In a WP article I found you can fold a Mobius strip in the shape of a regular pentagon, which is rather neat. So I got a strip of paper and tried it. Here's the result and you can see it is a series of triangles, each folded over the one before.
How do we know this really is a Mobius strip? Well. if it is, it must not have a 'front' and a 'back' but just be a single surface. Here's an argument to show this is indeed the case. Assume it has does have a front and a back and let's try to colour the front red and the back green.
So number the triangles and take the visible part of Triangle 1 for be on the front, so we colour it red.
Triangle 2 is folded over Triangle 1 and the visible part of Triangle 2 must have come from behind, so it should be coloured the opposite colour, green.
Triangle 3 is next folded over Triangle 2 and by a similar argument the colour should reverse again, so the visible part of Triangle 3 has to be red.
Similarly Triangle 4 must then be green.
But now we are stuck! Triangle 5 should be the opposite colour to Triangle 4, hence red, and that would make Triangle 1 green. But we know already it is red and not green, so we have a contradiction, and the only way out is to conclude that we can't identify a 'front' and a 'back', and we are dealing with a one-sided surface.
Here's the sequence and the impasse.
I think we could fold a Mobius strip in the shape of a regular heptagon, or a polygon with any odd number of sides. I haven't made a physical model but a heptagonal version would look like this
Interestingly I had a argument with Copilot, because I showed it a picture of the pentagonal case and asked it it was a Mobius stript. CP said no, because this was a flat figure. So I explained it was was not just a plane figure and folded from a strip of paper.
CP took this on board but still insisted we did not have a Mobius strip. So then I gave it the proof, more or less as presented above, and it agreed it had been wrong, and said this must therefore be a 'non-orientable surface', i.e. no distinguishable front and back (and no consistent definition of clockwise vs counterclockwise). I was quite surprised, these AIs often double down, but here it was as though I had persuaded it and it followed my reasoning.