This is actually what i did in my work. As you can see, the different blocks aren't well connected. If you have an idea, please let me know.
 Thanks for your help.

This is the original picture

Hello Yves,
 
You could do everything with the create face tool. This is probably the simplest to do here.
I will show here a workflow using primitives, split, create face and deletion of faces.

It seem it is limited to 5 images per post .... and to publish in inverse order ...  :-(
 
Here the rest of the steps :