Hi, hope everyone's having a good holiday.
I just realised that a toratope and it's expanded rotatope have the same holes in the minimal frame, but not in other frames. In fact they don't even have the same number of frames. So it's not sufficient to work out the homology groups just for rotatopes. We have a whole lot more stuff to work out
For example, a filled in (31) is basically a sphere, but a filled in (211) is a circle and a 4-frame 32 is a pentasphere. I'll figure some more out later. I'll be pretty busy for most of the next two weeks though.