Yeah, also it may seem obvious that a bagel sandwich sliced in the traditional would fall into the {top,bottom} Sandwich category, but they provide no formal d

Yeah, also it may seem obvious that a bagel sandwich sliced in the traditional would fall into the {top,bottom} Sandwich category, but they provide no formal descriptions of smoothing. I'm sure I could construct some wildly-non-homotopic constructs that would defy the "obvious" smoothing. (Is an uncut bagel a Toast or an "air" Sushi?) If I were arguing for this rule, though, I'd say that the unlisted combinations should collapse to the listed ones based on curvature. {side,bottom} collapses to either Toast or Taco, and {side,back,bottom} collapses to any of Toast, Quiche, or Taco.