I'm sorry, but can you explain what a regular interval means, here? If it means a regular interval of time, what happened to your "construction of time", if you simply introduce it?5......….Let P_T advance by one (rotate relative to S_1,2,3) at regular intervals.

In mathematics, a rotation is simply a thing that exists (and you can prove it! quite easily with geometry and some symbols), you don't have to rotate anything in "real time"; time isn't in the picture at all.