P.S. I am not entirely sure that the subject I am referring to is in fact the one called "Lego Teichmuller". I am referring to the relations between the absolute Galois group $\text{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ and geometric objects like Riemann surfaces, covering spaces, moduli spaces, and Teichmuller spaces. The projective line with three points removed $\mathbb{P}-\{0,1,\infty\}$ seems to occupy a special place in this subject. I believe the linked articles should convey better what I am looking for.