Thanks. Do you know if this works in general? (I mean, blowing up toric varieties coming from polytopes along a reduced union of invariant subvariaties corresponding to shaving off parts of the polytope "the same amount")? If so, is there a place where I can read about it? In this particular case, if you do not shave the edges off the same amount, then I think you get one of the iterated blow-ups. Thank you!