This was inspired by Tanya Sienko (if that means anything!!)
It is possible for each of the six faces to have a capital "T" on them.
That is, each face looks like
X X X O X O O X O
1) How many classes are there?
2) How many members are in each class?
3) How easy is it to get to them from solved?
[in a few days, I don't want to spoil the fun]
Good luck, and happy hacking.