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I am still looking to understand the combinatorial rule – if any – which for a given type of hyperbolic tesselation constructs the corresponding chord diagram – if any – stage-wise.
One can see the first three such stages for the the $\{5,4\}$ tessalation in this Fig 6.. Apparently these authors use an algoirthm called “vertex inflation”, apparently due to arXiv:1805.02665.
So I guess I know one place where to look now. But I still feel that the rule “Schlaefli symbol $\mapsto$ chord diagram” that I am after must be something nice and simple that is known in the maths literature?
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