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What happens when two infinite lines stop intersecting and become parallel?
Have a look at Homogeneous Coordinates. Quote from Wikipedia: "They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates". This model might give you more insight of how you can think of points in infinity.
Wrapped hexagon topology
Thanks, that is exactly what I wanted. I didn't realize that the tube should be twisted before connecting the ends.