Can anyone suggest some code that will determine the number of edges and area of polygons in a plot?

We need to find and store the number of edges, as well as the areas, of each of the polygons generated by the code (and shown the plot) provided in my previous post here. Any help you could offer us would be great. Thank you in advance!

[Steve]

By "number of edges" we mean we need to find the number of edges (neighbors) for every complete polygon (excluding incomplete polygon pieces along the outer borders).