For the Icosahedron we go back to using triangles: there are 20 in all, with 5 at each vertex.
What’s next? Well, sadly this is the end of the simple Platonic solids: if you want to know, go to Why there are only 5 Regular Solids. But there are lots more to come if we vary the rules a bit: our next step is The 13 Semi-Regular (Archimedean) Polyhedra.