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E12" 2.00000 0.39718 -1.84225 -1.12889 1.39388 1.68251 -0.72562 -1.97071 -0.05711 1.94802 0.83083 -1.61803 -1.47348 1.03279 1.88369 -0.28463 -1.99674 -0.50844 1.79480 1.22130 -1.30972 -1.74149 0.61803 1.98696 0.17115 -1.91899 -0.93333 1.54828 0.00000 -2.00000 -0.39718 1.12889 -1.68251 1.97071 -1.94802 1.61803 -1.03279 0.28463 0.50844 -1.22130 1.74149 -1.98696 1.91899 -1.54828 0.93333 -0.17115 -0.61803 1.30972 -1.79480 1.99674 -1.88369 1.47348 -0.83083 0.05711 0.72562 -1.39388 1.84225 0.00000 ... ... ..... ....... ......... ........... ............. E13' 2.00000 0.17115 -1.97071 -0.50844 1.88369 0.83083 -1.74149 -1.12889 1.54828 1.39388 -1.30972 -1.61803 1.03279 1.79480 -0.72562 -1.91899 0.39718 1.98696 -0.05711 -1.99674 -0.28463 1.94802 0.61803 -1.84225 -0.93333 1.68251 1.22130 -1.47348 0.00000 2.00000 0.17115 -0.50844 0.83083 -1.12889 1.39388 -1.61803 1.79480 -1.91899 1.98696 -1.99674 1.94802 -1.84225 1.68251 -1.47348 1.22130 -0.93333 0.61803 -0.28463 -0.05711 0.39718 -0.72562 1.03279 -1.30972 1.54828 -1.74149 1.88369 -1.97071 0.00000 ... ... ..... ....... ......... ........... ............. E13" 2.00000 0.17115 -1.97071 -0.50844 1.88369 0.83083 -1.74149 -1.12889 1.54828 1.39388 -1.30972 -1.61803 1.03279 1.79480 -0.72562 -1.91899 0.39718 1.98696 -0.05711 -1.99674 -0.28463 1.94802 0.61803 -1.84225 -0.93333 1.68251 1.22130 -1.47348 0.00000 -2.00000 -0.17115 0.50844 -0.83083 1.12889 -1.39388 1.61803 -1.79480 1.91899 -1.98696 1.99674 -1.94802 1.84225 -1.68251 1.47348 -1.22130 0.93333 -0.61803 0.28463 0.05711 -0.39718 0.72562 -1.03279 1.30972 -1.54828 1.74149 -1.88369 1.97071 0.00000 ... ... ..... ....... ......... ........... ............. E14' 2.00000 -0.05711 -1.99674 0.17115 1.98696 -0.28463 -1.97071 0.39718 1.94802 -0.50844 -1.91899 0.61803 1.88369 -0.72562 -1.84225 0.83083 1.79480 -0.93333 -1.74149 1.03279 1.68251 -1.12889 -1.61803 1.22130 1.54828 -1.30972 -1.47348 1.39388 0.00000 2.00000 -0.05711 0.17115 -0.28463 0.39718 -0.50844 0.61803 -0.72562 0.83083 -0.93333 1.03279 -1.12889 1.22130 -1.30972 1.39388 -1.47348 1.54828 -1.61803 1.68251 -1.74149 1.79480 -1.84225 1.88369 -1.91899 1.94802 -1.97071 1.98696 -1.99674 0.00000 ... ... ..... ....... ......... ........... ............. E14" 2.00000 -0.05711 -1.99674 0.17115 1.98696 -0.28463 -1.97071 0.39718 1.94802 -0.50844 -1.91899 0.61803 1.88369 -0.72562 -1.84225 0.83083 1.79480 -0.93333 -1.74149 1.03279 1.68251 -1.12889 -1.61803 1.22130 1.54828 -1.30972 -1.47348 1.39388 0.00000 -2.00000 0.05711 -0.17115 0.28463 -0.39718 0.50844 -0.61803 0.72562 -0.83083 0.93333 -1.03279 1.12889 -1.22130 1.30972 -1.39388 1.47348 -1.54828 1.61803 -1.68251 1.74149 -1.79480 1.84225 -1.88369 1.91899 -1.94802 1.97071 -1.98696 1.99674 0.00000 ... ... ..... ....... ......... ........... ............. E15' 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 0.00000 2.00000 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 0.00000 ... ... ..... ....... ......... ........... ............. E15" 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 0.00000 -2.00000 0.28463 -0.83083 1.30972 -1.68251 1.91899 -2.00000 1.91899 -1.68251 1.30972 -0.83083 0.28463 0.28463 -0.83083 1.30972 -1.68251 1.91899 -2.00000 1.91899 -1.68251 1.30972 -0.83083 0.28463 0.28463 -0.83083 1.30972 -1.68251 1.91899 0.00000 ... ... ..... ....... ......... ........... ............. E16' 2.00000 -0.50844 -1.74149 1.39388 1.03279 -1.91899 -0.05711 1.94802 -0.93333 -1.47348 1.68251 0.61803 -1.99674 0.39718 1.79480 -1.30972 -1.12889 1.88369 0.17115 -1.97071 0.83083 1.54828 -1.61803 -0.72562 1.98696 -0.28463 -1.84225 1.22130 0.00000 2.00000 -0.50844 1.39388 -1.91899 1.94802 -1.47348 0.61803 0.39718 -1.30972 1.88369 -1.97071 1.54828 -0.72562 -0.28463 1.22130 -1.84225 1.98696 -1.61803 0.83083 0.17115 -1.12889 1.79480 -1.99674 1.68251 -0.93333 -0.05711 1.03279 -1.74149 0.00000 ... ... ..... ....... ......... ........... ............. E16" 2.00000 -0.50844 -1.74149 1.39388 1.03279 -1.91899 -0.05711 1.94802 -0.93333 -1.47348 1.68251 0.61803 -1.99674 0.39718 1.79480 -1.30972 -1.12889 1.88369 0.17115 -1.97071 0.83083 1.54828 -1.61803 -0.72562 1.98696 -0.28463 -1.84225 1.22130 0.00000 -2.00000 0.50844 -1.39388 1.91899 -1.94802 1.47348 -0.61803 -0.39718 1.30972 -1.88369 1.97071 -1.54828 0.72562 0.28463 -1.22130 1.84225 -1.98696 1.61803 -0.83083 -0.17115 1.12889 -1.79480 1.99674 -1.68251 0.93333 0.05711 -1.03279 1.74149 0.00000 ... ... ..... ....... ......... ........... ............. E17' 2.00000 -0.72562 -1.47348 1.79480 0.17115 -1.91899 1.22130 1.03279 -1.97071 0.39718 1.68251 -1.61803 -0.50844 1.98696 -0.93333 -1.30972 1.88369 -0.05711 -1.84225 1.39388 0.83083 -1.99674 0.61803 1.54828 -1.74149 -0.28463 1.94802 -1.12889 0.00000 2.00000 -0.72562 1.79480 -1.91899 1.03279 0.39718 -1.61803 1.98696 -1.30972 -0.05711 1.39388 -1.99674 1.54828 -0.28463 -1.12889 1.94802 -1.74149 0.61803 0.83083 -1.84225 1.88369 -0.93333 -0.50844 1.68251 -1.97071 1.22130 0.17115 -1.47348 0.00000 ... ... ..... ....... ......... ........... ............. E17" 2.00000 -0.72562 -1.47348 1.79480 0.17115 -1.91899 1.22130 1.03279 -1.97071 0.39718 1.68251 -1.61803 -0.50844 1.98696 -0.93333 -1.30972 1.88369 -0.05711 -1.84225 1.39388 0.83083 -1.99674 0.61803 1.54828 -1.74149 -0.28463 1.94802 -1.12889 0.00000 -2.00000 0.72562 -1.79480 1.91899 -1.03279 -0.39718 1.61803 -1.98696 1.30972 0.05711 -1.39388 1.99674 -1.54828 0.28463 1.12889 -1.94802 1.74149 -0.61803 -0.83083 1.84225 -1.88369 0.93333 0.50844 -1.68251 1.97071 -1.22130 -0.17115 1.47348 0.00000 ... ... ..... ....... ......... ........... ............. E18' 2.00000 -0.93333 -1.12889 1.98696 -0.72562 -1.30972 1.94802 -0.50844 -1.47348 1.88369 -0.28463 -1.61803 1.79480 -0.05711 -1.74149 1.68251 0.17115 -1.84225 1.54828 0.39718 -1.91899 1.39388 0.61803 -1.97071 1.22130 0.83083 -1.99674 1.03279 0.00000 2.00000 -0.93333 1.98696 -1.30972 -0.50844 1.88369 -1.61803 -0.05711 1.68251 -1.84225 0.39718 1.39388 -1.97071 0.83083 1.03279 -1.99674 1.22130 0.61803 -1.91899 1.54828 0.17115 -1.74149 1.79480 -0.28463 -1.47348 1.94802 -0.72562 -1.12889 0.00000 ... ... ..... ....... ......... ........... ............. E18" 2.00000 -0.93333 -1.12889 1.98696 -0.72562 -1.30972 1.94802 -0.50844 -1.47348 1.88369 -0.28463 -1.61803 1.79480 -0.05711 -1.74149 1.68251 0.17115 -1.84225 1.54828 0.39718 -1.91899 1.39388 0.61803 -1.97071 1.22130 0.83083 -1.99674 1.03279 0.00000 -2.00000 0.93333 -1.98696 1.30972 0.50844 -1.88369 1.61803 0.05711 -1.68251 1.84225 -0.39718 -1.39388 1.97071 -0.83083 -1.03279 1.99674 -1.22130 -0.61803 1.91899 -1.54828 -0.17115 1.74149 -1.79480 0.28463 1.47348 -1.94802 0.72562 1.12889 0.00000 ... ... ..... ....... ......... ........... ............. E19' 2.00000 -1.12889 -0.72562 1.94802 -1.47348 -0.28463 1.79480 -1.74149 0.17115 1.54828 -1.91899 0.61803 1.22130 -1.99674 1.03279 0.83083 -1.97071 1.39388 0.39718 -1.84225 1.68251 -0.05711 -1.61803 1.88369 -0.50844 -1.30972 1.98696 -0.93333 0.00000 2.00000 -1.12889 1.94802 -0.28463 -1.74149 1.54828 0.61803 -1.99674 0.83083 1.39388 -1.84225 -0.05711 1.88369 -1.30972 -0.93333 1.98696 -0.50844 -1.61803 1.68251 0.39718 -1.97071 1.03279 1.22130 -1.91899 0.17115 1.79480 -1.47348 -0.72562 0.00000 ... ... ..... ....... ......... ........... ............. E19" 2.00000 -1.12889 -0.72562 1.94802 -1.47348 -0.28463 1.79480 -1.74149 0.17115 1.54828 -1.91899 0.61803 1.22130 -1.99674 1.03279 0.83083 -1.97071 1.39388 0.39718 -1.84225 1.68251 -0.05711 -1.61803 1.88369 -0.50844 -1.30972 1.98696 -0.93333 0.00000 -2.00000 1.12889 -1.94802 0.28463 1.74149 -1.54828 -0.61803 1.99674 -0.83083 -1.39388 1.84225 0.05711 -1.88369 1.30972 0.93333 -1.98696 0.50844 1.61803 -1.68251 -0.39718 1.97071 -1.03279 -1.22130 1.91899 -0.17115 -1.79480 1.47348 0.72562 0.00000 ... ... ..... ....... ......... ........... ............. E20' 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.00000 2.00000 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 2.00000 -0.28463 -1.91899 0.83083 1.68251 -1.30972 -1.30972 1.68251 0.83083 -1.91899 -0.28463 0.00000 ... ... ..... ....... ......... ........... ............. E20" 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.83083 -1.91899 1.68251 -0.28463 -1.30972 2.00000 -1.30972 -0.28463 1.68251 -1.91899 0.83083 0.00000 -2.00000 1.30972 -1.68251 -0.83083 1.91899 0.28463 -2.00000 0.28463 1.91899 -0.83083 -1.68251 1.30972 1.30972 -1.68251 -0.83083 1.91899 0.28463 -2.00000 0.28463 1.91899 -0.83083 -1.68251 1.30972 1.30972 -1.68251 -0.83083 1.91899 0.28463 0.00000 ... ... ..... ....... ......... ........... ............. E21' 2.00000 -1.47348 0.17115 1.22130 -1.97071 1.68251 -0.50844 -0.93333 1.88369 -1.84225 0.83083 0.61803 -1.74149 1.94802 -1.12889 -0.28463 1.54828 -1.99674 1.39388 -0.05711 -1.30972 1.98696 -1.61803 0.39718 1.03279 -1.91899 1.79480 -0.72562 0.00000 2.00000 -1.47348 1.22130 1.68251 -0.93333 -1.84225 0.61803 1.94802 -0.28463 -1.99674 -0.05711 1.98696 0.39718 -1.91899 -0.72562 1.79480 1.03279 -1.61803 -1.30972 1.39388 1.54828 -1.12889 -1.74149 0.83083 1.88369 -0.50844 -1.97071 0.17115 0.00000 ... ... ..... ....... ......... ........... ............. E21" 2.00000 -1.47348 0.17115 1.22130 -1.97071 1.68251 -0.50844 -0.93333 1.88369 -1.84225 0.83083 0.61803 -1.74149 1.94802 -1.12889 -0.28463 1.54828 -1.99674 1.39388 -0.05711 -1.30972 1.98696 -1.61803 0.39718 1.03279 -1.91899 1.79480 -0.72562 0.00000 -2.00000 1.47348 -1.22130 -1.68251 0.93333 1.84225 -0.61803 -1.94802 0.28463 1.99674 0.05711 -1.98696 -0.39718 1.91899 0.72562 -1.79480 -1.03279 1.61803 1.30972 -1.39388 -1.54828 1.12889 1.74149 -0.83083 -1.88369 0.50844 1.97071 -0.17115 0.00000 ... ... ..... ....... ......... ........... ............. E22' 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 0.00000 2.00000 -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 0.00000 ... ... ..... ....... ......... ........... ............. E22" 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 0.00000 -2.00000 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 0.00000 ... ... ..... ....... ......... ........... ............. E23' 2.00000 -1.74149 1.03279 -0.05711 -0.93333 1.68251 -1.99674 1.79480 -1.12889 0.17115 0.83083 -1.61803 1.98696 -1.84225 1.22130 -0.28463 -0.72562 1.54828 -1.97071 1.88369 -1.30972 0.39718 0.61803 -1.47348 1.94802 -1.91899 1.39388 -0.50844 0.00000 2.00000 -1.74149 -0.05711 1.68251 1.79480 0.17115 -1.61803 -1.84225 -0.28463 1.54828 1.88369 0.39718 -1.47348 -1.91899 -0.50844 1.39388 1.94802 0.61803 -1.30972 -1.97071 -0.72562 1.22130 1.98696 0.83083 -1.12889 -1.99674 -0.93333 1.03279 0.00000 ... ... ..... ....... ......... ........... ............. E23" 2.00000 -1.74149 1.03279 -0.05711 -0.93333 1.68251 -1.99674 1.79480 -1.12889 0.17115 0.83083 -1.61803 1.98696 -1.84225 1.22130 -0.28463 -0.72562 1.54828 -1.97071 1.88369 -1.30972 0.39718 0.61803 -1.47348 1.94802 -1.91899 1.39388 -0.50844 0.00000 -2.00000 1.74149 0.05711 -1.68251 -1.79480 -0.17115 1.61803 1.84225 0.28463 -1.54828 -1.88369 -0.39718 1.47348 1.91899 0.50844 -1.39388 -1.94802 -0.61803 1.30972 1.97071 0.72562 -1.22130 -1.98696 -0.83083 1.12889 1.99674 0.93333 -1.03279 0.00000 ... ... ..... ....... ......... ........... ............. E24' 2.00000 -1.84225 1.39388 -0.72562 -0.05711 0.83083 -1.47348 1.88369 -1.99674 1.79480 -1.30972 0.61803 0.17115 -0.93333 1.54828 -1.91899 1.98696 -1.74149 1.22130 -0.50844 -0.28463 1.03279 -1.61803 1.94802 -1.97071 1.68251 -1.12889 0.39718 0.00000 2.00000 -1.84225 -0.72562 0.83083 1.88369 1.79480 0.61803 -0.93333 -1.91899 -1.74149 -0.50844 1.03279 1.94802 1.68251 0.39718 -1.12889 -1.97071 -1.61803 -0.28463 1.22130 1.98696 1.54828 0.17115 -1.30972 -1.99674 -1.47348 -0.05711 1.39388 0.00000 ... ... ..... ....... ......... ........... ............. E24" 2.00000 -1.84225 1.39388 -0.72562 -0.05711 0.83083 -1.47348 1.88369 -1.99674 1.79480 -1.30972 0.61803 0.17115 -0.93333 1.54828 -1.91899 1.98696 -1.74149 1.22130 -0.50844 -0.28463 1.03279 -1.61803 1.94802 -1.97071 1.68251 -1.12889 0.39718 0.00000 -2.00000 1.84225 0.72562 -0.83083 -1.88369 -1.79480 -0.61803 0.93333 1.91899 1.74149 0.50844 -1.03279 -1.94802 -1.68251 -0.39718 1.12889 1.97071 1.61803 0.28463 -1.22130 -1.98696 -1.54828 -0.17115 1.30972 1.99674 1.47348 0.05711 -1.39388 0.00000 ... ... ..... ....... ......... ........... ............. E25' 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 0.00000 2.00000 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 2.00000 1.68251 0.83083 -0.28463 -1.30972 -1.91899 -1.91899 -1.30972 -0.28463 0.83083 1.68251 0.00000 ... ... ..... ....... ......... ........... ............. E25" 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 -0.28463 0.83083 -1.30972 1.68251 -1.91899 2.00000 -1.91899 1.68251 -1.30972 0.83083 -0.28463 0.00000 -2.00000 1.91899 1.30972 0.28463 -0.83083 -1.68251 -2.00000 -1.68251 -0.83083 0.28463 1.30972 1.91899 1.91899 1.30972 0.28463 -0.83083 -1.68251 -2.00000 -1.68251 -0.83083 0.28463 1.30972 1.91899 1.91899 1.30972 0.28463 -0.83083 -1.68251 0.00000 ... ... ..... ....... ......... ........... ............. E26' 2.00000 -1.97071 1.88369 -1.74149 1.54828 -1.30972 1.03279 -0.72562 0.39718 -0.05711 -0.28463 0.61803 -0.93333 1.22130 -1.47348 1.68251 -1.84225 1.94802 -1.99674 1.98696 -1.91899 1.79480 -1.61803 1.39388 -1.12889 0.83083 -0.50844 0.17115 0.00000 2.00000 -1.97071 -1.74149 -1.30972 -0.72562 -0.05711 0.61803 1.22130 1.68251 1.94802 1.98696 1.79480 1.39388 0.83083 0.17115 -0.50844 -1.12889 -1.61803 -1.91899 -1.99674 -1.84225 -1.47348 -0.93333 -0.28463 0.39718 1.03279 1.54828 1.88369 0.00000 ... ... ..... ....... ......... ........... ............. E26" 2.00000 -1.97071 1.88369 -1.74149 1.54828 -1.30972 1.03279 -0.72562 0.39718 -0.05711 -0.28463 0.61803 -0.93333 1.22130 -1.47348 1.68251 -1.84225 1.94802 -1.99674 1.98696 -1.91899 1.79480 -1.61803 1.39388 -1.12889 0.83083 -0.50844 0.17115 0.00000 -2.00000 1.97071 1.74149 1.30972 0.72562 0.05711 -0.61803 -1.22130 -1.68251 -1.94802 -1.98696 -1.79480 -1.39388 -0.83083 -0.17115 0.50844 1.12889 1.61803 1.91899 1.99674 1.84225 1.47348 0.93333 0.28463 -0.39718 -1.03279 -1.54828 -1.88369 0.00000 ... ... ..... ....... ......... ........... ............. E27' 2.00000 -1.99674 1.98696 -1.97071 1.94802 -1.91899 1.88369 -1.84225 1.79480 -1.74149 1.68251 -1.61803 1.54828 -1.47348 1.39388 -1.30972 1.22130 -1.12889 1.03279 -0.93333 0.83083 -0.72562 0.61803 -0.50844 0.39718 -0.28463 0.17115 -0.05711 0.00000 2.00000 -1.99674 -1.97071 -1.91899 -1.84225 -1.74149 -1.61803 -1.47348 -1.30972 -1.12889 -0.93333 -0.72562 -0.50844 -0.28463 -0.05711 0.17115 0.39718 0.61803 0.83083 1.03279 1.22130 1.39388 1.54828 1.68251 1.79480 1.88369 1.94802 1.98696 0.00000 ... ... ..... ....... ......... ........... ............. E27" 2.00000 -1.99674 1.98696 -1.97071 1.94802 -1.91899 1.88369 -1.84225 1.79480 -1.74149 1.68251 -1.61803 1.54828 -1.47348 1.39388 -1.30972 1.22130 -1.12889 1.03279 -0.93333 0.83083 -0.72562 0.61803 -0.50844 0.39718 -0.28463 0.17115 -0.05711 0.00000 -2.00000 1.99674 1.97071 1.91899 1.84225 1.74149 1.61803 1.47348 1.30972 1.12889 0.93333 0.72562 0.50844 0.28463 0.05711 -0.17115 -0.39718 -0.61803 -0.83083 -1.03279 -1.22130 -1.39388 -1.54828 -1.68251 -1.79480 -1.88369 -1.94802 -1.98696 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996738207852 = 2*cos(2*π/110) = 2*cos(π/55) 1.986963470697 = 2*cos(4*π/110) = 2*cos(2*π/55) 1.970707671695 = 2*cos(6*π/110) = 2*cos(3*π/55) 1.948023833885 = 2*cos(8*π/110) = 2*cos(4*π/55) 1.918985947229 = 2*cos(10*π/110) = 2*cos(π/11) 1.883688727279 = 2*cos(12*π/110) = 2*cos(6*π/55) 1.842247306230 = 2*cos(14*π/110) = 2*cos(7*π/55) 1.794796857383 = 2*cos(16*π/110) = 2*cos(8*π/55) 1.741492154240 = 2*cos(18*π/110) = 2*cos(9*π/55) 1.682507065662 = 2*cos(20*π/110) = 2*cos(2*π/11) 1.618033988750 = 2*cos(22*π/110) = 2*cos(π/5) = (√5+1)/2 1.548283221278 = 2*cos(24*π/110) = 2*cos(12*π/55) 1.473482275753 = 2*cos(26*π/110) = 2*cos(13*π/55) 1.393875137311 = 2*cos(28*π/110) = 2*cos(14*π/55) 1.309721467891 = 2*cos(30*π/110) = 2*cos(3*π/11) 1.221295759271 = 2*cos(32*π/110) = 2*cos(16*π/55) 1.128886437734 = 2*cos(34*π/110) = 2*cos(17*π/55) 1.032794923278 = 2*cos(36*π/110) = 2*cos(18*π/55) 0.933334646451 = 2*cos(38*π/110) = 2*cos(19*π/55) 0.830830026004 = 2*cos(40*π/110) = 2*cos(4*π/11) 0.725615410701 = 2*cos(42*π/110) = 2*cos(21*π/55) 0.618033988750 = 2*cos(44*π/110) = 2*cos(2*π/5) = (√5−1)/2 0.508436668387 = 2*cos(46*π/110) = 2*cos(23*π/55) 0.397180933291 = 2*cos(48*π/110) = 2*cos(24*π/55) 0.284629676547 = 2*cos(50*π/110) = 2*cos(5*π/11) 0.171150016958 = 2*cos(52*π/110) = 2*cos(26*π/55) 0.057112101587 = 2*cos(54*π/110) = 2*cos(27*π/55) Symmetry of Rotations and Cartesian products A1' d+g+i+k+m z2, z4, z6 A2' R Rz A2" p+f+h+j+l z, z3, z5 E1' p+f+h+j+l {x, y}, {xz2, yz2}, {xz4, yz4} E1" R+d+g+i+k+m {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} E2' d+g+i+k+m {x2−y2, xy}, {z2(x2−y2), xyz2}, {z4(x2−y2), xyz4} E2" f+h+j+l {z(x2−y2), xyz}, {z3(x2−y2), xyz3} E3' f+h+j+l {x(x2−3y2), y(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)} E3" g+i+k+m {xz(x2−3y2), yz(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E4' g+i+k+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E4" h+j+l {z((x2−y2)2−4x2y2), xyz(x2−y2)} E5' 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)} E5" 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)} E6' i+k+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E6" j+l E7' j+l E7" k+m E8' k+m E8" l E9' l E9" m E10' m Notes: α The order of the D55h point group is 220, and the order of the principal axis (S55) is 110. The group has 58 irreducible representations. β The D55h point group is isomorphic to D55d, C110v and D110. γ The D55h point group is generated by two symmetry elements, S55 and either a perpendicular C2′ or a vertical σv. Also, the group may be generated from two σv planes, or a σv and a C2′ (some pairs will yield smaller groups, though; choosing a minimum angle is safe). The canonical choice, however, is to use redundant generators: C55, C2′ and σh. δ The group contains one set of C2′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. Similarly, the single set of symmetry planes denoted σd contains the xz plane but not the yz plane. ε The lowest nonvanishing multipole moment in D55h 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. For this group, however, some of the irrational characters cannot be expressed by a closed algebraic form using real numbers only.
D53h | ||
D54h | ||
C55 C55v C55h D55 | D55h | D55d |
D56h | ||
D57h |
This Character Table for the D55h point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.