98904 1.61803 0.41582 -1.00000 -1.90211 -1.82709 -0.81347 0.61803 1.73205 1.95630 1.17557 -0.20906 -1.48629 -2.00000 0.00000 0.00000 -2.00000 1.48629 0.20906 -1.17557 -1.95630 -1.73205 -0.61803 0.81347 1.82709 1.90211 1.00000 -0.41582 -1.61803 -1.98904 -1.33826 0.00000 1.33826 1.98904 1.61803 0.41582 -1.00000 -1.90211 -1.82709 -0.81347 0.61803 1.73205 1.95630 1.17557 -0.20906 -1.48629 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8u 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 0.00000 0.00000 -2.00000 -1.33826 0.20906 1.61803 1.95630 1.00000 -0.61803 -1.82709 -1.82709 -0.61803 1.00000 1.95630 1.61803 0.20906 -1.33826 -2.00000 -1.33826 0.20906 1.61803 1.95630 1.00000 -0.61803 -1.82709 -1.82709 -0.61803 1.00000 1.95630 1.61803 0.20906 -1.33826 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9u 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 0.00000 0.00000 -2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 -2.00000 -1.17557 0.61803 1.90211 1.61803 0.00000 -1.61803 -1.90211 -0.61803 1.17557 2.00000 1.17557 -0.61803 -1.90211 -1.61803 0.00000 1.61803 1.90211 0.61803 -1.17557 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10u 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 0.00000 0.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11u 2.00000 0.81347 -1.33826 -1.90211 -0.20906 1.73205 1.61803 -0.41582 -1.95630 -1.17557 1.00000 1.98904 0.61803 -1.48629 -1.82709 0.00000 1.82709 1.48629 -0.61803 -1.98904 -1.00000 1.17557 1.95630 0.41582 -1.61803 -1.73205 0.20906 1.90211 1.33826 -0.81347 -2.00000 0.00000 0.00000 -2.00000 0.81347 -1.33826 -1.90211 -0.20906 1.73205 1.61803 -0.41582 -1.95630 -1.17557 1.00000 1.98904 0.61803 -1.48629 -1.82709 0.00000 1.82709 1.48629 -0.61803 -1.98904 -1.00000 1.17557 1.95630 0.41582 -1.61803 -1.73205 0.20906 1.90211 1.33826 -0.81347 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12u 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.00000 0.00000 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13u 2.00000 0.41582 -1.82709 -1.17557 1.33826 1.73205 -0.61803 -1.98904 -0.20906 1.90211 1.00000 -1.48629 -1.61803 0.81347 1.95630 0.00000 -1.95630 -0.81347 1.61803 1.48629 -1.00000 -1.90211 0.20906 1.98904 0.61803 -1.73205 -1.33826 1.17557 1.82709 -0.41582 -2.00000 0.00000 0.00000 -2.00000 0.41582 -1.82709 -1.17557 1.33826 1.73205 -0.61803 -1.98904 -0.20906 1.90211 1.00000 -1.48629 -1.61803 0.81347 1.95630 0.00000 -1.95630 -0.81347 1.61803 1.48629 -1.00000 -1.90211 0.20906 1.98904 0.61803 -1.73205 -1.33826 1.17557 1.82709 -0.41582 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E15u 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000 -2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16u 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 0.00000 0.00000 -2.00000 0.20906 1.95630 -0.61803 -1.82709 1.00000 1.61803 -1.33826 -1.33826 1.61803 1.00000 -1.82709 -0.61803 1.95630 0.20906 -2.00000 0.20906 1.95630 -0.61803 -1.82709 1.00000 1.61803 -1.33826 -1.33826 1.61803 1.00000 -1.82709 -0.61803 1.95630 0.20906 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17u 2.00000 -0.41582 -1.82709 1.17557 1.33826 -1.73205 -0.61803 1.98904 -0.20906 -1.90211 1.00000 1.48629 -1.61803 -0.81347 1.95630 0.00000 -1.95630 0.81347 1.61803 -1.48629 -1.00000 1.90211 0.20906 -1.98904 0.61803 1.73205 -1.33826 -1.17557 1.82709 0.41582 -2.00000 0.00000 0.00000 -2.00000 -0.41582 -1.82709 1.17557 1.33826 -1.73205 -0.61803 1.98904 -0.20906 -1.90211 1.00000 1.48629 -1.61803 -0.81347 1.95630 0.00000 -1.95630 0.81347 1.61803 -1.48629 -1.00000 1.90211 0.20906 -1.98904 0.61803 1.73205 -1.33826 -1.17557 1.82709 0.41582 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18u 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 0.00000 0.00000 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19u 2.00000 -0.81347 -1.33826 1.90211 -0.20906 -1.73205 1.61803 0.41582 -1.95630 1.17557 1.00000 -1.98904 0.61803 1.48629 -1.82709 0.00000 1.82709 -1.48629 -0.61803 1.98904 -1.00000 -1.17557 1.95630 -0.41582 -1.61803 1.73205 0.20906 -1.90211 1.33826 0.81347 -2.00000 0.00000 0.00000 -2.00000 -0.81347 -1.33826 1.90211 -0.20906 -1.73205 1.61803 0.41582 -1.95630 1.17557 1.00000 -1.98904 0.61803 1.48629 -1.82709 0.00000 1.82709 -1.48629 -0.61803 1.98904 -1.00000 -1.17557 1.95630 -0.41582 -1.61803 1.73205 0.20906 -1.90211 1.33826 0.81347 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20u 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21u 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 0.00000 0.00000 -2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 -2.00000 1.17557 0.61803 -1.90211 1.61803 0.00000 -1.61803 1.90211 -0.61803 -1.17557 2.00000 -1.17557 -0.61803 1.90211 -1.61803 0.00000 1.61803 -1.90211 0.61803 1.17557 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22u 2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 -2.00000 1.33826 0.20906 -1.61803 1.95630 -1.00000 -0.61803 1.82709 -1.82709 0.61803 1.00000 -1.95630 1.61803 -0.20906 -1.33826 2.00000 0.00000 0.00000 -2.00000 1.33826 0.20906 -1.61803 1.95630 -1.00000 -0.61803 1.82709 -1.82709 0.61803 1.00000 -1.95630 1.61803 -0.20906 -1.33826 2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E23u 2.00000 -1.48629 0.20906 1.17557 -1.95630 1.73205 -0.61803 -0.81347 1.82709 -1.90211 1.00000 0.41582 -1.61803 1.98904 -1.33826 0.00000 1.33826 -1.98904 1.61803 -0.41582 -1.00000 1.90211 -1.82709 0.81347 0.61803 -1.73205 1.95630 -1.17557 -0.20906 1.48629 -2.00000 0.00000 0.00000 -2.00000 -1.48629 0.20906 1.17557 -1.95630 1.73205 -0.61803 -0.81347 1.82709 -1.90211 1.00000 0.41582 -1.61803 1.98904 -1.33826 0.00000 1.33826 -1.98904 1.61803 -0.41582 -1.00000 1.90211 -1.82709 0.81347 0.61803 -1.73205 1.95630 -1.17557 -0.20906 1.48629 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24u 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 0.00000 0.00000 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E25u 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 0.00000 0.00000 -2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26u 2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 -2.00000 1.82709 -1.33826 0.61803 0.20906 -1.00000 1.61803 -1.95630 1.95630 -1.61803 1.00000 -0.20906 -0.61803 1.33826 -1.82709 2.00000 0.00000 0.00000 -2.00000 1.82709 -1.33826 0.61803 0.20906 -1.00000 1.61803 -1.95630 1.95630 -1.61803 1.00000 -0.20906 -0.61803 1.33826 -1.82709 2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27u 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 0.00000 0.00000 -2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 -2.00000 1.90211 -1.61803 1.17557 -0.61803 0.00000 0.61803 -1.17557 1.61803 -1.90211 2.00000 -1.90211 1.61803 -1.17557 0.61803 0.00000 -0.61803 1.17557 -1.61803 1.90211 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E28u 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 0.00000 0.00000 -2.00000 1.95630 -1.82709 1.61803 -1.33826 1.00000 -0.61803 0.20906 0.20906 -0.61803 1.00000 -1.33826 1.61803 -1.82709 1.95630 -2.00000 1.95630 -1.82709 1.61803 -1.33826 1.00000 -0.61803 0.20906 0.20906 -0.61803 1.00000 -1.33826 1.61803 -1.82709 1.95630 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29u 2.00000 -1.98904 1.95630 -1.90211 1.82709 -1.73205 1.61803 -1.48629 1.33826 -1.17557 1.00000 -0.81347 0.61803 -0.41582 0.20906 0.00000 -0.20906 0.41582 -0.61803 0.81347 -1.00000 1.17557 -1.33826 1.48629 -1.61803 1.73205 -1.82709 1.90211 -1.95630 1.98904 -2.00000 0.00000 0.00000 -2.00000 -1.98904 1.95630 -1.90211 1.82709 -1.73205 1.61803 -1.48629 1.33826 -1.17557 1.00000 -0.81347 0.61803 -0.41582 0.20906 0.00000 -0.20906 0.41582 -0.61803 0.81347 -1.00000 1.17557 -1.33826 1.48629 -1.61803 1.73205 -1.82709 1.90211 -1.95630 1.98904 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.989043790737 = 2*cos(2*π/60) = 2*cos(π/30) = (√15+√3+√10−2*√5)/4 1.956295201468 = 2*cos(4*π/60) = 2*cos(π/15) = (√5−1+√30+6*√5)/4 1.902113032590 = 2*cos(6*π/60) = 2*cos(π/10) = (√10+2*√5)/2 1.827090915285 = 2*cos(8*π/60) = 2*cos(2*π/15) = (1+√5+√30−6*√5)/4 1.732050807569 = 2*cos(10*π/60) = 2*cos(π/6) = √3 1.618033988750 = 2*cos(12*π/60) = 2*cos(π/5) = (√5+1)/2 1.486289650955 = 2*cos(14*π/60) = 2*cos(7*π/30) = (√15−√3+√10+2*√5)/4 1.338261212718 = 2*cos(16*π/60) = 2*cos(4*π/15) = (1−√5+√30+6*√5)/4 1.175570504585 = 2*cos(18*π/60) = 2*cos(3*π/10) = (√10−2*√5)/2 0.813473286152 = 2*cos(22*π/60) = 2*cos(11*π/30) = (√15+√3−√10−2*√5)/4 0.618033988750 = 2*cos(24*π/60) = 2*cos(2*π/5) = (√5−1)/2 0.415823381636 = 2*cos(26*π/60) = 2*cos(13*π/30) = (√3−√15+√10+2*√5)/4 0.209056926535 = 2*cos(28*π/60) = 2*cos(7*π/15) = (√30−6*√5−√5−1)/4 Symmetry of Rotations and Cartesian products A1g d+g+i+k+m z2, z4, z6 A2g R Rz E1g R+d+g+i+k+m {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} E2g d+g+i+k+m {x2−y2, xy}, {z2(x2−y2), xyz2}, {z4(x2−y2), xyz4} E3g g+i+k+m {xz(x2−3y2), yz(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E4g g+i+k+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E5g i+k+m {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2−y2)((5−2√5)x2−y2)} E6g i+k+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E7g k+m E8g k+m E9g m E10g m A2u p+f+h+j+l z, z3, z5 E1u p+f+h+j+l {x, y}, {xz2, yz2}, {xz4, yz4} E2u f+h+j+l {z(x2−y2), xyz}, {z3(x2−y2), xyz3} E3u f+h+j+l {x(x2−3y2), y(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)} E4u h+j+l {z((x2−y2)2−4x2y2), xyz(x2−y2)} E5u h+j+l {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2−y2)((5−2√5)x2−y2)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the D60h point group is 240, and the order of the principal axis (C60) is 60. The group has 66 irreducible representations. β The D60h point group is generated by three symmetry elements that are canonically chosen C60, C2′ and i. Other choices include σh instead of i, or any of C2″, σv or σd instead of C2′. Also, some ternary combinations of C2′, C2″, σv and σd act as generators. Lastly, the S60 can be chosen, together with i or σh and any one of C2′, C2″, σv or σd. γ There are two different sets of twofold symmetry axes perpendicular to the principal axis (z axis in standard orientation). By convention, the set denoted as C2′ contains both the x and y axes. δ There are two different sets of symmetry planes containing the principal axis (z axis in standard orientation). By convention, the set denoted as σv contains both the xz and the yz planes. ε The lowest nonvanishing multipole moment in D60h is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. θ The point group corresponds to a constructible polygon, as the order of the principal axis is a product of any number of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers. ι The fact that the regular pentagon is constructible is known since antiquity; Eukleides already discovered a construction for it. The double cosine of 2π/5 is equal to the reciprocal of the Golden Ratio of (1+√5)/2 = 1.61803. Regular polygons of order 30,60,120 etc. are derived from the pentagon by overlaying it with a triangle and successive halving of angles.
D58h | ||
D59h | ||
C60 C60v C60h D60 | D60h | D60d S60 |
D61h | ||
D62h |
This Character Table for the D60h point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.