[Math] Triangulation of double-holed torus to calculate fundamental group

Question

Show that the fundamental group of the double-holed torus is given by: $\pi_1=<a, b, c, d | aba^{-1}b^{-1}=cdc^{-1}d^{-1}>$

I have ended up with the following identification diagram representing the space:

I am stuck with triangulating this space with simplices. Please could you help me with this?

After this I can find the generators $a, b, c$ and $d$ on the remaining 1-simplices that generate the fundamental group

Answer 1

Here is the image. Now just stretch the part where you glued for the connected sum and you get your triangulated octagon.