generate the fixed field of formula_56. The Galois correspondence implies that every subfield of formula_60 can be constructed this way. For example, for formula_61, the fixed field is formula_62 and if formula_63 then the fixed field is formula_64. The fixed field of formula_54 is the base field formula_66 where is the -invariant written in terms of the modular lambda function:formula_67Similar examples can be constructed for each of the symmetry groups of the platonic solids as these also have faithful actions on the projective line formula_68 and hence on formula_69.