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I think you are describing what is called a "mobius strip". It has two sides, but if you try to draw a line on it, you eventually find that the line is on both sides.It can be made as follows: Cut a 2" wide strip of paper at least 18-24" long. Make a circle, or loop with it. Turn one end over once, and then attach the ends. That's a mobius strip.

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Q: What is a piece of paper with only one side?
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