Last night I worked this out. Now I have to stop the bits and pieces spinning.
The phase-space of 4D is a bi-spherical tegum or prism. The bits on the tegum ends belong to the clifford rotations, those on te prism joins belong to the rotation of great arrows.
Each line through the centre belongs to a rotation-speed of a specifice direction.
The five-dimensional version is to replace these axies with a full 5D space.