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There is a way to partition a sphere into six subsets such that, using only isometries, you can build two spheres, identical to the first one, with those six subsets.


I thought this was interesting so I googled it. "Oh, that's cool", I thought, "I don't understand anything in the titles of the first 10 results."

https://www.google.com/search?q=sphere+subset+isometric




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