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I have some problems understanding the geometrical construction of Klein's quartic.

Starting from the fundamental region [itex]R=\{z\in \mathbb{H}| |z|>1,-\frac{1}{2}\leq Re(z) \leq \frac{1}{2}\}[/itex], how can I obtain a 14-gon with 336 triangles?

Moreover, how does the group PSL(2,7) act on this figure? Why the edges' identifications are exactly 1-6, 3-8, 5-10...?

Can I ask for your help, please?

Thank you in advance!

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# Klein's quartic

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