Information for point groups with fivefold rotational axis

Sometimes representations for fivefold axis are defined in terms of

Here you can find the definitions and relationships:

cos(2

/5) = (5^½ - 1) / 4
cos(4

/5) = - (5^½ + 1) / 4

= (5^½ + 1) / 2

2cos(2

/5) =

- 1
2cos(4

/5) = -

exp(i

) = cos(

) + isin(

)