Seems like a solid choice, Sarah doesn’t even question your pick and moves on. “Right so, next we have to partition our Dini orbits by our group H so that we can get two points both of which will belong to the same orbit once rotated. You’re still following all of this right?”
You rub your eyes like you fell asleep to some lecture and woke up in the middle of the test. Where did all of these definitions come from, now you have to write something on the board, this feels like a critical step, what does she mean H, and where are all these M’s from. You’re too embarrassed to ask and figure out what means what.
“This is a pretty important step; we need enough pieces of our S^2 unit sphere that we can piece them together twice!”
What paradoxical decomposition do you go with?
A1=S(a)M, A2=S(b^−1)MUM\B , A3=S(a^−1)M, A4=S(b)BUMUB
A1=S(b^−1)M\B, A2=S(a)MUMUB, A3=S(b)B, A4=S(a^−1)M