nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyz6v2rsmc8tufcfh95x8vlz8q4gf7pctpucsj3rajrxsav62ny5fv528eua (nprofile…8eua) That’s so frustrating, because SO(3) is one of the easiest Lie groups by far to visualise without having to worry about higher dimensions!
And once you have that model of it — as a sphere with antipodal points identified — you can easily understand cool things like the Dirac belt trick, and why an electron needs to be rotated twice to return to its original state:
https://www.gregegan.net/APPLETS/21/21.html