Earlier today, I was wondering about the topology of sandwiches.

A simple open-face sandwich is essentially a two-dimensional sandwich - you have only the surface area of the single piece of bread to work with (most open-face sandwiches will pile toppings on toppings, but let's overlook this for now). If an open-face sandwich is the two-dimensional sandwich, it's not a stretch to consider the traditional sandwich to be a three-dimensional sandwich, since you use the volume between the two pieces of bread for your sandwich constituency.

What would happen if we were to extend the sandwich to a fourth dimension? It's been a while since I've read Flatland, so I can barely wrap my head around the concept. Would you have a sandwich that would change depending on what part of it is in our 3D space? A sandwich that you eat before you finish making it? A sandwich with another sandwich inside itself?