Sandwich Theory: Part II

Last year I described a classification of sandwiches and their relatives: Sandwich Theory, which I still believe in. However, I recently came across this image in an imgur post:

It made me realize that there were several classes of sandwiches I overlooked.

First, I must address a common class of sandwiches I also overlooked, the club. A club sandwich is a subset of the true sandwich, but contains an interior slice of bread. You could also consider a club to be a compound sandwich, which means a club is actually two sandwiches combined together as one.

What if I added a third  layer? I would call that a double club. And so on, as more layers are added, generalized as an n-club (a term I just made up).

club

This leads me to a new class of sandwiches, which I will generalize as Complex Sandwiches

Complex Sandwiches

You could keep adding layers to infinity, which is fine, but there is no rule that the bread slices’ faces must be parallel, nor be opposite facing. This means you could build an n-club that looped back around, forming a loop.

torus1

This poses an interesting question: is it still a sandwich? As far as I know, there is no requirement that the outer faces of the bread must be exposed. If this is true, I can reduce this to a toroidal 1-club, which is topologically the same as the bagel in question!

torus

So there we have it. The bagel is actually a toroidal peanut butter and jelly club sandwich

Taking this one step further, let’s remove one of the slices. You now have a regular toroidal sandwich, where the the outer faces of each slice are simultaneously the inner faces of the other slice. This however, does not technically qualify as a true sandwich, as there is only one piece of bread:

torus2

It is known that it is possible to create a mobius bagel, in which the a knife is rotated 360 degrees while slicing the bagel. This results in the two halves being linked.

You can also do the same, but only rotate the blade 180. Again, this is not a sandwich, because it is a single piece of bread

Of course, so far all of these are physically possible to create. If you remove the limitations of physics, there are so many possibliites…

What if instead of connect the outer faces, I connected the edges? I would get a “tubewich”. If I removed one of the “slices”, It would become an open face “tubewich”.

sandwichTube

While this seems like a new concept, The “tubewich” is actually topologically the same as a bagel

sandwichTube2

If I connect the other two ends of the tubewich I get a toroidal tubewich

torusTube

Or similarly a Kleinwich, where a single piece of bread forms both sides of an enclosed sandwich. Again, because it has a single piece of bread, it is not a true sandwich, though it does require technology to allow bread to phase through itself.

klein

Or a Spherewich

sphere

Of course, none of these are as elegant as the Triwich, or the Double Fold:

In conclusion, in the absence of gravity, and in cases, reality, sandwich possibilities are endless, a small slice of which have been presented here

compound

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