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

这是因为我们可以改变所有不同模。

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，这会严总数，因为排列这四个项目所有不同方都将单独计。

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.

但事实证明， 如果你考虑对这样一个多项进行置换群，就会发现该群性质表明不存在五次公。

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.

立方体旋转和四个对象排列之间这种特殊同构有点微妙，但对于好奇人来说， 您可能会喜欢花点时间认真思考立方体旋转如何排列其四个对角线。