I think a hot dog is a sandwich

[talah]

and also the two sides must be at least kind of parallel (like at a 30 degree angle max I think)

I'm interested in your hotdog modelling here. the dog can take various states of "push", for example a really shallow cut on the bun and the angle that a dog would naturally take if it was only depressed into the initial cut. Surely that would be 90 degrees bun spread at a minimum, in which case, you're saying that sometimes a hotdog with a bun is a sandwich and sometimes not.

[talah]

matt stoney's nightly routine notwithstanding, i'd say that a sandwich is most things pressed between parallel bread slices.