Klein’s quartic curve is a surface of genus 3: a 3-holed torus, shown here embedded in R^3. But this gives a distorted view of its geometry; in the true surface, all 336 triangles are congruent, and there is a symmetry of the whole surface that maps any of them into any other.pic.twitter.com/7yYHqnWSgK
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It can also be seen as a 14-sided polygon in the hyperbolic plane, with the edges identified as marked in this image.pic.twitter.com/c9nqd7HFSw
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It might not be obvious that these two forms have the same topology, but with a little stretching it’s possible to transform one into the other:pic.twitter.com/cCVJs3c4ub
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Replying to @gregeganSF
Thank you for this. I am enchanted. I had always wanted an animation of this sort, yet I despaired ever of producing one myself. I feel like a kid on Christmas morning.
1:54 PM - 5 Aug 2019
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