This will be a jargon filled technical post, skip it if that's not what your into. But if you like me, and find it fascinating and useful read on.
In an attempt to create polygonal objects using only Python one polygon at a time, I encountered the seemingly baffling way Maya numbers new edges. Well, after many failed Google searches (the Mesoamerican civilization complicates everything), I experimented enough to figure out how Maya decides what number goes to which edge. For these examples I use the gui version of the Append To Polygon Tool, but it can also be used with Python as the polyAppend method.
Take for example this polygonal object, note the edge numbers and vertex numbers. Pay particular attention to edge 1, because I will be appending a polygon to that edge.
So now note the new edges. The new vertex (5) is one more than the previous highest number vertex (4). We're adding two new edges, so we get edges that are one and two more than the previous highest number edges. Which all makes sense, but what is more confusing is how does maya decide which edge should be edge 7 and which should be edge 8?
The initial edge rule: Maya connects edges from the lowest vertex first, so in this case the edge connecting vertex 1 and vertex 5 ( the new one) will be numbered as one more than the previous highest number (7). The next edge will connect the previous edge and the other initial vertex, in this case that means edge 8 connects vertex 5 to vertex 2.
One more example, if a quad is created instead of a triangle, the edges follow the initial edge rule and then create new edges in the order of vertices that are created. So in this next example vertices 2 and 4 were the root vertices, and 5 was the edge I clicked with the append to polygon tool. I then created two new vertices starting with 6 and then 7. As you can see the edges start at vertex 2 (which is less than 4, following the initial edge rule) and go to vertex 6, then 7 and finally finishing at vertex 4, the second root vertex.
Hopefully this has clarified the numbering scheme Maya uses on edges and vertices during polygon creation.