Not exhaustive but a lens , but the 3D rotation groups SO(3) is not simply connected. The antipodal points Pac-Man and so while a 360 degree rotation is consid

Not exhaustive but a lens , but the 3D rotation groups SO(3) is not simply connected. The antipodal points Pac-Man and so while a 360 degree rotation is considered 'invariant' that only holds for rigid objects with no connections. Rolling up a hose, twirling a baton, or the belt trick shows that 720 is the real invariant rotation. Merge and Delete those two points at infinity and you get a donut.