Reading about the symmetries of a cube, here, they talk about (in the section "Details") "3 x rotation about a four fold axis" etc. I'm not quite sure what "four fold axis" means in the context. Can someone help? Also, since a cube is face transitive, it should be possible to define a group of rotations such that starting with one face, the rotations construct all the other faces. Is there a name for and easy way to identify this group? The full Octahedral symmetries (24) are much more than the faces.
2026-03-24 23:44:35.1774395875
What does "n-fold axis" mean in symmetry groups?
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A four fold axis of symmetry is one for which a rotation of $\pi/2$ exists, so that rotation is of order four. The symmetries of the cube are the full octahedral group: https://en.wikipedia.org/wiki/Octahedral_symmetry
Edit. The edit to the question provides the same wikipedia link. It's all there.