It turns out though, if you think about the group which permutes the roots of such a polynomial, there's something about the nature of this group that reveals that no quintic formula can exist.

事实证明， 如果你考虑一下置换这种多项式根群，这个群揭示了不存在五次程求根公式。

And that's because of all of the different patterns we can permute.

这是因为我可以改变所有不同模式。

This particular isomorphism between cube rotations and permutations of four objects is a bit subtle, but for the curious among you, you may enjoy taking a moment to think hard about how the rotations of a cube permute its four diagonals.

这种立转与四个对象排列之间同构关系有点微妙，但对于你中好奇人来说， 你可能会喜欢花点时间思考一下立转是如何对其四条对角线进行排列。

That however, would grossly overcount the  total number since all the different ways you can permute these four items would be  counted separately.

然而，这样会严重高估总数，因为这四种项目不同排列式会被单独计数。