[Telamond]

I think I've been staring at the octahedron for an hour or so, but I can't find the C3 rotational symmetry in it, and it's supposed to have 8 of them. Intuitively, I'm guessing 4 planes though, where one is clockwise and the other is counter-clockwise.

[jpg28]

Here, I have the answer for you. You can find the C3 axes when you insert an axis of rotation through the face of the octahedron. I believe there are four C3 axes, but if you count all the faces, maybe it's safe to assume that there's 8? But I'm pretty convinced that there are just 4. Eitherway, here's one of them.

P.S. I suggest you get a model of an octahedron so that you could see it better. Have a nice day!

[Telamond]

Ah!
Thank you so much! I see it perfectly now! I was going insane, I even made an origami octahedral and still couldn't see it!
There are 4 C3 axes, but you can rotate them clockwise and counter clockwise which would make it 8 C3 axes.
I think that's how it works, if not, all the character tables are wrong.

[jpg28]

Hahaha. I agree with you, and character tables are never [I guess] wrong. Have a nice day!