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When a square is wrapped at the edges, obtains a torus. Is it possible to do the same for a hexagon?

What is the shape/topology of wrapping a hexagon?

rectangle wrapped to torus hexagon

Note: I was just reading this https://github.com/aichallenge/aichallenge/wiki/Ants-Problem-Description and came up with this question. I'm a physicist.

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fyi if you take a $4g$-gon and identify sides $ababcdcd...$ you get a genus $g$ surface –  yoyo Jul 24 '11 at 13:53

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up vote 2 down vote accepted

It's still a torus, lol - just with a $180^{\circ}$ "Indian burn" relative to the square-wrapped version:

enter image description here

Image source: http://www.math.cornell.edu/~mec/Winter2009/Victor/part1.htm

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Thanks, that is exactly what I wanted. I didn't realize that the tube should be twisted before connecting the ends. –  whoplisp Jul 24 '11 at 11:03

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