# Computing fundamental group with Seifert-van Kampen theorem

I'd like to compute the fundamental (using Seifert-van Kampen theorem) group of a genus-2 surface and others inductively made surfaces (like connected triple torus ).I know that to compute the group of the first one I have to represent it as a quotient of a plain polyhedron (it's analogous to computing the f. group of a torus by representing it as a sguare).But I don't know how to do it in a latter examples.Is it posibble to somehow do it inducitevely?

• They can all be computed from polygonal presentations. It's not hard to guess the pattern. Mar 26 '16 at 15:45