nothing. it is just an example of a topological surface in R^3 with no interior, only 1 edge, and 1 face that can be constructed in our universe. pretty cool, but not really any more significant than saaay a coffee cup, which is a topological surface in R^3 with 1 face, no edges, an interior, and a hole, just like a donut.

The thing is that it is an object with no up or down side. Cut a strip of paper, give it a twist and stick the two ends together with glue. If you put a marker on the paper and keep drawing a line, you’ll cover both sides without lifting the pen.

And there’s a cool party trick too, perfect for a wedding or anniversary. If you cut the strip in halves on the line you drew, you’ll end up with two interlocked heart shapes 🙂

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