- #1

DaveC426913

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Now, there're two ways you can make a wrap-around screen into a torus - vertical or horizontal. You can join the top/bottom THEN the sides, which gets you a horizontal torus, or you can join the sides THEN the top/bottom, which gets you a vertical torus.

This seems kind of counter-inutitive to me - that you can get to two states that are equivalent but forever distinct.

Questions:

1] Are these two shapes topologically interchangeable? Can you start with one, and get to the other without tearing the surface?

2] Is there an intermediate/generic/more symmetical shape that exists halfway between those two?

3] Are there other foldings that give the same wraparound result?

What I'm trying to get at is that, from the point of view of a Flatlander living on the torus, is it possible for him to state (or be told) that he is living on a "vertical torus", not a "horizontal torus", and ne'er the twain shall meet?