For a continuous rotation representation in 3D, do you need at least 4 real variables?

Question

I'm pretty sure I have read this somewhere, but I just can't get to find this theorem anywhere.

Is there a theorem that states that for a continuous rotation representation you need at least 4 real variables?

Answer 1

Turns out, I found what I was looking for! Instead of putting the explanation, I'll rather leave the paper where I found my answer:

John Stuelpnagel - On the Parametrization of the Three-Dimensional Rotation Group, 1964