It is now my forever-headcanon that Bill was a Flatlander. 

He says that he comes from the second dimension, a place of “ flat minds in a flat world with flat dreams.” Like all Flatlanders, Bill has one eye that doubles as a mouth.

Flatland was a horribly restrictive and segregated society and I’m sure Bill hated it, and I’m kind of okay with him setting it all on fire.

This would also mean that as an isosceles triangle he’d have been a member of the serf/soldier class, the lowest rank a male Flatlander can have. (EDIT: Or possibly the equilateral merchant class, which seems to suit him better.) At least before he became all powerful and killed everybody.