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Hi. I had some experiences with dual maps to. It also appear in our electronics class. The idea (to me) is this: replace faces/area with points (in our class we call it meshes and nodes: faces -> meshes, points -> nodes) and points with faces. That area outside is also considered and in its dual its a point. This tutorial illustrated it as a very thick line, in our class we just represent it with a point and draw long lines to connect it to other parts.
Now when to faces share an line/edge, its dual are points connected together by a line/edge. When two points are connected together by a (...)