It turns out my conjecture about these was wrong. I expected that you could get the n'th homology group of a rotatope just by counting the n-spheres, except with an extra Z at the beginning and end. I've just found a few exceptions.
H222 = 1,3,0,1 as expected.
H322 = 1,2,3,0,1 where we expected 1,2,1,0,1
H332 = 1,1,2,4,0,1 where we expect 1,1,2,0,0,1
I can't see any connection yet. I'll have to do a few more.