- #1

lugita15

- 1,554

- 15

But the one thing I do know is that [itex]S_{4}[/itex] has 24 elements, and that seems like too many. The rotation group of a cube is generated by the following three elements: a 90 degree rotation about x, a 90 degree rotation about y, and a 90 degree rotation about z. But any rotation about z can be written as a composition of rotations about x and y, so it seems that the rotation group is just generated by the x-rotation and the y-rotation. If that's the case, then any rotation of a cube can be written as [itex]a^{m}b^{n}[/itex], where a is the rotation about x, b is the rotation about y, and m and n range from 1 to 4. Thus the rotation group should only have 16 elements. Where am I going wrong?

Any help would be greatly appreciated.

Thank You in Advance.