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Mathematical rotation problem
S4={( 1),( 1 ^ 2),( 1 ^ 3),( 1 ^ 4),(2 ^ 3),(2 ^ 4),(3 ^ 4),( 1 ^ 2 ^ 4),( 1 ^ 3 ^ 2),( 1 ^ 3 ^ 4), ( 1 ^ 3 ^ 4),( 1 ^ 4),( 1 ^ 4 ^ 2),( 1 ^ 4 ^ 3),(2 ^ 4 ^ 3),(2 ^ 4 ^ 3),( 1 ^ 3 ^ 4 ^ 4 ^ 4 ^ 4

Elements with different formats in S4 correspond to different yoke classes. Note that (1)=( 1)(2)(3)(4), (1 2 3)=( 1 2 3)(4) and so on, so the format of elements in S4 is as follows.

( 1) 4, ( 1) 1 (3) 1, ( 1) 2 (2) 1, (2) 2, (4) 6558.

( 1)^4={( 1)(2)(3)(4)},

(2)^2={( 1 2)(3 4),( 1 3)(2 4),( 1 4)(2 3)}。