I know ICN5D is into round things with holes, so i've been trying to figure out the 5D rotation space.

A phase space is a space where every point represents a different state. For rotations, we have a space where every point represents a different rotation mode and rotation speed.

For 2D, you have a number line. It spins one way when positive and the other when negative. Any point gives a speed.

For 3D, you have 3d space itself. This means that you pick a point, and the ray through it defines the north pole, and the distance is the speed as before.

For 4D, you have a 6D thing, this is a bi-glomo-hedric prism (or cartesian product of two 3-sphere-surfaces). In essence, three directions x1 x2 x3 define a left clifford rotation, and the axies y1 y2 y3 define a right clifford rotation. The radius is the speed. If you have equal left and right cliffords they give a single rotation in 2 axies and still in the other two. This is the bi-glomo-hedric prism thing. This space divides the 5-sphere (glomo-terix) into two halves, so it makes sense in 4D, that you can have 'left rotations' and 'right rotations' that have to pass through a 'wheel rotation'.

For 5D, it's a 10D thing. I don't have a name for it, but it's something like a bi-glomohedric-prism glomoterix comb. It seems to be a rototope, of the kind

( (iiiii) ((iii)(iii)))

In essence, we replace each diameter of the bi-glomohedric prism with a 5-sphere, which means that we add four dimensions to each of the six extant dimensions of the 4d rototope.

Just have to figure out how the odds and ends tie up.