Let's use this thread for talking about wiki articles on toratopes and homology groups.
I just have a couple of things to say for now.
1. I'm not sure about using vertical bars instead of numbers for toratopic notation. ((II)II) makes the dimension slightly more obvious, but (211) is a lot easier to read and it's still easy to add up the numbers.
2. The word for shapes that have the same homology groups is homeomorphic. I don't think homologous means anything in topology.
Also, I'll collect some of the rules I've come up with here, so we can put them in the wiki somewhere and make a table.
1. Cartesian products of two hyperspheres
HqSa x Sb = h0 + ha + hb + ha+b
This means that if a \= b then
H0 = Z
Ha = Z
Hb = Z
Ha+b =Z
and everything else is zero.
2. Cartesian product of anything with a circle
Hq A2 = Hq A ⊕ Hq-1 A