## Klein's quartic

Hi all!

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

Starting from the fundamental region $R=\{z\in \mathbb{H}| |z|>1,-\frac{1}{2}\leq Re(z) \leq \frac{1}{2}\}$, 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...?

 Quote by mery2 Hi all! I have some problems understanding the geometrical construction of Klein's quartic. Starting from the fundamental region $R=\{z\in \mathbb{H}| |z|>1,-\frac{1}{2}\leq Re(z) \leq \frac{1}{2}\}$, 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!