i can't really describe it to another but this is simple in my head. assuming for illustrative purposes you're always doing at least one rotation/fold in dimension(n-max) i just... collapse in/out and then rotate in one normal spatial direction

lilke... the vertices fold in and that will mean that they look like they're overlapping but that's just the poor projection of a 4th dimension onto 3 dimensional space and then there's a rotational aspect which is simpler in z dimension but more obvious/less overlapping in x or y