From @johncarlosbaez's thread https://twitter.com/johncarlosbaez/status/1195739505984073731 … I have realized that the hyperbolic manifold we have been flying through in some videos is kind of a 3D version. The genus 4 Riemann surfaces themselves can be seen as tot.geo. submanifolds (they look like circles).pic.twitter.com/nbJIPqd0tB
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Thanks! We do the same computations as usual for {4,3,5} tiling in the hyperboloid model, but in the field F₂₅ instead of reals. Two cells of the actual {4,3,5} are identified (in some orientation) iff the isometry matrix taking one to other computed in F₂₅ equals identity.
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The video is the dual {5,3,4} of course. Such symmetric manifolds are very natural, so I would not be surprised if this particular manifold has some name, or could be obtained in some other way.
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